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<html>
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<head>
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<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
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<title>Chapter 22. Graph coloring</title>
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<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot">
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<link rel="home" href="index.html" title="igraph Reference Manual">
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<link rel="up" href="index.html" title="igraph Reference Manual">
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<link rel="prev" href="igraph-Isomorphism.html" title="Chapter 21. Graph isomorphism">
|
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<link rel="next" href="igraph-Flows.html" title="Chapter 23. Maximum flows, minimum cuts and related measures">
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<link rel="stylesheet" href="https://stackpath.bootstrapcdn.com/font-awesome/4.7.0/css/font-awesome.min.css" type="text/css">
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<link rel="chapter" href="igraph-Introduction.html" title="Chapter 1. Introduction">
|
||||
<link rel="chapter" href="igraph-Installation.html" title="Chapter 2. Installation">
|
||||
<link rel="chapter" href="igraph-Tutorial.html" title="Chapter 3. Tutorial">
|
||||
<link rel="chapter" href="igraph-Basic.html" title="Chapter 4. Basic data types and interface">
|
||||
<link rel="chapter" href="igraph-Error.html" title="Chapter 5. Error handling">
|
||||
<link rel="chapter" href="igraph-Memory.html" title="Chapter 6. Memory (de)allocation">
|
||||
<link rel="chapter" href="igraph-Data-structures.html" title="Chapter 7. Data structure library: vector, matrix, other data types">
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||||
<link rel="chapter" href="igraph-Random.html" title="Chapter 8. Random numbers">
|
||||
<link rel="chapter" href="igraph-Iterators.html" title="Chapter 9. Vertex and edge selectors and sequences, iterators">
|
||||
<link rel="chapter" href="igraph-Attributes.html" title="Chapter 10. Graph, vertex and edge attributes">
|
||||
<link rel="chapter" href="igraph-Generators.html" title="Chapter 11. Deterministic graph generators">
|
||||
<link rel="chapter" href="igraph-Games.html" title='Chapter 12. Stochastic graph generators ("games")'>
|
||||
<link rel="chapter" href="igraph-Bipartite.html" title="Chapter 13. Bipartite, i.e. two-mode graphs">
|
||||
<link rel="chapter" href="igraph-Spatial.html" title="Chapter 14. Spatial graphs">
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||||
<link rel="chapter" href="igraph-Operators.html" title="Chapter 15. Graph operators">
|
||||
<link rel="chapter" href="igraph-Visitors.html" title="Chapter 16. Graph visitors">
|
||||
<link rel="chapter" href="igraph-Structural.html" title="Chapter 17. Structural properties of graphs">
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||||
<link rel="chapter" href="igraph-Cycles.html" title="Chapter 18. Graph cycles">
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||||
<link rel="chapter" href="igraph-Cliques.html" title="Chapter 19. Cliques and independent vertex sets">
|
||||
<link rel="chapter" href="igraph-Motifs.html" title="Chapter 20. Graph motifs, dyad census and triad census">
|
||||
<link rel="chapter" href="igraph-Isomorphism.html" title="Chapter 21. Graph isomorphism">
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||||
<link rel="chapter" href="igraph-Coloring.html" title="Chapter 22. Graph coloring">
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||||
<link rel="chapter" href="igraph-Flows.html" title="Chapter 23. Maximum flows, minimum cuts and related measures">
|
||||
<link rel="chapter" href="igraph-Separators.html" title="Chapter 24. Vertex separators">
|
||||
<link rel="chapter" href="igraph-Community.html" title="Chapter 25. Detecting community structure">
|
||||
<link rel="chapter" href="igraph-Graphlets.html" title="Chapter 26. Graphlets">
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||||
<link rel="chapter" href="igraph-HRG.html" title="Chapter 27. Hierarchical random graphs">
|
||||
<link rel="chapter" href="igraph-Embedding.html" title="Chapter 28. Embedding of graphs">
|
||||
<link rel="chapter" href="igraph-Layout.html" title="Chapter 29. Generating layouts for graph drawing">
|
||||
<link rel="chapter" href="igraph-Processes.html" title="Chapter 30. Processes on graphs">
|
||||
<link rel="chapter" href="igraph-Foreign.html" title="Chapter 31. Reading and writing graphs from and to files">
|
||||
<link rel="chapter" href="igraph-Linalg.html" title="Chapter 32. Using BLAS, LAPACK and ARPACK for igraph matrices and graphs">
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||||
<link rel="chapter" href="igraph-Nongraph.html" title="Chapter 33. Non-graph related functions">
|
||||
<link rel="chapter" href="igraph-Advanced.html" title="Chapter 34. Advanced igraph programming">
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||||
<link rel="chapter" href="igraph-Glossary.html" title="Chapter 35. Glossary">
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||||
<link rel="chapter" href="igraph-Licenses.html" title="Chapter 36. Licenses for igraph and this manual">
|
||||
<link rel="index" href="ix01.html" title="Index">
|
||||
</head>
|
||||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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<div class="navigation-header mb-4" width="100%" summary="Navigation header"><div class="btn-group">
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<a accesskey="p" class="btn btn-light" href="igraph-Isomorphism.html"><i class="fa fa-chevron-left"></i>
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Previous
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</a><a accesskey="h" class="btn btn-light" href="index.html"><i class="fa fa-home"></i>
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Home
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</a><a accesskey="n" class="btn btn-light" href="igraph-Flows.html"><i class="fa fa-chevron-right"></i>
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Next
|
||||
</a>
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</div></div>
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||||
<div class="chapter">
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<div class="titlepage"><div><div><h1 class="title">
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<a name="igraph-Coloring"></a>Chapter 22. Graph coloring</h1></div></div></div>
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<div class="toc"><dl class="toc">
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<dt><span class="section"><a href="igraph-Coloring.html#igraph_vertex_coloring_greedy">1. <code class="function">igraph_vertex_coloring_greedy</code> — Computes a vertex coloring using a greedy algorithm.</a></span></dt>
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<dt><span class="section"><a href="igraph-Coloring.html#igraph_coloring_greedy_t">2. <code class="function">igraph_coloring_greedy_t</code> — Ordering heuristics for greedy graph coloring.</a></span></dt>
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<dt><span class="section"><a href="igraph-Coloring.html#igraph_is_vertex_coloring">3. <code class="function">igraph_is_vertex_coloring</code> — Checks whether a vertex coloring is valid.</a></span></dt>
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<dt><span class="section"><a href="igraph-Coloring.html#igraph_is_bipartite_coloring">4. <code class="function">igraph_is_bipartite_coloring</code> — Checks whether a bipartite vertex coloring is valid.</a></span></dt>
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<dt><span class="section"><a href="igraph-Coloring.html#igraph_is_edge_coloring">5. <code class="function">igraph_is_edge_coloring</code> — Checks whether an edge coloring is valid.</a></span></dt>
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<dt><span class="section"><a href="igraph-Coloring.html#igraph_is_perfect">6. <code class="function">igraph_is_perfect</code> — Checks if the graph is perfect.</a></span></dt>
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</dl></div>
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<div class="section">
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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
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<a name="igraph_vertex_coloring_greedy"></a>1. <code class="function">igraph_vertex_coloring_greedy</code> — Computes a vertex coloring using a greedy algorithm.</h2></div></div></div>
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<a class="indexterm" name="id-1.23.2.2"></a><p>
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</p>
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<div class="informalexample"><pre class="programlisting">
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igraph_error_t igraph_vertex_coloring_greedy(const igraph_t *graph, igraph_vector_int_t *colors, igraph_coloring_greedy_t heuristic);
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</pre></div>
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<p>
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</p>
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<p>
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This function assigns a "color"—represented as a non-negative integer—to
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each vertex of the graph in such a way that neighboring vertices never have
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the same color. The obtained coloring is not necessarily minimal.
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</p>
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<p>
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Vertices are colored greedily, one by one, always choosing the smallest color
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index that differs from that of already colored neighbors. Vertices are picked
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in an order determined by the speified heuristic.
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Colors are represented by non-negative integers 0, 1, 2, ...
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</p>
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<p><b>Arguments: </b>
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</p>
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<div class="variablelist"><table border="0" class="variablelist">
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<colgroup>
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<col align="left" valign="top">
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<col>
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</colgroup>
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<tbody>
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<tr>
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<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
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<td><p>
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The input graph.
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</p></td>
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</tr>
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<tr>
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<td><p><span class="term"><em class="parameter"><code>colors</code></em>:</span></p></td>
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<td><p>
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Pointer to an initialized integer vector. The vertex colors will be stored here.
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</p></td>
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</tr>
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<tr>
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<td><p><span class="term"><em class="parameter"><code>heuristic</code></em>:</span></p></td>
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<td><p>
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The vertex ordering heuristic to use during greedy coloring.
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See <a class="link" href="igraph-Coloring.html#igraph_coloring_greedy_t" title="2. igraph_coloring_greedy_t — Ordering heuristics for greedy graph coloring."><code class="function">igraph_coloring_greedy_t</code></a> for more information.</p></td>
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</tr>
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</tbody>
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||||
</table></div>
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<p>
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||||
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||||
</p>
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<p><b>Returns: </b></p>
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<div class="variablelist"><table border="0" class="variablelist">
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<colgroup>
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<col align="left" valign="top">
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<col>
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</colgroup>
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<tbody><tr>
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<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
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<td><p>
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Error code.
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</p></td>
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</tr></tbody>
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||||
</table></div>
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<p>
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|
||||
</p>
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<p><b>See also: </b></p>
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<div class="variablelist"><table border="0" class="variablelist">
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<colgroup>
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<col align="left" valign="top">
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<col>
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</colgroup>
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<tbody><tr>
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<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
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<td><p>
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igraph_is_vertex_coloring() to check if a coloring is valid, i.e. if all
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edges connect vertices of different colors.
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</p></td>
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</tr></tbody>
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</table></div>
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<p>
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|
||||
</p>
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<div class="hideshow" onClick="toggle(this, event)">
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||||
<div class="example">
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||||
<a name="id-1.23.2.11.1"></a><p class="title"><b>Example 22.1. File <code class="code">examples/simple/coloring.c</code></b></p>
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<div class="example-contents">
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<pre class="programlisting"><span class="strong"><strong>#include</strong></span> <igraph.h>
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int <span class="strong"><strong>main</strong></span>(void) {
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igraph_t graph;
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igraph_vector_int_t colors;
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igraph_bool_t valid_coloring;
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<span class="emphasis"><em>/* Initialize the library. */</em></span>
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<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_setup" title="4.1. igraph_setup — Initializes the igraph library.">igraph_setup</a></strong></span>();
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<span class="emphasis"><em>/* Setting a seed makes the result of erdos_renyi_game_gnm deterministic. */</em></span>
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<span class="strong"><strong><a class="link" href="igraph-Random.html#igraph_rng_seed" title="3.3. igraph_rng_seed — Seeds a random number generator.">igraph_rng_seed</a></strong></span>(<span class="strong"><strong><a class="link" href="igraph-Random.html#igraph_rng_default" title="2.1. igraph_rng_default — Query the default random number generator.">igraph_rng_default</a></strong></span>(), 42);
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<span class="emphasis"><em>/* IGRAPH_UNDIRECTED and IGRAPH_NO_LOOPS are both equivalent to 0/FALSE, but</em></span>
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<span class="emphasis"><em> communicate intent better in this context. */</em></span>
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<span class="strong"><strong><a class="link" href="igraph-Games.html#igraph_erdos_renyi_game_gnm" title="1.1. igraph_erdos_renyi_game_gnm — Generates a random (Erdős-Rényi) graph with a fixed number of edges.">igraph_erdos_renyi_game_gnm</a></strong></span>(&graph, 1000, 10000, IGRAPH_UNDIRECTED, IGRAPH_SIMPLE_SW, IGRAPH_EDGE_UNLABELED);
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<span class="emphasis"><em>/* As with all igraph functions, the vector in which the result is returned must</em></span>
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<span class="emphasis"><em> be initialized in advance. */</em></span>
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<span class="strong"><strong>igraph_vector_int_init</strong></span>(&colors, 0);
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<span class="strong"><strong><a class="link" href="igraph-Coloring.html#igraph_vertex_coloring_greedy" title="1. igraph_vertex_coloring_greedy — Computes a vertex coloring using a greedy algorithm.">igraph_vertex_coloring_greedy</a></strong></span>(&graph, &colors, IGRAPH_COLORING_GREEDY_COLORED_NEIGHBORS);
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<span class="emphasis"><em>/* Verify that the colouring is valid, i.e. no two adjacent vertices have the same colour. */</em></span>
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<span class="strong"><strong><a class="link" href="igraph-Coloring.html#igraph_is_vertex_coloring" title="3. igraph_is_vertex_coloring — Checks whether a vertex coloring is valid.">igraph_is_vertex_coloring</a></strong></span>(&graph, &colors, &valid_coloring);
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<span class="strong"><strong><a class="link" href="igraph-Error.html#IGRAPH_ASSERT" title="5.5.6. IGRAPH_ASSERT — igraph-specific replacement for assert().">IGRAPH_ASSERT</a></strong></span>(valid_coloring);
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<span class="emphasis"><em>/* Destroy data structure when we are done. */</em></span>
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<span class="strong"><strong>igraph_vector_int_destroy</strong></span>(&colors);
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<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_destroy" title="5.1.4. igraph_destroy — Frees the memory allocated for a graph object.">igraph_destroy</a></strong></span>(&graph);
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<span class="strong"><strong>return</strong></span> 0;
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}
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</pre>
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<p></p>
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</div>
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</div>
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<br class="example-break">
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</div>
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<p>
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</p>
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</div>
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<div class="section">
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||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
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<a name="igraph_coloring_greedy_t"></a>2. <code class="function">igraph_coloring_greedy_t</code> — Ordering heuristics for greedy graph coloring.</h2></div></div></div>
|
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<a class="indexterm" name="id-1.23.3.2"></a><p>
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</p>
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<pre class="programlisting">
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typedef enum {
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IGRAPH_COLORING_GREEDY_COLORED_NEIGHBORS = 0,
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IGRAPH_COLORING_GREEDY_DSATUR = 1
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} igraph_coloring_greedy_t;
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</pre>
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<p>
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</p>
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<p>
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||||
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Ordering heuristics for <a class="link" href="igraph-Coloring.html#igraph_vertex_coloring_greedy" title="1. igraph_vertex_coloring_greedy — Computes a vertex coloring using a greedy algorithm."><code class="function">igraph_vertex_coloring_greedy()</code></a>.
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</p>
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<p><b>Values: </b>
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</p>
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<div class="variablelist"><table border="0" class="variablelist">
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<colgroup>
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<col align="left" valign="top">
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<col>
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</colgroup>
|
||||
<tbody>
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<tr>
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<td><p><span class="term"><code class="constant">IGRAPH_COLORING_GREEDY_COLORED_NEIGHBORS</code>:</span></p></td>
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<td><p>
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Choose the vertex with largest number of already colored neighbors.
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</p></td>
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</tr>
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<tr>
|
||||
<td><p><span class="term"><code class="constant">IGRAPH_COLORING_GREEDY_DSATUR</code>:</span></p></td>
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||||
<td><p>
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||||
Choose the vertex with largest number of unique colors in its neighborhood, i.e. its
|
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"saturation degree". When multiple vertices have the same saturation degree, choose
|
||||
the one with the most not yet colored neighbors. Added in igraph 0.10.4. This heuristic
|
||||
is known as "DSatur", and was proposed in
|
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Daniel Brélaz: New methods to color the vertices of a graph,
|
||||
Commun. ACM 22, 4 (1979), 251–256. <a class="ulink" href="https://doi.org/10.1145/359094.359101" target="_top">https://doi.org/10.1145/359094.359101</a></p></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="igraph_is_vertex_coloring"></a>3. <code class="function">igraph_is_vertex_coloring</code> — Checks whether a vertex coloring is valid.</h2></div></div></div>
|
||||
<a class="indexterm" name="id-1.23.4.2"></a><p>
|
||||
</p>
|
||||
<div class="informalexample"><pre class="programlisting">
|
||||
igraph_error_t igraph_is_vertex_coloring(
|
||||
const igraph_t *graph,
|
||||
const igraph_vector_int_t *types,
|
||||
igraph_bool_t *res);
|
||||
</pre></div>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
|
||||
|
||||
|
||||
This function checks whether the given vertex type/color assignment is a valid
|
||||
vertex coloring, i.e., no two adjacent vertices have the same color.
|
||||
Self-loops are ignored.
|
||||
|
||||
</p>
|
||||
<p><b>Arguments: </b>
|
||||
</p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The input graph.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>types</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The vertex types/colors as an integer vector.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Pointer to a boolean, the result is stored here.
|
||||
</p></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
</p>
|
||||
<p><b>Returns: </b></p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||||
<td><p>
|
||||
Error code.
|
||||
</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
Time complexity: O(|E|), linear in the number of edges.
|
||||
|
||||
</p>
|
||||
<div class="hideshow" onClick="toggle(this, event)">
|
||||
<div class="example">
|
||||
<a name="id-1.23.4.8.1"></a><p class="title"><b>Example 22.2. File <code class="code">examples/simple/coloring.c</code></b></p>
|
||||
<div class="example-contents">
|
||||
<pre class="programlisting"><span class="strong"><strong>#include</strong></span> <igraph.h>
|
||||
|
||||
int <span class="strong"><strong>main</strong></span>(void) {
|
||||
igraph_t graph;
|
||||
igraph_vector_int_t colors;
|
||||
igraph_bool_t valid_coloring;
|
||||
|
||||
<span class="emphasis"><em>/* Initialize the library. */</em></span>
|
||||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_setup" title="4.1. igraph_setup — Initializes the igraph library.">igraph_setup</a></strong></span>();
|
||||
|
||||
<span class="emphasis"><em>/* Setting a seed makes the result of erdos_renyi_game_gnm deterministic. */</em></span>
|
||||
<span class="strong"><strong><a class="link" href="igraph-Random.html#igraph_rng_seed" title="3.3. igraph_rng_seed — Seeds a random number generator.">igraph_rng_seed</a></strong></span>(<span class="strong"><strong><a class="link" href="igraph-Random.html#igraph_rng_default" title="2.1. igraph_rng_default — Query the default random number generator.">igraph_rng_default</a></strong></span>(), 42);
|
||||
|
||||
<span class="emphasis"><em>/* IGRAPH_UNDIRECTED and IGRAPH_NO_LOOPS are both equivalent to 0/FALSE, but</em></span>
|
||||
<span class="emphasis"><em> communicate intent better in this context. */</em></span>
|
||||
<span class="strong"><strong><a class="link" href="igraph-Games.html#igraph_erdos_renyi_game_gnm" title="1.1. igraph_erdos_renyi_game_gnm — Generates a random (Erdős-Rényi) graph with a fixed number of edges.">igraph_erdos_renyi_game_gnm</a></strong></span>(&graph, 1000, 10000, IGRAPH_UNDIRECTED, IGRAPH_SIMPLE_SW, IGRAPH_EDGE_UNLABELED);
|
||||
|
||||
<span class="emphasis"><em>/* As with all igraph functions, the vector in which the result is returned must</em></span>
|
||||
<span class="emphasis"><em> be initialized in advance. */</em></span>
|
||||
<span class="strong"><strong>igraph_vector_int_init</strong></span>(&colors, 0);
|
||||
<span class="strong"><strong><a class="link" href="igraph-Coloring.html#igraph_vertex_coloring_greedy" title="1. igraph_vertex_coloring_greedy — Computes a vertex coloring using a greedy algorithm.">igraph_vertex_coloring_greedy</a></strong></span>(&graph, &colors, IGRAPH_COLORING_GREEDY_COLORED_NEIGHBORS);
|
||||
|
||||
<span class="emphasis"><em>/* Verify that the colouring is valid, i.e. no two adjacent vertices have the same colour. */</em></span>
|
||||
<span class="strong"><strong><a class="link" href="igraph-Coloring.html#igraph_is_vertex_coloring" title="3. igraph_is_vertex_coloring — Checks whether a vertex coloring is valid.">igraph_is_vertex_coloring</a></strong></span>(&graph, &colors, &valid_coloring);
|
||||
<span class="strong"><strong><a class="link" href="igraph-Error.html#IGRAPH_ASSERT" title="5.5.6. IGRAPH_ASSERT — igraph-specific replacement for assert().">IGRAPH_ASSERT</a></strong></span>(valid_coloring);
|
||||
|
||||
<span class="emphasis"><em>/* Destroy data structure when we are done. */</em></span>
|
||||
<span class="strong"><strong>igraph_vector_int_destroy</strong></span>(&colors);
|
||||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_destroy" title="5.1.4. igraph_destroy — Frees the memory allocated for a graph object.">igraph_destroy</a></strong></span>(&graph);
|
||||
|
||||
<span class="strong"><strong>return</strong></span> 0;
|
||||
}
|
||||
</pre>
|
||||
<p></p>
|
||||
</div>
|
||||
</div>
|
||||
<br class="example-break">
|
||||
</div>
|
||||
<p>
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="igraph_is_bipartite_coloring"></a>4. <code class="function">igraph_is_bipartite_coloring</code> — Checks whether a bipartite vertex coloring is valid.</h2></div></div></div>
|
||||
<a class="indexterm" name="id-1.23.5.2"></a><p>
|
||||
</p>
|
||||
<div class="informalexample"><pre class="programlisting">
|
||||
igraph_error_t igraph_is_bipartite_coloring(
|
||||
const igraph_t *graph,
|
||||
const igraph_vector_bool_t *types,
|
||||
igraph_bool_t *res,
|
||||
igraph_neimode_t *mode);
|
||||
</pre></div>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
|
||||
|
||||
|
||||
This function checks whether the given vertex type assignment is a valid
|
||||
bipartite coloring, i.e., no two adjacent vertices have the same type.
|
||||
Additionally, for directed graphs, it determines the mode of edge directions.
|
||||
Self-loops are ignored.
|
||||
|
||||
</p>
|
||||
<p><b>Arguments: </b>
|
||||
</p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The input graph.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>types</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The vertex types as a boolean vector.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Pointer to a boolean, the result is stored here.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>mode</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Pointer to store the edge direction mode. Can be <code class="constant">NULL</code> if not needed.
|
||||
If all edges go from false to true vertices, <code class="constant">IGRAPH_OUT</code> is returned.
|
||||
If all edges go from true to false vertices, <code class="constant">IGRAPH_IN</code> is returned.
|
||||
If edges go in both directions or graph is undirected, <code class="constant">IGRAPH_ALL</code> is returned.
|
||||
</p></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
</p>
|
||||
<p><b>Returns: </b></p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||||
<td><p>
|
||||
Error code.
|
||||
</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
Time complexity: O(|E|), linear in the number of edges.
|
||||
|
||||
</p>
|
||||
<p><b>See also: </b></p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||||
<td><p>
|
||||
igraph_is_bipartite() to determine whether a graph is bipartite,
|
||||
i.e. 2-colorable, and find such a coloring.
|
||||
</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="igraph_is_edge_coloring"></a>5. <code class="function">igraph_is_edge_coloring</code> — Checks whether an edge coloring is valid.</h2></div></div></div>
|
||||
<a class="indexterm" name="id-1.23.6.2"></a><p>
|
||||
</p>
|
||||
<div class="informalexample"><pre class="programlisting">
|
||||
igraph_error_t igraph_is_edge_coloring(
|
||||
const igraph_t *graph,
|
||||
const igraph_vector_int_t *types,
|
||||
igraph_bool_t *res);
|
||||
</pre></div>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
|
||||
|
||||
|
||||
This function checks whether the given edge color assignment is a valid
|
||||
edge coloring, i.e., no two adjacent edges have the same color.
|
||||
|
||||
Note that this function does not consider self-edges (loops) as being
|
||||
adjacent to themselves, so graphs with self-loops may still be considered
|
||||
to have a valid edge coloring.
|
||||
|
||||
</p>
|
||||
<p><b>Arguments: </b>
|
||||
</p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The input graph.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>types</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The edge colors as an integer vector.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Pointer to a boolean, the result is stored here.
|
||||
</p></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
</p>
|
||||
<p><b>Returns: </b></p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||||
<td><p>
|
||||
Error code.
|
||||
</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
Time complexity: O(|V|*d*log(d)), where d is the maximum degree.
|
||||
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="igraph_is_perfect"></a>6. <code class="function">igraph_is_perfect</code> — Checks if the graph is perfect.</h2></div></div></div>
|
||||
<a class="indexterm" name="id-1.23.7.2"></a><p>
|
||||
</p>
|
||||
<div class="informalexample"><pre class="programlisting">
|
||||
igraph_error_t igraph_is_perfect(const igraph_t *graph, igraph_bool_t *perfect);
|
||||
</pre></div>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
|
||||
|
||||
|
||||
A perfect graph is an undirected graph in which the chromatic number of every induced
|
||||
subgraph equals the order of the largest clique of that subgraph.
|
||||
The chromatic number of a graph G is the smallest number of colors needed to
|
||||
color the vertices of G so that no two adjacent vertices share the same color.
|
||||
|
||||
</p>
|
||||
<p>
|
||||
Warning: This function may create the complement of the graph internally,
|
||||
which consumes a lot of memory. For moderately sized graphs, consider
|
||||
decomposing them into biconnected components and running the check separately
|
||||
on each component.
|
||||
|
||||
</p>
|
||||
<p>
|
||||
This implementation is based on the strong perfect graph theorem which was
|
||||
conjectured by Claude Berge and proved by Maria Chudnovsky, Neil Robertson,
|
||||
Paul Seymour, and Robin Thomas.
|
||||
|
||||
</p>
|
||||
<p><b>Arguments: </b>
|
||||
</p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The input graph. It is expected to be undirected and simple.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>perfect</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Pointer to an integer, the result will be stored here.
|
||||
</p></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
</p>
|
||||
<p><b>Returns: </b></p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||||
<td><p>
|
||||
Error code.
|
||||
</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
Time complexity: worst case exponenital, often faster in practice.
|
||||
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
<table class="navigation-footer" width="100%" summary="Navigation footer" cellpadding="2" cellspacing="0"><tr valign="middle">
|
||||
<td align="left"><a accesskey="p" href="igraph-Isomorphism.html"><b>← Chapter 21. Graph isomorphism</b></a></td>
|
||||
<td align="right"><a accesskey="n" href="igraph-Flows.html"><b>Chapter 23. Maximum flows, minimum cuts and related measures →</b></a></td>
|
||||
</tr></table>
|
||||
</body>
|
||||
</html>
|
||||
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|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
|
||||
<title>Chapter 28. Embedding of graphs</title>
|
||||
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot">
|
||||
<link rel="home" href="index.html" title="igraph Reference Manual">
|
||||
<link rel="up" href="index.html" title="igraph Reference Manual">
|
||||
<link rel="prev" href="igraph-HRG.html" title="Chapter 27. Hierarchical random graphs">
|
||||
<link rel="next" href="igraph-Layout.html" title="Chapter 29. Generating layouts for graph drawing">
|
||||
<script type="text/javascript" src="toggle.js"></script><link rel="stylesheet" href="style.css" type="text/css">
|
||||
<link rel="stylesheet" href="https://stackpath.bootstrapcdn.com/font-awesome/4.7.0/css/font-awesome.min.css" type="text/css">
|
||||
<link rel="chapter" href="igraph-Introduction.html" title="Chapter 1. Introduction">
|
||||
<link rel="chapter" href="igraph-Installation.html" title="Chapter 2. Installation">
|
||||
<link rel="chapter" href="igraph-Tutorial.html" title="Chapter 3. Tutorial">
|
||||
<link rel="chapter" href="igraph-Basic.html" title="Chapter 4. Basic data types and interface">
|
||||
<link rel="chapter" href="igraph-Error.html" title="Chapter 5. Error handling">
|
||||
<link rel="chapter" href="igraph-Memory.html" title="Chapter 6. Memory (de)allocation">
|
||||
<link rel="chapter" href="igraph-Data-structures.html" title="Chapter 7. Data structure library: vector, matrix, other data types">
|
||||
<link rel="chapter" href="igraph-Random.html" title="Chapter 8. Random numbers">
|
||||
<link rel="chapter" href="igraph-Iterators.html" title="Chapter 9. Vertex and edge selectors and sequences, iterators">
|
||||
<link rel="chapter" href="igraph-Attributes.html" title="Chapter 10. Graph, vertex and edge attributes">
|
||||
<link rel="chapter" href="igraph-Generators.html" title="Chapter 11. Deterministic graph generators">
|
||||
<link rel="chapter" href="igraph-Games.html" title='Chapter 12. Stochastic graph generators ("games")'>
|
||||
<link rel="chapter" href="igraph-Bipartite.html" title="Chapter 13. Bipartite, i.e. two-mode graphs">
|
||||
<link rel="chapter" href="igraph-Spatial.html" title="Chapter 14. Spatial graphs">
|
||||
<link rel="chapter" href="igraph-Operators.html" title="Chapter 15. Graph operators">
|
||||
<link rel="chapter" href="igraph-Visitors.html" title="Chapter 16. Graph visitors">
|
||||
<link rel="chapter" href="igraph-Structural.html" title="Chapter 17. Structural properties of graphs">
|
||||
<link rel="chapter" href="igraph-Cycles.html" title="Chapter 18. Graph cycles">
|
||||
<link rel="chapter" href="igraph-Cliques.html" title="Chapter 19. Cliques and independent vertex sets">
|
||||
<link rel="chapter" href="igraph-Motifs.html" title="Chapter 20. Graph motifs, dyad census and triad census">
|
||||
<link rel="chapter" href="igraph-Isomorphism.html" title="Chapter 21. Graph isomorphism">
|
||||
<link rel="chapter" href="igraph-Coloring.html" title="Chapter 22. Graph coloring">
|
||||
<link rel="chapter" href="igraph-Flows.html" title="Chapter 23. Maximum flows, minimum cuts and related measures">
|
||||
<link rel="chapter" href="igraph-Separators.html" title="Chapter 24. Vertex separators">
|
||||
<link rel="chapter" href="igraph-Community.html" title="Chapter 25. Detecting community structure">
|
||||
<link rel="chapter" href="igraph-Graphlets.html" title="Chapter 26. Graphlets">
|
||||
<link rel="chapter" href="igraph-HRG.html" title="Chapter 27. Hierarchical random graphs">
|
||||
<link rel="chapter" href="igraph-Embedding.html" title="Chapter 28. Embedding of graphs">
|
||||
<link rel="chapter" href="igraph-Layout.html" title="Chapter 29. Generating layouts for graph drawing">
|
||||
<link rel="chapter" href="igraph-Processes.html" title="Chapter 30. Processes on graphs">
|
||||
<link rel="chapter" href="igraph-Foreign.html" title="Chapter 31. Reading and writing graphs from and to files">
|
||||
<link rel="chapter" href="igraph-Linalg.html" title="Chapter 32. Using BLAS, LAPACK and ARPACK for igraph matrices and graphs">
|
||||
<link rel="chapter" href="igraph-Nongraph.html" title="Chapter 33. Non-graph related functions">
|
||||
<link rel="chapter" href="igraph-Advanced.html" title="Chapter 34. Advanced igraph programming">
|
||||
<link rel="chapter" href="igraph-Glossary.html" title="Chapter 35. Glossary">
|
||||
<link rel="chapter" href="igraph-Licenses.html" title="Chapter 36. Licenses for igraph and this manual">
|
||||
<link rel="index" href="ix01.html" title="Index">
|
||||
</head>
|
||||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
||||
<div class="navigation-header mb-4" width="100%" summary="Navigation header"><div class="btn-group">
|
||||
<a accesskey="p" class="btn btn-light" href="igraph-HRG.html"><i class="fa fa-chevron-left"></i>
|
||||
Previous
|
||||
</a><a accesskey="h" class="btn btn-light" href="index.html"><i class="fa fa-home"></i>
|
||||
Home
|
||||
</a><a accesskey="n" class="btn btn-light" href="igraph-Layout.html"><i class="fa fa-chevron-right"></i>
|
||||
Next
|
||||
</a>
|
||||
</div></div>
|
||||
<div class="chapter">
|
||||
<div class="titlepage"><div><div><h1 class="title">
|
||||
<a name="igraph-Embedding"></a>Chapter 28. Embedding of graphs</h1></div></div></div>
|
||||
<div class="toc"><dl class="toc"><dt><span class="section"><a href="igraph-Embedding.html#spectral-embedding">1. Spectral embedding</a></span></dt></dl></div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="spectral-embedding"></a>1. Spectral embedding</h2></div></div></div>
|
||||
<div class="toc"><dl class="toc">
|
||||
<dt><span class="section"><a href="igraph-Embedding.html#igraph_adjacency_spectral_embedding">1.1. <code class="function">igraph_adjacency_spectral_embedding</code> — Adjacency spectral embedding</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Embedding.html#igraph_laplacian_spectral_embedding">1.2. <code class="function">igraph_laplacian_spectral_embedding</code> — Spectral embedding of the Laplacian of a graph</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Embedding.html#igraph_dim_select">1.3. <code class="function">igraph_dim_select</code> — Dimensionality selection.</a></span></dt>
|
||||
</dl></div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="igraph_adjacency_spectral_embedding"></a>1.1. <code class="function">igraph_adjacency_spectral_embedding</code> — Adjacency spectral embedding</h3></div></div></div>
|
||||
<a class="indexterm" name="id-1.29.2.2.2"></a><p>
|
||||
</p>
|
||||
<div class="informalexample"><pre class="programlisting">
|
||||
igraph_error_t igraph_adjacency_spectral_embedding(const igraph_t *graph,
|
||||
igraph_int_t n,
|
||||
const igraph_vector_t *weights,
|
||||
igraph_eigen_which_position_t which,
|
||||
igraph_bool_t scaled,
|
||||
igraph_matrix_t *X,
|
||||
igraph_matrix_t *Y,
|
||||
igraph_vector_t *D,
|
||||
const igraph_vector_t *cvec,
|
||||
igraph_arpack_options_t *options);
|
||||
</pre></div>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
|
||||
|
||||
|
||||
Spectral decomposition of the adjacency matrices of graphs.
|
||||
This function computes an <code class="literal">n</code>-dimensional Euclidean
|
||||
representation of the graph based on its adjacency
|
||||
matrix, A. This representation is computed via the singular value
|
||||
decomposition of the adjacency matrix, A=U D V^T. In the case,
|
||||
where the graph is a random dot product graph generated using latent
|
||||
position vectors in R^n for each vertex, the embedding will
|
||||
provide an estimate of these latent vectors.
|
||||
|
||||
</p>
|
||||
<p>
|
||||
For undirected graphs, the latent positions are calculated as
|
||||
X = U^n D^(1/2) where U^n equals to the first no columns of U, and
|
||||
D^(1/2) is a diagonal matrix containing the square root of the selected
|
||||
singular values on the diagonal.
|
||||
|
||||
</p>
|
||||
<p>
|
||||
For directed graphs, the embedding is defined as the pair
|
||||
X = U^n D^(1/2), Y = V^n D^(1/2).
|
||||
(For undirected graphs U=V, so it is sufficient to keep one of them.)
|
||||
|
||||
</p>
|
||||
<p><b>Arguments: </b>
|
||||
</p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The input graph, can be directed or undirected.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>n</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
An integer scalar. This value is the embedding dimension of
|
||||
the spectral embedding. Should be smaller than the number of
|
||||
vertices. The largest n-dimensional non-zero
|
||||
singular values are used for the spectral embedding.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>weights</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Optional edge weights. Supply a null pointer for
|
||||
unweighted graphs.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>which</code></em>:</span></p></td>
|
||||
<td>
|
||||
<p>
|
||||
Which eigenvalues (or singular values, for directed
|
||||
graphs) to use, possible values:
|
||||
</p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><p><span class="term"><code class="constant">IGRAPH_EIGEN_LM</code></span></p></td>
|
||||
<td><p>
|
||||
|
||||
the ones with the largest magnitude
|
||||
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><code class="constant">IGRAPH_EIGEN_LA</code></span></p></td>
|
||||
<td><p>
|
||||
|
||||
the (algebraic) largest ones
|
||||
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><code class="constant">IGRAPH_EIGEN_SA</code></span></p></td>
|
||||
<td><p>
|
||||
|
||||
the (algebraic) smallest ones.
|
||||
|
||||
</p></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
For directed graphs, <code class="literal">IGRAPH_EIGEN_LM</code> and
|
||||
<code class="literal">IGRAPH_EIGEN_LA</code> are the same because singular
|
||||
values are used for the ordering instead of eigenvalues.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>scaled</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Whether to return X and Y (if <code class="constant">scaled</code> is true), or
|
||||
U and V.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>X</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Initialized matrix, the estimated latent positions are
|
||||
stored here.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>Y</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Initialized matrix or a null pointer. If not a null
|
||||
pointer, then the second half of the latent positions are
|
||||
stored here. (For undirected graphs, this always equals X.)
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>D</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Initialized vector or a null pointer. If not a null
|
||||
pointer, then the eigenvalues (for undirected graphs) or the
|
||||
singular values (for directed graphs) are stored here.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>cvec</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
A numeric vector, its length is the number vertices in the
|
||||
graph. This vector is added to the diagonal of the adjacency
|
||||
matrix, before performing the SVD.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>options</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Options to ARPACK. See <a class="link" href="igraph-Linalg.html#igraph_arpack_options_t" title="3.1.1. igraph_arpack_options_t — Options for ARPACK."><code class="function">igraph_arpack_options_t</code></a>
|
||||
for details. Supply <code class="constant">NULL</code> to use the defaults. Note that the
|
||||
function overwrites the <code class="literal">n</code> (number of vertices),
|
||||
<code class="literal">nev</code> and <code class="literal">which</code> parameters and it always
|
||||
starts the calculation from a random start vector.
|
||||
</p></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
</p>
|
||||
<p><b>Returns: </b></p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||||
<td><p>
|
||||
Error code.
|
||||
</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="igraph_laplacian_spectral_embedding"></a>1.2. <code class="function">igraph_laplacian_spectral_embedding</code> — Spectral embedding of the Laplacian of a graph</h3></div></div></div>
|
||||
<a class="indexterm" name="id-1.29.2.3.2"></a><p>
|
||||
</p>
|
||||
<div class="informalexample"><pre class="programlisting">
|
||||
igraph_error_t igraph_laplacian_spectral_embedding(const igraph_t *graph,
|
||||
igraph_int_t n,
|
||||
const igraph_vector_t *weights,
|
||||
igraph_eigen_which_position_t which,
|
||||
igraph_laplacian_spectral_embedding_type_t type,
|
||||
igraph_bool_t scaled,
|
||||
igraph_matrix_t *X,
|
||||
igraph_matrix_t *Y,
|
||||
igraph_vector_t *D,
|
||||
igraph_arpack_options_t *options);
|
||||
</pre></div>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
|
||||
|
||||
|
||||
This function essentially does the same as
|
||||
<a class="link" href="igraph-Embedding.html#igraph_adjacency_spectral_embedding" title="1.1. igraph_adjacency_spectral_embedding — Adjacency spectral embedding"><code class="function">igraph_adjacency_spectral_embedding</code></a>, but works on the Laplacian
|
||||
of the graph, instead of the adjacency matrix.
|
||||
</p>
|
||||
<p><b>Arguments: </b>
|
||||
</p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The input graph.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>n</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The number of eigenvectors (or singular vectors if the graph
|
||||
is directed) to use for the embedding.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>weights</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Optional edge weights. Supply a null pointer for
|
||||
unweighted graphs.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>which</code></em>:</span></p></td>
|
||||
<td>
|
||||
<p>
|
||||
Which eigenvalues (or singular values, for directed
|
||||
graphs) to use, possible values:
|
||||
</p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><p><span class="term"><code class="constant">IGRAPH_EIGEN_LM</code></span></p></td>
|
||||
<td><p>
|
||||
|
||||
the ones with the largest magnitude
|
||||
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><code class="constant">IGRAPH_EIGEN_LA</code></span></p></td>
|
||||
<td><p>
|
||||
|
||||
the (algebraic) largest ones
|
||||
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><code class="constant">IGRAPH_EIGEN_SA</code></span></p></td>
|
||||
<td><p>
|
||||
|
||||
the (algebraic) smallest ones.
|
||||
|
||||
</p></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
For directed graphs, <code class="literal">IGRAPH_EIGEN_LM</code> and
|
||||
<code class="literal">IGRAPH_EIGEN_LA</code> are the same because singular
|
||||
values are used for the ordering instead of eigenvalues.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>type</code></em>:</span></p></td>
|
||||
<td>
|
||||
<p>
|
||||
The type of the Laplacian to use. Various definitions
|
||||
exist for the Laplacian of a graph, and one can choose
|
||||
between them with this argument. Possible values:
|
||||
</p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><p><span class="term"><code class="constant">IGRAPH_EMBEDDING_D_A</code></span></p></td>
|
||||
<td><p>
|
||||
|
||||
means D - A where D is the
|
||||
degree matrix and A is the adjacency matrix
|
||||
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><code class="constant">IGRAPH_EMBEDDING_DAD</code></span></p></td>
|
||||
<td><p>
|
||||
|
||||
means Di times A times Di,
|
||||
where Di is the inverse of the square root of the degree matrix;
|
||||
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><code class="constant">IGRAPH_EMBEDDING_I_DAD</code></span></p></td>
|
||||
<td><p>
|
||||
|
||||
means I - Di A Di, where I
|
||||
is the identity matrix.
|
||||
|
||||
</p></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>scaled</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Whether to return X and Y (if <code class="constant">scaled</code> is true), or
|
||||
U and V.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>X</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Initialized matrix, the estimated latent positions are
|
||||
stored here.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>Y</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Initialized matrix or a null pointer. If not a null
|
||||
pointer, then the second half of the latent positions are
|
||||
stored here. (For undirected graphs, this always equals X.)
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>D</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Initialized vector or a null pointer. If not a null
|
||||
pointer, then the eigenvalues (for undirected graphs) or the
|
||||
singular values (for directed graphs) are stored here.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>options</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Options to ARPACK. See <a class="link" href="igraph-Linalg.html#igraph_arpack_options_t" title="3.1.1. igraph_arpack_options_t — Options for ARPACK."><code class="function">igraph_arpack_options_t</code></a>
|
||||
for details. Supply <code class="constant">NULL</code> to use the defaults. Note that the
|
||||
function overwrites the <code class="literal">n</code> (number of vertices),
|
||||
<code class="literal">nev</code> and <code class="literal">which</code> parameters and it always
|
||||
starts the calculation from a random start vector.
|
||||
</p></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
</p>
|
||||
<p><b>Returns: </b></p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||||
<td><p>
|
||||
Error code.
|
||||
</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
</p>
|
||||
<p><b>See also: </b></p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||||
<td><p>
|
||||
<a class="link" href="igraph-Embedding.html#igraph_adjacency_spectral_embedding" title="1.1. igraph_adjacency_spectral_embedding — Adjacency spectral embedding"><code class="function">igraph_adjacency_spectral_embedding</code></a> to embed the adjacency
|
||||
matrix.
|
||||
</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="igraph_dim_select"></a>1.3. <code class="function">igraph_dim_select</code> — Dimensionality selection.</h3></div></div></div>
|
||||
<a class="indexterm" name="id-1.29.2.4.2"></a><p>
|
||||
</p>
|
||||
<div class="informalexample"><pre class="programlisting">
|
||||
igraph_error_t igraph_dim_select(const igraph_vector_t *sv, igraph_int_t *dim);
|
||||
</pre></div>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
|
||||
|
||||
|
||||
Dimensionality selection for singular values using
|
||||
profile likelihood.
|
||||
|
||||
</p>
|
||||
<p>
|
||||
The input of the function is a numeric vector which contains
|
||||
the measure of "importance" for each dimension.
|
||||
|
||||
</p>
|
||||
<p>
|
||||
For spectral embedding, these are the singular values of the adjacency
|
||||
matrix. The singular values are assumed to be generated from a
|
||||
Gaussian mixture distribution with two components that have different
|
||||
means and same variance. The dimensionality d is chosen to
|
||||
maximize the likelihood when the d largest singular values are
|
||||
assigned to one component of the mixture and the rest of the singular
|
||||
values assigned to the other component.
|
||||
|
||||
</p>
|
||||
<p>
|
||||
This function can also be used for the general separation problem,
|
||||
where we assume that the left and the right of the vector are coming
|
||||
from two normal distributions, with different means, and we want
|
||||
to know their border.
|
||||
|
||||
</p>
|
||||
<p><b>Arguments: </b>
|
||||
</p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>sv</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
A numeric vector, the ordered singular values.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>dim</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The result is stored here.
|
||||
</p></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
</p>
|
||||
<p><b>Returns: </b></p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||||
<td><p>
|
||||
Error code.
|
||||
</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
Time complexity: O(n), n is the number of values in sv.
|
||||
|
||||
</p>
|
||||
<p><b>See also: </b></p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||||
<td><p>
|
||||
<a class="link" href="igraph-Embedding.html#igraph_adjacency_spectral_embedding" title="1.1. igraph_adjacency_spectral_embedding — Adjacency spectral embedding"><code class="function">igraph_adjacency_spectral_embedding()</code></a>.
|
||||
</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<table class="navigation-footer" width="100%" summary="Navigation footer" cellpadding="2" cellspacing="0"><tr valign="middle">
|
||||
<td align="left"><a accesskey="p" href="igraph-HRG.html"><b>← Chapter 27. Hierarchical random graphs</b></a></td>
|
||||
<td align="right"><a accesskey="n" href="igraph-Layout.html"><b>Chapter 29. Generating layouts for graph drawing →</b></a></td>
|
||||
</tr></table>
|
||||
</body>
|
||||
</html>
|
||||
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||||
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|
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|
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<link rel="chapter" href="igraph-Random.html" title="Chapter 8. Random numbers">
|
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<link rel="chapter" href="igraph-Iterators.html" title="Chapter 9. Vertex and edge selectors and sequences, iterators">
|
||||
<link rel="chapter" href="igraph-Attributes.html" title="Chapter 10. Graph, vertex and edge attributes">
|
||||
<link rel="chapter" href="igraph-Generators.html" title="Chapter 11. Deterministic graph generators">
|
||||
<link rel="chapter" href="igraph-Games.html" title='Chapter 12. Stochastic graph generators ("games")'>
|
||||
<link rel="chapter" href="igraph-Bipartite.html" title="Chapter 13. Bipartite, i.e. two-mode graphs">
|
||||
<link rel="chapter" href="igraph-Spatial.html" title="Chapter 14. Spatial graphs">
|
||||
<link rel="chapter" href="igraph-Operators.html" title="Chapter 15. Graph operators">
|
||||
<link rel="chapter" href="igraph-Visitors.html" title="Chapter 16. Graph visitors">
|
||||
<link rel="chapter" href="igraph-Structural.html" title="Chapter 17. Structural properties of graphs">
|
||||
<link rel="chapter" href="igraph-Cycles.html" title="Chapter 18. Graph cycles">
|
||||
<link rel="chapter" href="igraph-Cliques.html" title="Chapter 19. Cliques and independent vertex sets">
|
||||
<link rel="chapter" href="igraph-Motifs.html" title="Chapter 20. Graph motifs, dyad census and triad census">
|
||||
<link rel="chapter" href="igraph-Isomorphism.html" title="Chapter 21. Graph isomorphism">
|
||||
<link rel="chapter" href="igraph-Coloring.html" title="Chapter 22. Graph coloring">
|
||||
<link rel="chapter" href="igraph-Flows.html" title="Chapter 23. Maximum flows, minimum cuts and related measures">
|
||||
<link rel="chapter" href="igraph-Separators.html" title="Chapter 24. Vertex separators">
|
||||
<link rel="chapter" href="igraph-Community.html" title="Chapter 25. Detecting community structure">
|
||||
<link rel="chapter" href="igraph-Graphlets.html" title="Chapter 26. Graphlets">
|
||||
<link rel="chapter" href="igraph-HRG.html" title="Chapter 27. Hierarchical random graphs">
|
||||
<link rel="chapter" href="igraph-Embedding.html" title="Chapter 28. Embedding of graphs">
|
||||
<link rel="chapter" href="igraph-Layout.html" title="Chapter 29. Generating layouts for graph drawing">
|
||||
<link rel="chapter" href="igraph-Processes.html" title="Chapter 30. Processes on graphs">
|
||||
<link rel="chapter" href="igraph-Foreign.html" title="Chapter 31. Reading and writing graphs from and to files">
|
||||
<link rel="chapter" href="igraph-Linalg.html" title="Chapter 32. Using BLAS, LAPACK and ARPACK for igraph matrices and graphs">
|
||||
<link rel="chapter" href="igraph-Nongraph.html" title="Chapter 33. Non-graph related functions">
|
||||
<link rel="chapter" href="igraph-Advanced.html" title="Chapter 34. Advanced igraph programming">
|
||||
<link rel="chapter" href="igraph-Glossary.html" title="Chapter 35. Glossary">
|
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<link rel="chapter" href="igraph-Licenses.html" title="Chapter 36. Licenses for igraph and this manual">
|
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<link rel="index" href="ix01.html" title="Index">
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<a accesskey="p" class="btn btn-light" href="igraph-Advanced.html"><i class="fa fa-chevron-left"></i>
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Previous
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</a><a accesskey="h" class="btn btn-light" href="index.html"><i class="fa fa-home"></i>
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Home
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</a><a accesskey="n" class="btn btn-light" href="igraph-Licenses.html"><i class="fa fa-chevron-right"></i>
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Next
|
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</div></div>
|
||||
<div class="chapter">
|
||||
<div class="titlepage"><div><div><h1 class="title">
|
||||
<a name="igraph-Glossary"></a>Chapter 35. Glossary</h1></div></div></div>
|
||||
<p>
|
||||
This glossary defines common terms used throughout the igraph
|
||||
documentation.
|
||||
</p>
|
||||
<div class="itemizedlist"><ul class="itemizedlist compact" style="list-style-type: disc; ">
|
||||
<li class="listitem"><p>
|
||||
<span class="strong"><strong>attribute</strong></span>: A piece of data
|
||||
associated with a vertex, an edge, or the graph itself. The
|
||||
igraph C library currently supports numeric, string and Boolean
|
||||
attribute values, and provides a means for implementing
|
||||
attribute handlers that support custom types.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<span class="strong"><strong>adjacent</strong></span>: Two vertices are
|
||||
called <span class="strong"><strong>adjacent</strong></span> if there is
|
||||
an edge connecting them. This term describes a vertex-to-vertex
|
||||
relation.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<span class="strong"><strong>adjacency list</strong></span>: A data
|
||||
structure that associates a list of neighbours (i.e. adjacent
|
||||
vertices) to each vertex.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<span class="strong"><strong>adjacency matrix</strong></span>: A
|
||||
representation of a graph as a square matrix.
|
||||
<code class="literal">A_ij</code> gives the number of edge endpoints
|
||||
connecting from the <code class="literal">i</code>th vertex to the
|
||||
<code class="literal">j</code>th vertex. Conventionally, the diagonal of
|
||||
the adjacency matrix of an undirected graph contains
|
||||
<span class="emphasis"><em>twice</em></span> the number of self-loops. All igraph
|
||||
functions follow this convention unless noted otherwise.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<span class="strong"><strong>biadjacency matrix</strong></span>: Analogous
|
||||
to the adjacency matrix, but used for bipartite graphs. Element
|
||||
<code class="literal">B_ij</code> gives the number of edges from the
|
||||
<code class="literal">i</code>th vertex of the first group to the
|
||||
<code class="literal">j</code>th vertex of the second group.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<span class="strong"><strong>bipartite graph</strong></span>: A graph
|
||||
whose vertices can be partitioned into two groups in such a way
|
||||
that connections are present only between members of different
|
||||
groups.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<span class="strong"><strong>complete graph</strong></span>: Also called
|
||||
<span class="strong"><strong>full graph</strong></span> within the context
|
||||
of igraph, a graph in which all pairs of vertices are connected
|
||||
to each other.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<span class="strong"><strong>connected graph</strong></span>: A connected
|
||||
graph consists of a single component, in which any vertex is
|
||||
reachable from any other. In igraph, the null graph is not
|
||||
considered connected, as it has not one, but zero components.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<span class="strong"><strong>edge</strong></span>: A
|
||||
<span class="strong"><strong>connection</strong></span> between two
|
||||
vertices, also called a <span class="strong"><strong>link</strong></span>.
|
||||
In igraph, edges are referred to by integer indices called
|
||||
<span class="strong"><strong>edge IDs</strong></span>.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<span class="strong"><strong>finalizer stack</strong></span>: A global
|
||||
stack used internally by igraph to keep track of currently
|
||||
allocated objects and their destructors, so that they can be
|
||||
automatically destroyed in case of an error.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<span class="strong"><strong>game</strong></span>: Within igraph, this
|
||||
term is used for stochastic graph generators, i.e. functions
|
||||
that sample from random graph models.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<span class="strong"><strong>graph</strong></span> or
|
||||
<span class="strong"><strong>network</strong></span>: A set of vertices
|
||||
with connections between them. In igraph, graphs may carry
|
||||
associated data in the form of vertex, edge or graph attributes.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<span class="strong"><strong>incident</strong></span>: An edge is called
|
||||
<span class="strong"><strong>incident</strong></span> to the vertices that
|
||||
are its endpoints. This term describes a vertex-to-edge
|
||||
relation.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<span class="strong"><strong>incidence list</strong></span>: A data
|
||||
structure that associates a list of incident edges to each
|
||||
vertex.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<span class="strong"><strong>incidence matrix</strong></span>: A matrix
|
||||
describing the incidence relation between vertices (rows) and
|
||||
edges (columns).
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<span class="strong"><strong>membership vector</strong></span>: Membership
|
||||
vectors are a means of encoding a partitioning of items, usually
|
||||
vertices, into several groups. The <code class="literal">i</code>th
|
||||
element of the vector gives an integer identifier of the group
|
||||
the <code class="literal">i</code>th vertex belongs to. Membership vectors
|
||||
are typically used to describe a vertex clustering obtained
|
||||
through community detection, or by identifying the connected
|
||||
components of a graph.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<span class="strong"><strong>multi-edges</strong></span> or
|
||||
<span class="strong"><strong>parallel edges</strong></span>: More than one
|
||||
edge connecting the same two vertices. In a directed graph,
|
||||
<code class="literal">a -> b, a -> b</code> are considered parallel
|
||||
edges, but <code class="literal">a -> b, a <- b</code> are not.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<span class="strong"><strong>null graph</strong></span>: A graph with no
|
||||
vertices (and no edges).
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<span class="strong"><strong>self-loop</strong></span>,
|
||||
<span class="strong"><strong>self-edge</strong></span>, or simply
|
||||
<span class="strong"><strong>loop</strong></span>: An edge that connects a
|
||||
vertex to itself.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<span class="strong"><strong>simple graph</strong></span>: A graph that
|
||||
does not have self-loops or multi-edges.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<span class="strong"><strong>singleton graph</strong></span>: A graph
|
||||
having a single vertex. This term usually refers to a single
|
||||
vertex with no edges, but note that self-loops may in principle
|
||||
be present.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<span class="strong"><strong>vertex</strong></span>: Graphs consist of
|
||||
vertices, also called <span class="strong"><strong>nodes</strong></span>,
|
||||
that are connected to each other. In igraph, vertices are
|
||||
referred to by integer indices called
|
||||
<span class="strong"><strong>vertex IDs</strong></span>.
|
||||
</p></li>
|
||||
</ul></div>
|
||||
</div>
|
||||
<table class="navigation-footer" width="100%" summary="Navigation footer" cellpadding="2" cellspacing="0"><tr valign="middle">
|
||||
<td align="left"><a accesskey="p" href="igraph-Advanced.html"><b>← Chapter 34. Advanced igraph programming</b></a></td>
|
||||
<td align="right"><a accesskey="n" href="igraph-Licenses.html"><b>Chapter 36. Licenses for igraph and this manual →</b></a></td>
|
||||
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|
||||
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|
||||
<html>
|
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<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
|
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<title>Chapter 26. Graphlets</title>
|
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<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot">
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|
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|
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<link rel="chapter" href="igraph-Installation.html" title="Chapter 2. Installation">
|
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<link rel="chapter" href="igraph-Tutorial.html" title="Chapter 3. Tutorial">
|
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<link rel="chapter" href="igraph-Basic.html" title="Chapter 4. Basic data types and interface">
|
||||
<link rel="chapter" href="igraph-Error.html" title="Chapter 5. Error handling">
|
||||
<link rel="chapter" href="igraph-Memory.html" title="Chapter 6. Memory (de)allocation">
|
||||
<link rel="chapter" href="igraph-Data-structures.html" title="Chapter 7. Data structure library: vector, matrix, other data types">
|
||||
<link rel="chapter" href="igraph-Random.html" title="Chapter 8. Random numbers">
|
||||
<link rel="chapter" href="igraph-Iterators.html" title="Chapter 9. Vertex and edge selectors and sequences, iterators">
|
||||
<link rel="chapter" href="igraph-Attributes.html" title="Chapter 10. Graph, vertex and edge attributes">
|
||||
<link rel="chapter" href="igraph-Generators.html" title="Chapter 11. Deterministic graph generators">
|
||||
<link rel="chapter" href="igraph-Games.html" title='Chapter 12. Stochastic graph generators ("games")'>
|
||||
<link rel="chapter" href="igraph-Bipartite.html" title="Chapter 13. Bipartite, i.e. two-mode graphs">
|
||||
<link rel="chapter" href="igraph-Spatial.html" title="Chapter 14. Spatial graphs">
|
||||
<link rel="chapter" href="igraph-Operators.html" title="Chapter 15. Graph operators">
|
||||
<link rel="chapter" href="igraph-Visitors.html" title="Chapter 16. Graph visitors">
|
||||
<link rel="chapter" href="igraph-Structural.html" title="Chapter 17. Structural properties of graphs">
|
||||
<link rel="chapter" href="igraph-Cycles.html" title="Chapter 18. Graph cycles">
|
||||
<link rel="chapter" href="igraph-Cliques.html" title="Chapter 19. Cliques and independent vertex sets">
|
||||
<link rel="chapter" href="igraph-Motifs.html" title="Chapter 20. Graph motifs, dyad census and triad census">
|
||||
<link rel="chapter" href="igraph-Isomorphism.html" title="Chapter 21. Graph isomorphism">
|
||||
<link rel="chapter" href="igraph-Coloring.html" title="Chapter 22. Graph coloring">
|
||||
<link rel="chapter" href="igraph-Flows.html" title="Chapter 23. Maximum flows, minimum cuts and related measures">
|
||||
<link rel="chapter" href="igraph-Separators.html" title="Chapter 24. Vertex separators">
|
||||
<link rel="chapter" href="igraph-Community.html" title="Chapter 25. Detecting community structure">
|
||||
<link rel="chapter" href="igraph-Graphlets.html" title="Chapter 26. Graphlets">
|
||||
<link rel="chapter" href="igraph-HRG.html" title="Chapter 27. Hierarchical random graphs">
|
||||
<link rel="chapter" href="igraph-Embedding.html" title="Chapter 28. Embedding of graphs">
|
||||
<link rel="chapter" href="igraph-Layout.html" title="Chapter 29. Generating layouts for graph drawing">
|
||||
<link rel="chapter" href="igraph-Processes.html" title="Chapter 30. Processes on graphs">
|
||||
<link rel="chapter" href="igraph-Foreign.html" title="Chapter 31. Reading and writing graphs from and to files">
|
||||
<link rel="chapter" href="igraph-Linalg.html" title="Chapter 32. Using BLAS, LAPACK and ARPACK for igraph matrices and graphs">
|
||||
<link rel="chapter" href="igraph-Nongraph.html" title="Chapter 33. Non-graph related functions">
|
||||
<link rel="chapter" href="igraph-Advanced.html" title="Chapter 34. Advanced igraph programming">
|
||||
<link rel="chapter" href="igraph-Glossary.html" title="Chapter 35. Glossary">
|
||||
<link rel="chapter" href="igraph-Licenses.html" title="Chapter 36. Licenses for igraph and this manual">
|
||||
<link rel="index" href="ix01.html" title="Index">
|
||||
</head>
|
||||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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||||
<div class="navigation-header mb-4" width="100%" summary="Navigation header"><div class="btn-group">
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<a accesskey="p" class="btn btn-light" href="igraph-Community.html"><i class="fa fa-chevron-left"></i>
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Previous
|
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</a><a accesskey="h" class="btn btn-light" href="index.html"><i class="fa fa-home"></i>
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Home
|
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</a><a accesskey="n" class="btn btn-light" href="igraph-HRG.html"><i class="fa fa-chevron-right"></i>
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Next
|
||||
</a>
|
||||
</div></div>
|
||||
<div class="chapter">
|
||||
<div class="titlepage"><div><div><h1 class="title">
|
||||
<a name="igraph-Graphlets"></a>Chapter 26. Graphlets</h1></div></div></div>
|
||||
<div class="toc"><dl class="toc">
|
||||
<dt><span class="section"><a href="igraph-Graphlets.html#about-graphlets">1. Introduction</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Graphlets.html#performing-graphlet-decomposition">2. Performing graphlet decomposition</a></span></dt>
|
||||
</dl></div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="about-graphlets"></a>1. Introduction</h2></div></div></div>
|
||||
<p>
|
||||
Graphlet decomposition models a weighted undirected graph
|
||||
via the union of potentially overlapping dense social groups.
|
||||
This is done by a two-step algorithm. In the first step, a candidate
|
||||
set of groups (a candidate basis) is created by finding cliques
|
||||
in the thresholded input graph. In the second step,
|
||||
the graph is projected onto the candidate basis, resulting in a
|
||||
weight coefficient for each clique in the candidate basis.
|
||||
</p>
|
||||
<p>
|
||||
For more information on graphlet decomposition, see
|
||||
Hossein Azari Soufiani and Edoardo M Airoldi: "Graphlet decomposition of a weighted network",
|
||||
<a class="ulink" href="https://arxiv.org/abs/1203.2821" target="_top">https://arxiv.org/abs/1203.2821</a> and <a class="ulink" href="http://proceedings.mlr.press/v22/azari12/azari12.pdf" target="_top">http://proceedings.mlr.press/v22/azari12/azari12.pdf</a>
|
||||
</p>
|
||||
<p>
|
||||
igraph contains three functions for performing the graphlet
|
||||
decomponsition of a graph. The first is <a class="link" href="igraph-Graphlets.html#igraph_graphlets" title="2.1. igraph_graphlets — Calculate graphlets basis and project the graph on it."><code class="function">igraph_graphlets()</code></a>, which
|
||||
performs both steps of the method and returns a list of subgraphs
|
||||
with their corresponding weights. The other two functions
|
||||
correspond to the first and second steps of the algorithm, and they are
|
||||
useful if the user wishes to perform them individually:
|
||||
<a class="link" href="igraph-Graphlets.html#igraph_graphlets_candidate_basis" title="2.2. igraph_graphlets_candidate_basis — Calculate a candidate graphlets basis"><code class="function">igraph_graphlets_candidate_basis()</code></a> and
|
||||
<a class="link" href="igraph-Graphlets.html#igraph_graphlets_project" title="2.3. igraph_graphlets_project — Project a graph on a graphlets basis."><code class="function">igraph_graphlets_project()</code></a>.
|
||||
</p>
|
||||
<p>
|
||||
<em><span class="remark">
|
||||
Note: The term "graphlet" is used for several unrelated concepts
|
||||
in the literature. If you are looking to count induced subgraphs, see
|
||||
<a class="link" href="igraph-Motifs.html#igraph_motifs_randesu" title="4.1. igraph_motifs_randesu — Count the number of motifs in a graph."><code class="function">igraph_motifs_randesu()</code></a> and <a class="link" href="igraph-Isomorphism.html#igraph_subisomorphic_lad" title="4.1. igraph_subisomorphic_lad — Check subgraph isomorphism with the LAD algorithm"><code class="function">igraph_subisomorphic_lad()</code></a>.
|
||||
</span></em>
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="performing-graphlet-decomposition"></a>2. Performing graphlet decomposition</h2></div></div></div>
|
||||
<div class="toc"><dl class="toc">
|
||||
<dt><span class="section"><a href="igraph-Graphlets.html#igraph_graphlets">2.1. <code class="function">igraph_graphlets</code> — Calculate graphlets basis and project the graph on it.</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Graphlets.html#igraph_graphlets_candidate_basis">2.2. <code class="function">igraph_graphlets_candidate_basis</code> — Calculate a candidate graphlets basis</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Graphlets.html#igraph_graphlets_project">2.3. <code class="function">igraph_graphlets_project</code> — Project a graph on a graphlets basis.</a></span></dt>
|
||||
</dl></div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="igraph_graphlets"></a>2.1. <code class="function">igraph_graphlets</code> — Calculate graphlets basis and project the graph on it.</h3></div></div></div>
|
||||
<a class="indexterm" name="id-1.27.3.2.2"></a><p>
|
||||
</p>
|
||||
<div class="informalexample"><pre class="programlisting">
|
||||
igraph_error_t igraph_graphlets(const igraph_t *graph,
|
||||
const igraph_vector_t *weights,
|
||||
igraph_vector_int_list_t *cliques,
|
||||
igraph_vector_t *Mu, igraph_int_t niter);
|
||||
</pre></div>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
|
||||
|
||||
|
||||
This function simply calls <a class="link" href="igraph-Graphlets.html#igraph_graphlets_candidate_basis" title="2.2. igraph_graphlets_candidate_basis — Calculate a candidate graphlets basis"><code class="function">igraph_graphlets_candidate_basis()</code></a>
|
||||
and <a class="link" href="igraph-Graphlets.html#igraph_graphlets_project" title="2.3. igraph_graphlets_project — Project a graph on a graphlets basis."><code class="function">igraph_graphlets_project()</code></a>, and then orders the graphlets
|
||||
according to decreasing weights.
|
||||
|
||||
</p>
|
||||
<p><b>Arguments: </b>
|
||||
</p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The input graph, it must be a simple graph, edge directions are
|
||||
ignored.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>weights</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Weights of the edges, a vector.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>cliques</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
An initialized list of integer vectors. The graphlet basis is
|
||||
stored here. Each element of the list is an integer vector of
|
||||
vertex IDs, encoding a single basis subgraph.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>Mu</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
An initialized vector, the weights of the graphlets will
|
||||
be stored here.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>niter</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The number of iterations to perform for the projection step.
|
||||
</p></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
</p>
|
||||
<p><b>Returns: </b></p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||||
<td><p>
|
||||
Error code.
|
||||
</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
See also: <a class="link" href="igraph-Graphlets.html#igraph_graphlets_candidate_basis" title="2.2. igraph_graphlets_candidate_basis — Calculate a candidate graphlets basis"><code class="function">igraph_graphlets_candidate_basis()</code></a> and
|
||||
<a class="link" href="igraph-Graphlets.html#igraph_graphlets_project" title="2.3. igraph_graphlets_project — Project a graph on a graphlets basis."><code class="function">igraph_graphlets_project()</code></a>.
|
||||
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="igraph_graphlets_candidate_basis"></a>2.2. <code class="function">igraph_graphlets_candidate_basis</code> — Calculate a candidate graphlets basis</h3></div></div></div>
|
||||
<a class="indexterm" name="id-1.27.3.3.2"></a><p>
|
||||
</p>
|
||||
<div class="informalexample"><pre class="programlisting">
|
||||
igraph_error_t igraph_graphlets_candidate_basis(const igraph_t *graph,
|
||||
const igraph_vector_t *weights,
|
||||
igraph_vector_int_list_t *cliques,
|
||||
igraph_vector_t *thresholds);
|
||||
</pre></div>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
|
||||
|
||||
|
||||
</p>
|
||||
<p><b>Arguments: </b>
|
||||
</p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The input graph, it must be a simple graph, edge directions are
|
||||
ignored.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>weights</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Weights of the edges, a vector.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>cliques</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
An initialized list of integer vectors. The graphlet basis is
|
||||
stored here. Each element of the list is an integer vector of
|
||||
vertex IDs, encoding a single basis subgraph.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>thresholds</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
An initialized vector, the (highest possible)
|
||||
weight thresholds for finding the basis subgraphs are stored
|
||||
here.
|
||||
</p></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
</p>
|
||||
<p><b>Returns: </b></p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||||
<td><p>
|
||||
Error code.
|
||||
</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
See also: <a class="link" href="igraph-Graphlets.html#igraph_graphlets" title="2.1. igraph_graphlets — Calculate graphlets basis and project the graph on it."><code class="function">igraph_graphlets()</code></a> and <a class="link" href="igraph-Graphlets.html#igraph_graphlets_project" title="2.3. igraph_graphlets_project — Project a graph on a graphlets basis."><code class="function">igraph_graphlets_project()</code></a>.
|
||||
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="igraph_graphlets_project"></a>2.3. <code class="function">igraph_graphlets_project</code> — Project a graph on a graphlets basis.</h3></div></div></div>
|
||||
<a class="indexterm" name="id-1.27.3.4.2"></a><p>
|
||||
</p>
|
||||
<div class="informalexample"><pre class="programlisting">
|
||||
igraph_error_t igraph_graphlets_project(const igraph_t *graph,
|
||||
const igraph_vector_t *weights,
|
||||
const igraph_vector_int_list_t *cliques,
|
||||
igraph_vector_t *Mu, igraph_bool_t startMu,
|
||||
igraph_int_t niter);
|
||||
</pre></div>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
|
||||
|
||||
|
||||
Note that the graph projected does not have to be the same that
|
||||
was used to calculate the graphlet basis, but it is assumed that
|
||||
it has the same number of vertices, and the vertex IDs of the two
|
||||
graphs match.
|
||||
|
||||
</p>
|
||||
<p><b>Arguments: </b>
|
||||
</p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The input graph, it must be a simple graph, edge directions are
|
||||
ignored.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>weights</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Weights of the edges in the input graph, a vector.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>cliques</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
An initialized list of integer vectors. The graphlet basis is
|
||||
stored here. Each element of the list is an integer vector of
|
||||
vertex IDs, encoding a single basis subgraph.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>Mu</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
An initialized vector, the weights of the graphlets will
|
||||
be stored here. This vector is also used to initialize the
|
||||
the weight vector for the iterative algorithm, if the
|
||||
<code class="constant">startMu</code> argument is true.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>startMu</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
If true, then the supplied Mu vector is
|
||||
used as the starting point of the iteration. Otherwise a
|
||||
constant 1 vector is used.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>niter</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The number of iterations to perform.
|
||||
</p></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
</p>
|
||||
<p><b>Returns: </b></p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||||
<td><p>
|
||||
Error code.
|
||||
</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
See also: <a class="link" href="igraph-Graphlets.html#igraph_graphlets" title="2.1. igraph_graphlets — Calculate graphlets basis and project the graph on it."><code class="function">igraph_graphlets()</code></a> and
|
||||
<a class="link" href="igraph-Graphlets.html#igraph_graphlets_candidate_basis" title="2.2. igraph_graphlets_candidate_basis — Calculate a candidate graphlets basis"><code class="function">igraph_graphlets_candidate_basis()</code></a>.
|
||||
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<table class="navigation-footer" width="100%" summary="Navigation footer" cellpadding="2" cellspacing="0"><tr valign="middle">
|
||||
<td align="left"><a accesskey="p" href="igraph-Community.html"><b>← Chapter 25. Detecting community structure</b></a></td>
|
||||
<td align="right"><a accesskey="n" href="igraph-HRG.html"><b>Chapter 27. Hierarchical random graphs →</b></a></td>
|
||||
</tr></table>
|
||||
</body>
|
||||
</html>
|
||||
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|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
|
||||
<title>Chapter 2. Installation</title>
|
||||
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot">
|
||||
<link rel="home" href="index.html" title="igraph Reference Manual">
|
||||
<link rel="up" href="index.html" title="igraph Reference Manual">
|
||||
<link rel="prev" href="igraph-Introduction.html" title="Chapter 1. Introduction">
|
||||
<link rel="next" href="igraph-Tutorial.html" title="Chapter 3. Tutorial">
|
||||
<script type="text/javascript" src="toggle.js"></script><link rel="stylesheet" href="style.css" type="text/css">
|
||||
<link rel="stylesheet" href="https://stackpath.bootstrapcdn.com/font-awesome/4.7.0/css/font-awesome.min.css" type="text/css">
|
||||
<link rel="chapter" href="igraph-Introduction.html" title="Chapter 1. Introduction">
|
||||
<link rel="chapter" href="igraph-Installation.html" title="Chapter 2. Installation">
|
||||
<link rel="chapter" href="igraph-Tutorial.html" title="Chapter 3. Tutorial">
|
||||
<link rel="chapter" href="igraph-Basic.html" title="Chapter 4. Basic data types and interface">
|
||||
<link rel="chapter" href="igraph-Error.html" title="Chapter 5. Error handling">
|
||||
<link rel="chapter" href="igraph-Memory.html" title="Chapter 6. Memory (de)allocation">
|
||||
<link rel="chapter" href="igraph-Data-structures.html" title="Chapter 7. Data structure library: vector, matrix, other data types">
|
||||
<link rel="chapter" href="igraph-Random.html" title="Chapter 8. Random numbers">
|
||||
<link rel="chapter" href="igraph-Iterators.html" title="Chapter 9. Vertex and edge selectors and sequences, iterators">
|
||||
<link rel="chapter" href="igraph-Attributes.html" title="Chapter 10. Graph, vertex and edge attributes">
|
||||
<link rel="chapter" href="igraph-Generators.html" title="Chapter 11. Deterministic graph generators">
|
||||
<link rel="chapter" href="igraph-Games.html" title='Chapter 12. Stochastic graph generators ("games")'>
|
||||
<link rel="chapter" href="igraph-Bipartite.html" title="Chapter 13. Bipartite, i.e. two-mode graphs">
|
||||
<link rel="chapter" href="igraph-Spatial.html" title="Chapter 14. Spatial graphs">
|
||||
<link rel="chapter" href="igraph-Operators.html" title="Chapter 15. Graph operators">
|
||||
<link rel="chapter" href="igraph-Visitors.html" title="Chapter 16. Graph visitors">
|
||||
<link rel="chapter" href="igraph-Structural.html" title="Chapter 17. Structural properties of graphs">
|
||||
<link rel="chapter" href="igraph-Cycles.html" title="Chapter 18. Graph cycles">
|
||||
<link rel="chapter" href="igraph-Cliques.html" title="Chapter 19. Cliques and independent vertex sets">
|
||||
<link rel="chapter" href="igraph-Motifs.html" title="Chapter 20. Graph motifs, dyad census and triad census">
|
||||
<link rel="chapter" href="igraph-Isomorphism.html" title="Chapter 21. Graph isomorphism">
|
||||
<link rel="chapter" href="igraph-Coloring.html" title="Chapter 22. Graph coloring">
|
||||
<link rel="chapter" href="igraph-Flows.html" title="Chapter 23. Maximum flows, minimum cuts and related measures">
|
||||
<link rel="chapter" href="igraph-Separators.html" title="Chapter 24. Vertex separators">
|
||||
<link rel="chapter" href="igraph-Community.html" title="Chapter 25. Detecting community structure">
|
||||
<link rel="chapter" href="igraph-Graphlets.html" title="Chapter 26. Graphlets">
|
||||
<link rel="chapter" href="igraph-HRG.html" title="Chapter 27. Hierarchical random graphs">
|
||||
<link rel="chapter" href="igraph-Embedding.html" title="Chapter 28. Embedding of graphs">
|
||||
<link rel="chapter" href="igraph-Layout.html" title="Chapter 29. Generating layouts for graph drawing">
|
||||
<link rel="chapter" href="igraph-Processes.html" title="Chapter 30. Processes on graphs">
|
||||
<link rel="chapter" href="igraph-Foreign.html" title="Chapter 31. Reading and writing graphs from and to files">
|
||||
<link rel="chapter" href="igraph-Linalg.html" title="Chapter 32. Using BLAS, LAPACK and ARPACK for igraph matrices and graphs">
|
||||
<link rel="chapter" href="igraph-Nongraph.html" title="Chapter 33. Non-graph related functions">
|
||||
<link rel="chapter" href="igraph-Advanced.html" title="Chapter 34. Advanced igraph programming">
|
||||
<link rel="chapter" href="igraph-Glossary.html" title="Chapter 35. Glossary">
|
||||
<link rel="chapter" href="igraph-Licenses.html" title="Chapter 36. Licenses for igraph and this manual">
|
||||
<link rel="index" href="ix01.html" title="Index">
|
||||
</head>
|
||||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
||||
<div class="navigation-header mb-4" width="100%" summary="Navigation header"><div class="btn-group">
|
||||
<a accesskey="p" class="btn btn-light" href="igraph-Introduction.html"><i class="fa fa-chevron-left"></i>
|
||||
Previous
|
||||
</a><a accesskey="h" class="btn btn-light" href="index.html"><i class="fa fa-home"></i>
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||||
Home
|
||||
</a><a accesskey="n" class="btn btn-light" href="igraph-Tutorial.html"><i class="fa fa-chevron-right"></i>
|
||||
Next
|
||||
</a>
|
||||
</div></div>
|
||||
<div class="chapter">
|
||||
<div class="titlepage"><div><div><h1 class="title">
|
||||
<a name="igraph-Installation"></a>Chapter 2. Installation</h1></div></div></div>
|
||||
<div class="toc"><dl class="toc">
|
||||
<dt><span class="section"><a href="igraph-Installation.html#igraph-Installation-prerequisites">1. Prerequisites</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Installation.html#igraph-Installation-installation">2. Installation</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Installation.html#igraph-Installation-building-the-documentation">3. Building the documentation</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Installation.html#igraph-Installation-notes-for-package-maintainers">4. Notes for package maintainers</a></span></dt>
|
||||
</dl></div>
|
||||
<p>
|
||||
This chapter describes building igraph from source code and installing it.
|
||||
The source archive of the latest stable release is always available
|
||||
<a class="ulink" href="https://igraph.org/c/#downloads" target="_top">from the igraph website</a>.
|
||||
igraph is also included in many Linux distributions, as well as several package
|
||||
managers such as <a class="ulink" href="https://vcpkg.io/" target="_top">vcpkg</a> (convenient on Windows),
|
||||
<a class="ulink" href="https://www.macports.org/" target="_top">MacPorts</a> (macOS) and
|
||||
<a class="ulink" href="https://brew.sh/" target="_top">Homebrew</a> (macOS), which provide an easier
|
||||
means of installation. If you decide to use them, please consult their documentation
|
||||
on how to install packages.
|
||||
</p>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="igraph-Installation-prerequisites"></a>1. Prerequisites</h2></div></div></div>
|
||||
<p>
|
||||
To build igraph from sources, you will need at least:
|
||||
</p>
|
||||
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
|
||||
<li class="listitem"><p>
|
||||
<a class="ulink" href="https://cmake.org" target="_top">CMake</a> 3.18 or later
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
C and C++ compilers
|
||||
</p></li>
|
||||
</ul></div>
|
||||
<p>
|
||||
Visual Studio 2015 and later are supported. Earlier Visual Studio
|
||||
versions may or may not work.
|
||||
</p>
|
||||
<p>
|
||||
Certain features also require the following libraries:
|
||||
</p>
|
||||
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem"><p>
|
||||
<a class="ulink" href="http://www.xmlsoft.org/" target="_top">libxml2</a>,
|
||||
required for GraphML support
|
||||
</p></li></ul></div>
|
||||
<p>
|
||||
igraph bundles a number of libraries for convenience. However, it is
|
||||
preferable to use external versions of these libraries, which may
|
||||
improve performance. These are:
|
||||
</p>
|
||||
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
|
||||
<li class="listitem"><p>
|
||||
<a class="ulink" href="https://gmplib.org/" target="_top">GMP</a> (the bundled
|
||||
alternative is Mini-GMP)
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<a class="ulink" href="https://www.gnu.org/software/glpk/" target="_top">GLPK</a> (version 4.57 or later)
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<a class="ulink" href="https://github.com/opencollab/arpack-ng" target="_top">ARPACK</a>
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<a class="ulink" href="https://github.com/ntamas/plfit" target="_top">plfit</a>
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
A library providing a
|
||||
<a class="ulink" href="https://www.netlib.org/blas/" target="_top">BLAS</a> API
|
||||
(available by default on macOS;
|
||||
<a class="ulink" href="http://www.openmathlib.org/OpenBLAS/" target="_top">OpenBLAS</a> is one
|
||||
option on other systems)
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
A library providing a
|
||||
<a class="ulink" href="https://www.netlib.org/lapack/" target="_top">LAPACK</a>
|
||||
API (available by default on macOS;
|
||||
<a class="ulink" href="http://www.openmathlib.org/OpenBLAS/" target="_top">OpenBLAS</a> is one
|
||||
option on other systems)
|
||||
</p></li>
|
||||
</ul></div>
|
||||
<p>
|
||||
When building the development version of igraph,
|
||||
<code class="literal">bison</code>, <code class="literal">flex</code> and
|
||||
<code class="literal">git</code> are also required. Released versions do not
|
||||
require these tools.
|
||||
</p>
|
||||
<p>
|
||||
To run the tests, <code class="literal">diff</code> is also required.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="igraph-Installation-installation"></a>2. Installation</h2></div></div></div>
|
||||
<div class="toc"><dl class="toc">
|
||||
<dt><span class="section"><a href="igraph-Installation.html#igraph-Installation-general-build-instructions">2.1. General build instructions</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Installation.html#igraph-Installation-specific-instructions-for-windows">2.2. Specific instructions for Windows</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Installation.html#igraph-Installation-notable-configuration-options">2.3. Notable configuration options</a></span></dt>
|
||||
</dl></div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="igraph-Installation-general-build-instructions"></a>2.1. General build instructions</h3></div></div></div>
|
||||
<p>
|
||||
igraph uses a
|
||||
<a class="ulink" href="https://cmake.org/cmake/help/latest/guide/user-interaction/index.html" target="_top">CMake-based
|
||||
build system</a>. To compile it,
|
||||
</p>
|
||||
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
|
||||
<li class="listitem">
|
||||
<p>
|
||||
Enter the directory where the igraph sources are:
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
$ cd igraph
|
||||
</pre>
|
||||
<p>
|
||||
</p>
|
||||
</li>
|
||||
<li class="listitem">
|
||||
<p>
|
||||
Create a new directory. This is where igraph will be built:
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
$ mkdir build
|
||||
$ cd build
|
||||
</pre>
|
||||
<p>
|
||||
</p>
|
||||
</li>
|
||||
<li class="listitem">
|
||||
<p>
|
||||
Run CMake, which will automatically configure igraph, and
|
||||
report the configuration:
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
$ cmake ..
|
||||
</pre>
|
||||
<p>
|
||||
To set a non-default installation location, such as
|
||||
<code class="literal">/opt/local</code>, use:
|
||||
</p>
|
||||
<pre class="programlisting">cmake .. -DCMAKE_INSTALL_PREFIX=/opt/local</pre>
|
||||
<p>
|
||||
</p>
|
||||
</li>
|
||||
<li class="listitem"><p>
|
||||
Check the output carefully, and ensure that all features you
|
||||
need are enabled. If CMake could not find certain libraries,
|
||||
some features such as GraphML support may have been
|
||||
automatically disabled.
|
||||
</p></li>
|
||||
<li class="listitem">
|
||||
<p>
|
||||
There are several ways to adjust the configuration:
|
||||
</p>
|
||||
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; ">
|
||||
<li class="listitem"><p>
|
||||
Run <code class="literal">ccmake .</code> on Unix-like systems or
|
||||
<code class="literal">cmake-gui</code> on Windows for a convenient
|
||||
interface.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
Simply edit the <code class="literal">CMakeCache.txt</code> file.
|
||||
Some of the relevant options are listed below.
|
||||
</p></li>
|
||||
</ul></div>
|
||||
</li>
|
||||
<li class="listitem"><p>
|
||||
Once the configuration has been adjusted, run
|
||||
<code class="literal">cmake ..</code> again.
|
||||
</p></li>
|
||||
<li class="listitem">
|
||||
<p>
|
||||
Once igraph has been successfully configured, it can be built,
|
||||
tested and installed using:
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
$ cmake --build .
|
||||
$ cmake --build . --target check
|
||||
$ cmake --install .
|
||||
</pre>
|
||||
<p>
|
||||
</p>
|
||||
</li>
|
||||
</ul></div>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="igraph-Installation-specific-instructions-for-windows"></a>2.2. Specific instructions for Windows</h3></div></div></div>
|
||||
<div class="toc"><dl class="toc">
|
||||
<dt><span class="section"><a href="igraph-Installation.html#igraph-Installation-microsoft-visual-studio">2.2.1. Microsoft Visual Studio</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Installation.html#igraph-Installation-msys2">2.2.2. MSYS2</a></span></dt>
|
||||
</dl></div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h4 class="title">
|
||||
<a name="igraph-Installation-microsoft-visual-studio"></a>2.2.1. Microsoft Visual Studio</h4></div></div></div>
|
||||
<p>
|
||||
With Visual Studio, the steps to build igraph are generally the
|
||||
same as above. However, since the Visual Studio CMake generator is
|
||||
a multi-configuration one, we must specify the configuration
|
||||
(typically Release or Debug) with each build command using the
|
||||
<code class="literal">--config</code> option:
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
mkdir build
|
||||
cd build
|
||||
cmake ..
|
||||
cmake --build . --config Release
|
||||
cmake --build . --target check --config Release
|
||||
</pre>
|
||||
<p>
|
||||
When building the development version, <code class="literal">bison</code>
|
||||
and <code class="literal">flex</code> must be available on the system.
|
||||
<a class="ulink" href="https://github.com/lexxmark/winflexbison" target="_top"><code class="literal">winflexbison</code></a>
|
||||
for Bison version 3.x can be useful for this purpose—make sure
|
||||
that the executables are in the system <code class="literal">PATH</code>.
|
||||
The easiest installation option is probably by installing
|
||||
<code class="literal">winflexbison3</code> from the
|
||||
<a class="ulink" href="https://chocolatey.org/packages/winflexbison3" target="_top">Chocolatey
|
||||
package manager</a>.
|
||||
</p>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h5 class="title">
|
||||
<a name="igraph-Installation-vcpkg"></a>2.2.1.1. vcpkg</h5></div></div></div>
|
||||
<p>
|
||||
Most external dependencies can be conveniently installed using
|
||||
<a class="ulink" href="https://github.com/microsoft/vcpkg#quick-start-windows" target="_top"><code class="literal">vcpkg</code></a>.
|
||||
Note that <code class="literal">igraph</code> bundles all dependencies
|
||||
except <code class="literal">libxml2</code>, which is needed for GraphML
|
||||
support.
|
||||
</p>
|
||||
<p>
|
||||
In order to use vcpkg integrate it in the build environment by executing
|
||||
<code class="literal">vcpkg.exe integrate install</code> on the command line.
|
||||
When configuring igraph, point CMake to the correct
|
||||
<code class="literal">vcpkg.cmake</code> file using <code class="literal">-DCMAKE_TOOLCHAIN_FILE=...</code>,
|
||||
as instructed.
|
||||
</p>
|
||||
<p>
|
||||
Additionally, it might be that you need to set the appropriate
|
||||
so-called triplet using
|
||||
<code class="literal">-DVCPKG_TARGET_TRIPLET</code> when running
|
||||
<code class="literal">cmake</code>, for exampling, setting it to
|
||||
<code class="literal">x64-windows</code> when using shared builds of packages or
|
||||
<code class="literal">x64-windows-static</code> when using static builds.
|
||||
Similarly, you also need to specify this target triplet when
|
||||
installing packages. For example, to install
|
||||
<code class="literal">libxml2</code> as a shared library, use
|
||||
<code class="literal">vcpkg.exe install libxml2:x64-windows</code> and to
|
||||
install <code class="literal">libxml2</code> as a static library, use
|
||||
<code class="literal">vcpkg.exe install libxml2:x64-windows-static</code>.
|
||||
In addition, there is the possibility to use a static library
|
||||
with dynamic runtime linking using the
|
||||
<code class="literal">x64-windows-static-md</code> triplet.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h4 class="title">
|
||||
<a name="igraph-Installation-msys2"></a>2.2.2. MSYS2</h4></div></div></div>
|
||||
<p>
|
||||
MSYS2 can be installed from <a class="ulink" href="https://www.msys2.org/" target="_top">msys2.org</a>. After installing MSYS2,
|
||||
ensure that it is up to date by opening a terminal and running
|
||||
<code class="literal">pacman -Syuu</code>.
|
||||
</p>
|
||||
<p>
|
||||
The instructions below assume that you want to compile for a 64-bit
|
||||
target.
|
||||
</p>
|
||||
<p>
|
||||
Install the following packages using <code class="literal">pacman -S</code>.
|
||||
</p>
|
||||
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
|
||||
<li class="listitem"><p>
|
||||
Minimal requirements:
|
||||
<code class="literal">mingw-w64-x86_64-toolchain</code>,
|
||||
<code class="literal">mingw-w64-x86_64-cmake</code>.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
Optional dependencies that enable certain features:
|
||||
<code class="literal">mingw-w64-x86_64-gmp</code>,
|
||||
<code class="literal">mingw-w64-x86_64-libxml2</code>
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
Optional external libraries for better performance:
|
||||
<code class="literal">mingw-w64-x86_64-openblas</code>,
|
||||
<code class="literal">mingw-w64-x86_64-arpack</code>,
|
||||
<code class="literal">mingw-w64-x86_64-glpk</code>
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
Only needed for running the tests: <code class="literal">diffutils</code>
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
Required only when building the development version:
|
||||
<code class="literal">git</code>, <code class="literal">bison</code>,
|
||||
<code class="literal">flex</code>
|
||||
</p></li>
|
||||
</ul></div>
|
||||
<p>
|
||||
The following command will install of these at once:
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
pacman -S \
|
||||
mingw-w64-x86_64-toolchain mingw-w64-x86_64-cmake \
|
||||
mingw-w64-x86_64-gmp mingw-w64-x86_64-libxml2 \
|
||||
mingw-w64-x86_64-openblas mingw-w64-x86_64-arpack \
|
||||
mingw-w64-x86_64-glpk diffutils git bison flex
|
||||
</pre>
|
||||
<p>
|
||||
In order to build igraph, follow the <span class="strong"><strong>General
|
||||
build instructions</strong></span> above, paying attention to the
|
||||
following:
|
||||
</p>
|
||||
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
|
||||
<li class="listitem"><p>
|
||||
When using MSYS2, start the <span class="quote">“<span class="quote">MSYS2 MinGW 64-bit</span>”</span>
|
||||
terminal, and <span class="emphasis"><em>not</em></span> the <span class="quote">“<span class="quote">MSYS2
|
||||
MSYS</span>”</span> one.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
Be sure to install the <code class="literal">mingw-w64-x86_64-cmake</code>
|
||||
package and not the <code class="literal">cmake</code> one. The latter
|
||||
will not work.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
When running <code class="literal">cmake</code>, pass the option
|
||||
<code class="literal">-G"MSYS Makefiles"</code>.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
Note that <code class="literal">ccmake</code> is not currently available.
|
||||
<code class="literal">cmake-gui</code> can be used only if the
|
||||
<code class="literal">mingw-w64-x86_64-qt5</code> package is installed.
|
||||
</p></li>
|
||||
</ul></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="igraph-Installation-notable-configuration-options"></a>2.3. Notable configuration options</h3></div></div></div>
|
||||
<p>
|
||||
The following options may be set to <code class="literal">ON</code> or
|
||||
<code class="literal">OFF</code>. Some of them have an <code class="literal">AUTO</code>
|
||||
setting, which chooses a reasonable default based on what libraries
|
||||
are available on the current system.
|
||||
</p>
|
||||
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
|
||||
<li class="listitem"><p>
|
||||
igraph bundles some of its dependencies for convenience. The
|
||||
<code class="literal">IGRAPH_USE_INTERNAL_XXX</code> flags control whether
|
||||
these should be used instead of external versions. Set them to
|
||||
<code class="literal">ON</code> to use the bundled
|
||||
(<span class="quote">“<span class="quote">vendored</span>”</span>) versions. Generally, external versions
|
||||
are preferable as they may be newer and usually provide better
|
||||
performance.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<code class="literal">IGRAPH_GLPK_SUPPORT</code>: whether to make use of
|
||||
the
|
||||
<a class="ulink" href="https://www.gnu.org/software/glpk/" target="_top">GLPK</a>
|
||||
library. Some features, such as finding a minimum feedback arc
|
||||
set or finding communities through exact modularity
|
||||
optimization, require this.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<code class="literal">IGRAPH_GRAPHML_SUPPORT</code>: whether to enable
|
||||
support for reading and writing
|
||||
<a class="ulink" href="http://graphml.graphdrawing.org/" target="_top">GraphML</a>
|
||||
files. Requires the
|
||||
<a class="ulink" href="http://xmlsoft.org/" target="_top">libxml2</a> library.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<code class="literal">IGRAPH_INFOMAP_SUPPORT</code>: whether to enable
|
||||
the Infomap community detection algorithm. The Infomap library
|
||||
is licensed under the GPLv3+. Compiling it into igraph causes
|
||||
GPLv3+ to apply to the resulting binary, instead of igraph's
|
||||
GPLv2+ license.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<code class="literal">IGRAPH_OPENMP_SUPPORT</code>: whether to use OpenMP
|
||||
parallelization to accelerate certain functions such as PageRank
|
||||
calculation. Compiler support is required.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<code class="literal">IGRAPH_ENABLE_LTO</code>: whether to build igraph
|
||||
with link-time optimization, which improves performance. Not
|
||||
supported with all compilers.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<code class="literal">IGRAPH_ENABLE_TLS</code>: whether to enable
|
||||
thread-local storage. Required when using igraph from multiple
|
||||
threads.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<code class="literal">IGRAPH_WARNINGS_AS_ERRORS</code>: whether to treat
|
||||
compiler warnings as errors. We strive to eliminate all compiler
|
||||
warnings during development so this switch is turned on by default.
|
||||
If your compiler prints warnings for some parts of the code that we
|
||||
did not anticipate, you can turn off this option to prevent the
|
||||
warnings from stopping the compilation.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<a class="ulink" href="https://cmake.org/cmake/help/latest/variable/BUILD_SHARED_LIBS.html" target="_top"><code class="literal">BUILD_SHARED_LIBS</code></a>:
|
||||
whether to build a shared library instead of a static one.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<code class="literal">BLA_VENDOR</code>: controls which library to use for
|
||||
<a class="ulink" href="https://cmake.org/cmake/help/latest/module/FindBLAS.html" target="_top">BLAS</a>
|
||||
and
|
||||
<a class="ulink" href="https://cmake.org/cmake/help/latest/module/FindLAPACK.html" target="_top">LAPACK</a>
|
||||
functionality.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
<a class="ulink" href="https://cmake.org/cmake/help/latest/variable/CMAKE_INSTALL_PREFIX.html" target="_top"><code class="literal">CMAKE_INSTALL_PREFIX</code></a>:
|
||||
the location where igraph will be installed.
|
||||
</p></li>
|
||||
</ul></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="igraph-Installation-building-the-documentation"></a>3. Building the documentation</h2></div></div></div>
|
||||
<p>
|
||||
Most users will not need to build the documentation, as the release
|
||||
tarball contains pre-built HTML documentation in the <code class="literal">doc</code>
|
||||
directory.
|
||||
</p>
|
||||
<p>
|
||||
To build the documentation for the development version, simply build the
|
||||
<code class="literal">html</code>, <code class="literal">pdf</code> or <code class="literal">info</code>
|
||||
targets for the HTML, PDF and Info versions of the documentation,
|
||||
respectively.
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
$ cmake --build . --target html
|
||||
</pre>
|
||||
<p>
|
||||
Building the HTML documentation requires Python 3, <code class="literal">xmlto</code>
|
||||
and <code class="literal">source-highlight</code>. On some platforms, it is necessary
|
||||
to explicitly install the docbook-xsl package as well. Building the PDF
|
||||
documentation also requires <code class="literal">xsltproc</code>,
|
||||
<code class="literal">xmllint</code> and <code class="literal">fop</code>. Building the Texinfo
|
||||
documentation also requires the docbook2X package, <code class="literal">xmllint</code>
|
||||
and <code class="literal">makeinfo</code>.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="igraph-Installation-notes-for-package-maintainers"></a>4. Notes for package maintainers</h2></div></div></div>
|
||||
<div class="toc"><dl class="toc">
|
||||
<dt><span class="section"><a href="igraph-Installation.html#igraph-Installation-auto-detection-of-dependencies">4.1. Auto-detection of dependencies</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Installation.html#igraph-Installation-shared-and-static-builds">4.2. Shared and static builds</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Installation.html#igraph-Installation-cross-compiling">4.3. Cross-compiling</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Installation.html#igraph-Installation-additional-notes">4.4. Additional notes</a></span></dt>
|
||||
</dl></div>
|
||||
<p>
|
||||
This section is for people who package igraph for Linux distros or
|
||||
other package managers. Please read it carefully before packaging
|
||||
igraph.
|
||||
</p>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="igraph-Installation-auto-detection-of-dependencies"></a>4.1. Auto-detection of dependencies</h3></div></div></div>
|
||||
<p>
|
||||
igraph bundles several of its dependencies (or simplified versions
|
||||
of its dependencies). During configuration time, it checks whether
|
||||
each dependency is present on the system. If yes, it uses it.
|
||||
Otherwise, it falls back to the bundled (<span class="quote">“<span class="quote">vendored</span>”</span>)
|
||||
version. In order to make configuration as deterministic as
|
||||
possible, you may want to disable this auto-detection. To do so, set
|
||||
each of the <code class="literal">IGRAPH_USE_INTERNAL_XXX</code> options
|
||||
described above. Additionally, set <code class="literal">BLA_VENDOR</code> to
|
||||
use the BLAS and LAPACK implementations of your choice. This should
|
||||
be the same BLAS and LAPACK library that igraph's other dependencies
|
||||
(e.g., ARPACK) are linked against.
|
||||
</p>
|
||||
<p>
|
||||
For example, to force igraph to use external versions of all
|
||||
dependencies except plfit, and to use OpenBLAS for BLAS/LAPACK, use
|
||||
</p>
|
||||
<p>
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
$ cmake .. \
|
||||
-DIGRAPH_USE_INTERNAL_BLAS=OFF \
|
||||
-DIGRAPH_USE_INTERNAL_LAPACK=OFF \
|
||||
-DIGRAPH_USE_INTERNAL_ARPACK=OFF \
|
||||
-DIGRAPH_USE_INTERNAL_GLPK=OFF \
|
||||
-DIGRAPH_USE_INTERNAL_GMP=OFF \
|
||||
-DIGRAPH_USE_INTERNAL_PLFIT=ON \
|
||||
-DBLA_VENDOR=OpenBLAS \
|
||||
-DIGRAPH_GRAPHML_SUPPORT=ON
|
||||
</pre>
|
||||
<p>
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="igraph-Installation-shared-and-static-builds"></a>4.2. Shared and static builds</h3></div></div></div>
|
||||
<p>
|
||||
On Windows, shared and static builds should not be installed in the same
|
||||
location. If you decide to do so anyway, keep in mind the following:
|
||||
Both builds contain an <code class="literal">igraph.lib</code> file. The static one
|
||||
should be renamed to avoid conflict. The headers from the static build
|
||||
are incompatible with the shared library. The headers from the shared build
|
||||
may be used with the static library, but <code class="literal">IGRAPH_STATIC</code>
|
||||
must be defined when compiling programs that will link to igraph statically.
|
||||
</p>
|
||||
<p>
|
||||
These issues do not affect Unix-like systems.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="igraph-Installation-cross-compiling"></a>4.3. Cross-compiling</h3></div></div></div>
|
||||
<p>
|
||||
When building igraph with an internal ARPACK, LAPACK or BLAS, it
|
||||
makes use of f2c, which compiles and runs the <code class="literal">arithchk</code>
|
||||
program at build time to detect the floating point characteristics of the
|
||||
current system. It writes the results into the <code class="literal">arith.h</code>
|
||||
header. However, running this program is not possible when cross-compiling
|
||||
without providing a userspace emulator that can run executables of the
|
||||
target platform on the host system. Therefore, when cross-compiling, you
|
||||
either need to provide such an emulator with the
|
||||
<code class="literal">CMAKE_CROSSCOMPILING_EMULATOR</code> option, or you need to
|
||||
specify a pre-generated version of the <code class="literal">arith.h</code> header
|
||||
file through the <code class="literal">F2C_EXTERNAL_ARITH_HEADER</code>
|
||||
CMake option. An example version of this header follows for the
|
||||
x86_64 and arm64 target architectures on macOS. Warning: Do not use this
|
||||
version of <code class="literal">arith.h</code> on other systems or architectures.
|
||||
</p>
|
||||
<p>
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
#define IEEE_8087
|
||||
#define Arith_Kind_ASL 1
|
||||
#define Long int
|
||||
#define Intcast (int)(long)
|
||||
#define Double_Align
|
||||
#define X64_bit_pointers
|
||||
#define NANCHECK
|
||||
#define QNaN0 0x0
|
||||
#define QNaN1 0x7ff80000
|
||||
</pre>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
igraph also checks whether the endianness of <code class="literal">uint64_t</code>
|
||||
matches the endianness of <code class="literal">double</code> on the platform
|
||||
being compiled. This is needed to ensure that certain functions in igraph's
|
||||
random number generator work properly. However, it is not possible to
|
||||
execute this check when cross-compiling without an emulator, so in this
|
||||
case igraph simply assumes that the endianness matches (which is the case
|
||||
for the vast majority of platforms anyway). The only case where you might
|
||||
run into problems is when you cross-compile for Apple Silicon
|
||||
(<code class="literal">arm64</code>) from an Intel-based Mac, in which case CMake
|
||||
might not realize that you are cross-compiling and will try to execute
|
||||
the check anyway. You can work around this by setting
|
||||
<code class="literal">IEEE754_DOUBLE_ENDIANNESS_MATCHES</code> to <code class="literal">ON</code>
|
||||
explicitly before invoking CMake.
|
||||
</p>
|
||||
<p>
|
||||
Providing an emulator in <code class="literal">CMAKE_CROSSCOMPILING_EMULATOR</code>
|
||||
has the added benefit that you can run the compiled unit tests on the
|
||||
host platform. We have experimented with cross-compiling to 64-bit ARM
|
||||
CPUs (<code class="literal">aarch64</code>) on 64-bit Intel CPUs (<code class="literal">amd64</code>),
|
||||
and we can confirm that using <code class="literal">qemu-aarch64</code> works as a
|
||||
cross-compiling emulator in this setup.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="igraph-Installation-additional-notes"></a>4.4. Additional notes</h3></div></div></div>
|
||||
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
|
||||
<li class="listitem"><p>
|
||||
As of igraph 0.10, there is no tangible benefit to using an
|
||||
external GMP, as igraph does not yet use GMP in any
|
||||
performance-critical way. The bundled Mini-GMP is sufficient.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
Link-time optimization noticeably improves the performance of
|
||||
some igraph functions. To enable it, use
|
||||
<code class="literal">-DIGRAPH_ENABLE_LTO=ON</code>.
|
||||
The <code class="literal">AUTO</code> setting is also supported, and will
|
||||
enable link-time optimization only if the current compiler
|
||||
supports it. Note that this is detected by CMake, and the
|
||||
detection is not always accurate.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
We saw occasional hangs on Windows when igraph was built for a
|
||||
32-bit target with MinGW and linked to OpenBLAS. We believe this
|
||||
to be an issue with OpenBLAS, not igraph. On this platform, you
|
||||
may want to opt for a different BLAS/LAPACK or the bundled
|
||||
BLAS/LAPACK.
|
||||
</p></li>
|
||||
</ul></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<table class="navigation-footer" width="100%" summary="Navigation footer" cellpadding="2" cellspacing="0"><tr valign="middle">
|
||||
<td align="left"><a accesskey="p" href="igraph-Introduction.html"><b>← Chapter 1. Introduction</b></a></td>
|
||||
<td align="right"><a accesskey="n" href="igraph-Tutorial.html"><b>Chapter 3. Tutorial →</b></a></td>
|
||||
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|
||||
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|
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</html>
|
||||
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|
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<head>
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|
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<link rel="home" href="index.html" title="igraph Reference Manual">
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<link rel="prev" href="index.html" title="igraph Reference Manual">
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<link rel="next" href="igraph-Installation.html" title="Chapter 2. Installation">
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<link rel="chapter" href="igraph-Installation.html" title="Chapter 2. Installation">
|
||||
<link rel="chapter" href="igraph-Tutorial.html" title="Chapter 3. Tutorial">
|
||||
<link rel="chapter" href="igraph-Basic.html" title="Chapter 4. Basic data types and interface">
|
||||
<link rel="chapter" href="igraph-Error.html" title="Chapter 5. Error handling">
|
||||
<link rel="chapter" href="igraph-Memory.html" title="Chapter 6. Memory (de)allocation">
|
||||
<link rel="chapter" href="igraph-Data-structures.html" title="Chapter 7. Data structure library: vector, matrix, other data types">
|
||||
<link rel="chapter" href="igraph-Random.html" title="Chapter 8. Random numbers">
|
||||
<link rel="chapter" href="igraph-Iterators.html" title="Chapter 9. Vertex and edge selectors and sequences, iterators">
|
||||
<link rel="chapter" href="igraph-Attributes.html" title="Chapter 10. Graph, vertex and edge attributes">
|
||||
<link rel="chapter" href="igraph-Generators.html" title="Chapter 11. Deterministic graph generators">
|
||||
<link rel="chapter" href="igraph-Games.html" title='Chapter 12. Stochastic graph generators ("games")'>
|
||||
<link rel="chapter" href="igraph-Bipartite.html" title="Chapter 13. Bipartite, i.e. two-mode graphs">
|
||||
<link rel="chapter" href="igraph-Spatial.html" title="Chapter 14. Spatial graphs">
|
||||
<link rel="chapter" href="igraph-Operators.html" title="Chapter 15. Graph operators">
|
||||
<link rel="chapter" href="igraph-Visitors.html" title="Chapter 16. Graph visitors">
|
||||
<link rel="chapter" href="igraph-Structural.html" title="Chapter 17. Structural properties of graphs">
|
||||
<link rel="chapter" href="igraph-Cycles.html" title="Chapter 18. Graph cycles">
|
||||
<link rel="chapter" href="igraph-Cliques.html" title="Chapter 19. Cliques and independent vertex sets">
|
||||
<link rel="chapter" href="igraph-Motifs.html" title="Chapter 20. Graph motifs, dyad census and triad census">
|
||||
<link rel="chapter" href="igraph-Isomorphism.html" title="Chapter 21. Graph isomorphism">
|
||||
<link rel="chapter" href="igraph-Coloring.html" title="Chapter 22. Graph coloring">
|
||||
<link rel="chapter" href="igraph-Flows.html" title="Chapter 23. Maximum flows, minimum cuts and related measures">
|
||||
<link rel="chapter" href="igraph-Separators.html" title="Chapter 24. Vertex separators">
|
||||
<link rel="chapter" href="igraph-Community.html" title="Chapter 25. Detecting community structure">
|
||||
<link rel="chapter" href="igraph-Graphlets.html" title="Chapter 26. Graphlets">
|
||||
<link rel="chapter" href="igraph-HRG.html" title="Chapter 27. Hierarchical random graphs">
|
||||
<link rel="chapter" href="igraph-Embedding.html" title="Chapter 28. Embedding of graphs">
|
||||
<link rel="chapter" href="igraph-Layout.html" title="Chapter 29. Generating layouts for graph drawing">
|
||||
<link rel="chapter" href="igraph-Processes.html" title="Chapter 30. Processes on graphs">
|
||||
<link rel="chapter" href="igraph-Foreign.html" title="Chapter 31. Reading and writing graphs from and to files">
|
||||
<link rel="chapter" href="igraph-Linalg.html" title="Chapter 32. Using BLAS, LAPACK and ARPACK for igraph matrices and graphs">
|
||||
<link rel="chapter" href="igraph-Nongraph.html" title="Chapter 33. Non-graph related functions">
|
||||
<link rel="chapter" href="igraph-Advanced.html" title="Chapter 34. Advanced igraph programming">
|
||||
<link rel="chapter" href="igraph-Glossary.html" title="Chapter 35. Glossary">
|
||||
<link rel="chapter" href="igraph-Licenses.html" title="Chapter 36. Licenses for igraph and this manual">
|
||||
<link rel="index" href="ix01.html" title="Index">
|
||||
</head>
|
||||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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<a accesskey="p" class="btn btn-light" href="index.html"><i class="fa fa-chevron-left"></i>
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Home
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</a><a accesskey="n" class="btn btn-light" href="igraph-Installation.html"><i class="fa fa-chevron-right"></i>
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Next
|
||||
</a>
|
||||
</div></div>
|
||||
<div class="chapter">
|
||||
<div class="titlepage"><div><div><h1 class="title">
|
||||
<a name="igraph-Introduction"></a>Chapter 1. Introduction</h1></div></div></div>
|
||||
<div class="toc"><dl class="toc">
|
||||
<dt><span class="section"><a href="igraph-Introduction.html#igraph-is-free-software">1. igraph is free software</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Introduction.html#citing-igraph">2. Citing igraph</a></span></dt>
|
||||
</dl></div>
|
||||
<p>
|
||||
igraph is a library for creating and manipulating graphs.
|
||||
You can look at it in two ways: first, igraph contains the implementation
|
||||
of quite a lot of graph algorithms. These include classic graph
|
||||
algorithms like graph isomorphism, graph girth and connectivity and
|
||||
also the new wave graph algorithms like transitivity, graph motifs and
|
||||
community structure detection. Skim through the table of contents
|
||||
or the index of this book to get an impression of what is available.</p>
|
||||
<p>
|
||||
Second, igraph provides a platform for developing and/or
|
||||
implementing graph algorithms. It has an efficient data structure
|
||||
for representing graphs, and a number of other data structures like
|
||||
flexible vectors, stacks, heaps, queues, adjacency lists that are useful for implementing graph algorithms. In fact these data structures evolved along with the
|
||||
implementation of the classic and non-classic graph algorithms which
|
||||
make up the major part of the igraph library. This way, they were fine-tuned
|
||||
and checked for correctness several times.
|
||||
</p>
|
||||
<p>
|
||||
Our main goal with developing igraph was to create a graph library
|
||||
which is efficient on large, but not extremely large graphs. More
|
||||
precisely, it is assumed that the graph(s) fit into the physical
|
||||
memory of the computer. Nowadays this means graphs with
|
||||
several million vertices and/or edges. Our definition of efficient is
|
||||
that it runs fast, both in theory and (more importantly) in practice.
|
||||
</p>
|
||||
<p>
|
||||
We believe that one of the big strengths of igraph is that it can be
|
||||
embedded into a higher-level language or environment. Three such
|
||||
embeddings (or interfaces if you look at them another way)
|
||||
are currently being developed by us: an R
|
||||
package, a Python extension module, and a Mathematica (Wolfram Language) package. Others are
|
||||
likely to come. High level languages such as R or Python make it
|
||||
possible to use graph routines with much greater comfort, without
|
||||
actually writing a single line of C code. They have some, usually very
|
||||
small, speed penalty compared to the C version, but add ease of use and much
|
||||
flexibility. This manual, however, covers only the C library. If you
|
||||
want to use Python, R or the Wolfram Language, please see the documentation written
|
||||
specifically for these interfaces and come back here only if you are
|
||||
interested in some detail which is not covered in those documents.
|
||||
</p>
|
||||
<p>
|
||||
We still consider igraph as a child project. It has much room for
|
||||
development and we are sure that it will improve a lot in the near
|
||||
future. Any feedback we can get from the users is very important for
|
||||
us, as most of the time these questions and comments guide us in what
|
||||
to add and what to improve.
|
||||
</p>
|
||||
<p>
|
||||
igraph is open source and distributed under the terms of the GNU GPL
|
||||
version 2 or (at your option) any later version.
|
||||
We strongly believe that all the algorithms used in science, let that
|
||||
be graph theory or not, should have an efficient open-source
|
||||
implementation allowing use and modification for anyone.
|
||||
</p>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="igraph-is-free-software"></a>1. igraph is free software</h2></div></div></div>
|
||||
<p>
|
||||
igraph library
|
||||
</p>
|
||||
<p>
|
||||
Copyright (C) 2003-2004 Gábor Csárdi <csardi.gabor@gmail.com>
|
||||
</p>
|
||||
<p>
|
||||
Copyright (C) 2005-2019 Gábor Csárdi <csardi.gabor@gmail.com> and Tamás Nepusz <ntamas@gmail.com>
|
||||
</p>
|
||||
<p>
|
||||
Copyright (C) 2020-2023 The igraph development team
|
||||
</p>
|
||||
<p>
|
||||
This program is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
</p>
|
||||
<p>
|
||||
This program is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
</p>
|
||||
<p>
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with this program; if not, write to the Free Software
|
||||
Foundation, Inc.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="citing-igraph"></a>2. Citing igraph</h2></div></div></div>
|
||||
<p>
|
||||
To cite igraph in publications, please use the following
|
||||
reference:
|
||||
</p>
|
||||
<p>
|
||||
Gábor Csárdi, Tamás Nepusz: The igraph software package for complex network
|
||||
research. InterJournal Complex Systems, 1695, 2006.
|
||||
</p>
|
||||
<p>
|
||||
The igraph C library is assigned the DOI <a class="ulink" href="https://doi.org/10.5281/zenodo.3630268" target="_top">10.5281/zenodo.3630268</a> on Zenodo.
|
||||
</p>
|
||||
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|
||||
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|
||||
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<link rel="chapter" href="igraph-Data-structures.html" title="Chapter 7. Data structure library: vector, matrix, other data types">
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<link rel="chapter" href="igraph-Random.html" title="Chapter 8. Random numbers">
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<link rel="chapter" href="igraph-Iterators.html" title="Chapter 9. Vertex and edge selectors and sequences, iterators">
|
||||
<link rel="chapter" href="igraph-Attributes.html" title="Chapter 10. Graph, vertex and edge attributes">
|
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<link rel="chapter" href="igraph-Generators.html" title="Chapter 11. Deterministic graph generators">
|
||||
<link rel="chapter" href="igraph-Games.html" title='Chapter 12. Stochastic graph generators ("games")'>
|
||||
<link rel="chapter" href="igraph-Bipartite.html" title="Chapter 13. Bipartite, i.e. two-mode graphs">
|
||||
<link rel="chapter" href="igraph-Spatial.html" title="Chapter 14. Spatial graphs">
|
||||
<link rel="chapter" href="igraph-Operators.html" title="Chapter 15. Graph operators">
|
||||
<link rel="chapter" href="igraph-Visitors.html" title="Chapter 16. Graph visitors">
|
||||
<link rel="chapter" href="igraph-Structural.html" title="Chapter 17. Structural properties of graphs">
|
||||
<link rel="chapter" href="igraph-Cycles.html" title="Chapter 18. Graph cycles">
|
||||
<link rel="chapter" href="igraph-Cliques.html" title="Chapter 19. Cliques and independent vertex sets">
|
||||
<link rel="chapter" href="igraph-Motifs.html" title="Chapter 20. Graph motifs, dyad census and triad census">
|
||||
<link rel="chapter" href="igraph-Isomorphism.html" title="Chapter 21. Graph isomorphism">
|
||||
<link rel="chapter" href="igraph-Coloring.html" title="Chapter 22. Graph coloring">
|
||||
<link rel="chapter" href="igraph-Flows.html" title="Chapter 23. Maximum flows, minimum cuts and related measures">
|
||||
<link rel="chapter" href="igraph-Separators.html" title="Chapter 24. Vertex separators">
|
||||
<link rel="chapter" href="igraph-Community.html" title="Chapter 25. Detecting community structure">
|
||||
<link rel="chapter" href="igraph-Graphlets.html" title="Chapter 26. Graphlets">
|
||||
<link rel="chapter" href="igraph-HRG.html" title="Chapter 27. Hierarchical random graphs">
|
||||
<link rel="chapter" href="igraph-Embedding.html" title="Chapter 28. Embedding of graphs">
|
||||
<link rel="chapter" href="igraph-Layout.html" title="Chapter 29. Generating layouts for graph drawing">
|
||||
<link rel="chapter" href="igraph-Processes.html" title="Chapter 30. Processes on graphs">
|
||||
<link rel="chapter" href="igraph-Foreign.html" title="Chapter 31. Reading and writing graphs from and to files">
|
||||
<link rel="chapter" href="igraph-Linalg.html" title="Chapter 32. Using BLAS, LAPACK and ARPACK for igraph matrices and graphs">
|
||||
<link rel="chapter" href="igraph-Nongraph.html" title="Chapter 33. Non-graph related functions">
|
||||
<link rel="chapter" href="igraph-Advanced.html" title="Chapter 34. Advanced igraph programming">
|
||||
<link rel="chapter" href="igraph-Glossary.html" title="Chapter 35. Glossary">
|
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<link rel="chapter" href="igraph-Licenses.html" title="Chapter 36. Licenses for igraph and this manual">
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<div class="chapter">
|
||||
<div class="titlepage"><div><div><h1 class="title">
|
||||
<a name="igraph-Licenses"></a>Chapter 36. Licenses for igraph and this manual</h1></div></div></div>
|
||||
<div class="toc"><dl class="toc">
|
||||
<dt><span class="section"><a href="igraph-Licenses.html#igraph-gpl">1. THE GNU GENERAL PUBLIC LICENSE</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Licenses.html#igraph-fdl">2. The GNU Free Documentation License</a></span></dt>
|
||||
</dl></div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div>
|
||||
<div><h2 class="title" style="clear: both">
|
||||
<a name="igraph-gpl"></a>1. THE GNU GENERAL PUBLIC LICENSE</h2></div>
|
||||
<div><p class="copyright">Copyright © 1989, 1991 Free Software Foundation, Inc.
|
||||
51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
</p></div>
|
||||
<div><div class="legalnotice">
|
||||
<a name="id-1.37.2.1.3"></a><p>
|
||||
Everyone is permitted to copy and distribute verbatim copies
|
||||
of this license document, but changing it is not allowed.
|
||||
</p>
|
||||
</div></div>
|
||||
</div></div>
|
||||
<div class="toc"><dl class="toc">
|
||||
<dt><span class="section"><a href="igraph-Licenses.html#id-1.37.2.3">1.1. Preamble</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Licenses.html#sectiongpl">1.2. GNU GENERAL PUBLIC LICENSE</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Licenses.html#id-1.37.2.5">1.3. How to Apply These Terms to Your New Programs</a></span></dt>
|
||||
</dl></div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="id-1.37.2.3"></a>1.1. Preamble</h3></div></div></div>
|
||||
<p>
|
||||
The licenses for most software are designed to take away your
|
||||
freedom to share and change it. By contrast, the GNU General Public
|
||||
License is intended to guarantee your freedom to share and change free
|
||||
software--to make sure the software is free for all its users. This
|
||||
General Public License applies to most of the Free Software
|
||||
Foundation's software and to any other program whose authors commit to
|
||||
using it. (Some other Free Software Foundation software is covered by
|
||||
the GNU Library General Public License instead.) You can apply it to
|
||||
your programs, too.
|
||||
</p>
|
||||
<p>
|
||||
When we speak of free software, we are referring to freedom, not
|
||||
price. Our General Public Licenses are designed to make sure that you
|
||||
have the freedom to distribute copies of free software (and charge for
|
||||
this service if you wish), that you receive source code or can get it
|
||||
if you want it, that you can change the software or use pieces of it
|
||||
in new free programs; and that you know you can do these things.
|
||||
</p>
|
||||
<p>
|
||||
To protect your rights, we need to make restrictions that forbid
|
||||
anyone to deny you these rights or to ask you to surrender the rights.
|
||||
These restrictions translate to certain responsibilities for you if you
|
||||
distribute copies of the software, or if you modify it.
|
||||
</p>
|
||||
<p>
|
||||
For example, if you distribute copies of such a program, whether
|
||||
gratis or for a fee, you must give the recipients all the rights that
|
||||
you have. You must make sure that they, too, receive or can get the
|
||||
source code. And you must show them these terms so they know their
|
||||
rights.
|
||||
</p>
|
||||
<p>
|
||||
We protect your rights with two steps: (1) copyright the software, and
|
||||
(2) offer you this license which gives you legal permission to copy,
|
||||
distribute and/or modify the software.
|
||||
</p>
|
||||
<p>
|
||||
Also, for each author's protection and ours, we want to make certain
|
||||
that everyone understands that there is no warranty for this free
|
||||
software. If the software is modified by someone else and passed on, we
|
||||
want its recipients to know that what they have is not the original, so
|
||||
that any problems introduced by others will not reflect on the original
|
||||
authors' reputations.
|
||||
</p>
|
||||
<p>
|
||||
Finally, any free program is threatened constantly by software
|
||||
patents. We wish to avoid the danger that redistributors of a free
|
||||
program will individually obtain patent licenses, in effect making the
|
||||
program proprietary. To prevent this, we have made it clear that any
|
||||
patent must be licensed for everyone's free use or not licensed at all.
|
||||
</p>
|
||||
<p>
|
||||
The precise terms and conditions for copying, distribution and
|
||||
modification follow.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div>
|
||||
<div><h3 class="title">
|
||||
<a name="sectiongpl"></a>1.2. GNU GENERAL PUBLIC LICENSE</h3></div>
|
||||
<div><h4 class="subtitle">TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION</h4></div>
|
||||
</div></div>
|
||||
<p>
|
||||
0. This License applies to any program or other work which contains
|
||||
a notice placed by the copyright holder saying it may be distributed
|
||||
under the terms of this General Public License. The "Program", below,
|
||||
refers to any such program or work, and a "work based on the Program"
|
||||
means either the Program or any derivative work under copyright law:
|
||||
that is to say, a work containing the Program or a portion of it,
|
||||
either verbatim or with modifications and/or translated into another
|
||||
language. (Hereinafter, translation is included without limitation in
|
||||
the term "modification".) Each licensee is addressed as "you".
|
||||
</p>
|
||||
<p>
|
||||
Activities other than copying, distribution and modification are not
|
||||
covered by this License; they are outside its scope. The act of
|
||||
running the Program is not restricted, and the output from the Program
|
||||
is covered only if its contents constitute a work based on the
|
||||
Program (independent of having been made by running the Program).
|
||||
Whether that is true depends on what the Program does.
|
||||
</p>
|
||||
<p>
|
||||
1. You may copy and distribute verbatim copies of the Program's
|
||||
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|
||||
conspicuously and appropriately publish on each copy an appropriate
|
||||
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|
||||
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|
||||
and give any other recipients of the Program a copy of this License
|
||||
along with the Program.
|
||||
</p>
|
||||
<p>
|
||||
You may charge a fee for the physical act of transferring a copy, and
|
||||
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|
||||
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|
||||
<p>
|
||||
2. You may modify your copy or copies of the Program or any portion
|
||||
of it, thus forming a work based on the Program, and copy and
|
||||
distribute such modifications or work under the terms of Section 1
|
||||
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|
||||
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|
||||
<div class="orderedlist"><ol class="orderedlist" type="a">
|
||||
<li class="listitem"><p>
|
||||
You must cause the modified files to carry prominent notices
|
||||
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||||
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|
||||
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|
||||
You must cause any work that you distribute or publish, that in
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||||
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|
||||
part thereof, to be licensed as a whole at no charge to all third
|
||||
parties under the terms of this License.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
If the modified program normally reads commands interactively
|
||||
when run, you must cause it, when started running for such
|
||||
interactive use in the most ordinary way, to print or display an
|
||||
announcement including an appropriate copyright notice and a
|
||||
notice that there is no warranty (or else, saying that you provide
|
||||
a warranty) and that users may redistribute the program under
|
||||
these conditions, and telling the user how to view a copy of this
|
||||
License. (Exception: if the Program itself is interactive but
|
||||
does not normally print such an announcement, your work based on
|
||||
the Program is not required to print an announcement.)
|
||||
</p></li>
|
||||
</ol></div>
|
||||
<p>
|
||||
These requirements apply to the modified work as a whole. If
|
||||
identifiable sections of that work are not derived from the Program,
|
||||
and can be reasonably considered independent and separate works in
|
||||
themselves, then this License, and its terms, do not apply to those
|
||||
sections when you distribute them as separate works. But when you
|
||||
distribute the same sections as part of a whole which is a work based
|
||||
on the Program, the distribution of the whole must be on the terms of
|
||||
this License, whose permissions for other licensees extend to the
|
||||
entire whole, and thus to each and every part regardless of who wrote it.
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||||
</p>
|
||||
<p>
|
||||
Thus, it is not the intent of this section to claim rights or contest
|
||||
your rights to work written entirely by you; rather, the intent is to
|
||||
exercise the right to control the distribution of derivative or
|
||||
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||||
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|
||||
<p>
|
||||
In addition, mere aggregation of another work not based on the Program
|
||||
with the Program (or with a work based on the Program) on a volume of
|
||||
a storage or distribution medium does not bring the other work under
|
||||
the scope of this License.
|
||||
</p>
|
||||
<p>
|
||||
3. You may copy and distribute the Program (or a work based on it,
|
||||
under Section 2) in object code or executable form under the terms of
|
||||
Sections 1 and 2 above provided that you also do one of the following:
|
||||
</p>
|
||||
<div class="orderedlist"><ol class="orderedlist" type="a">
|
||||
<li class="listitem"><p>
|
||||
Accompany it with the complete corresponding machine-readable
|
||||
source code, which must be distributed under the terms of Sections
|
||||
1 and 2 above on a medium customarily used for software interchange; or,
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
Accompany it with a written offer, valid for at least three
|
||||
years, to give any third party, for a charge no more than your
|
||||
cost of physically performing source distribution, a complete
|
||||
machine-readable copy of the corresponding source code, to be
|
||||
distributed under the terms of Sections 1 and 2 above on a medium
|
||||
customarily used for software interchange; or,
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
Accompany it with the information you received as to the offer
|
||||
to distribute corresponding source code. (This alternative is
|
||||
allowed only for noncommercial distribution and only if you
|
||||
received the program in object code or executable form with such
|
||||
an offer, in accord with Subsection b above.)
|
||||
</p></li>
|
||||
</ol></div>
|
||||
<p>
|
||||
The source code for a work means the preferred form of the work for
|
||||
making modifications to it. For an executable work, complete source
|
||||
code means all the source code for all modules it contains, plus any
|
||||
associated interface definition files, plus the scripts used to
|
||||
control compilation and installation of the executable. However, as a
|
||||
special exception, the source code distributed need not include
|
||||
anything that is normally distributed (in either source or binary
|
||||
form) with the major components (compiler, kernel, and so on) of the
|
||||
operating system on which the executable runs, unless that component
|
||||
itself accompanies the executable.
|
||||
</p>
|
||||
<p>
|
||||
If distribution of executable or object code is made by offering
|
||||
access to copy from a designated place, then offering equivalent
|
||||
access to copy the source code from the same place counts as
|
||||
distribution of the source code, even though third parties are not
|
||||
compelled to copy the source along with the object code.
|
||||
</p>
|
||||
<p>
|
||||
4. You may not copy, modify, sublicense, or distribute the Program
|
||||
except as expressly provided under this License. Any attempt
|
||||
otherwise to copy, modify, sublicense or distribute the Program is
|
||||
void, and will automatically terminate your rights under this License.
|
||||
However, parties who have received copies, or rights, from you under
|
||||
this License will not have their licenses terminated so long as such
|
||||
parties remain in full compliance.
|
||||
</p>
|
||||
<p>
|
||||
5. You are not required to accept this License, since you have not
|
||||
signed it. However, nothing else grants you permission to modify or
|
||||
distribute the Program or its derivative works. These actions are
|
||||
prohibited by law if you do not accept this License. Therefore, by
|
||||
modifying or distributing the Program (or any work based on the
|
||||
Program), you indicate your acceptance of this License to do so, and
|
||||
all its terms and conditions for copying, distributing or modifying
|
||||
the Program or works based on it.
|
||||
</p>
|
||||
<p>
|
||||
6. Each time you redistribute the Program (or any work based on the
|
||||
Program), the recipient automatically receives a license from the
|
||||
original licensor to copy, distribute or modify the Program subject to
|
||||
these terms and conditions. You may not impose any further
|
||||
restrictions on the recipients' exercise of the rights granted herein.
|
||||
You are not responsible for enforcing compliance by third parties to
|
||||
this License.
|
||||
</p>
|
||||
<p>
|
||||
7. If, as a consequence of a court judgment or allegation of patent
|
||||
infringement or for any other reason (not limited to patent issues),
|
||||
conditions are imposed on you (whether by court order, agreement or
|
||||
otherwise) that contradict the conditions of this License, they do not
|
||||
excuse you from the conditions of this License. If you cannot
|
||||
distribute so as to satisfy simultaneously your obligations under this
|
||||
License and any other pertinent obligations, then as a consequence you
|
||||
may not distribute the Program at all. For example, if a patent
|
||||
license would not permit royalty-free redistribution of the Program by
|
||||
all those who receive copies directly or indirectly through you, then
|
||||
the only way you could satisfy both it and this License would be to
|
||||
refrain entirely from distribution of the Program.
|
||||
</p>
|
||||
<p>
|
||||
If any portion of this section is held invalid or unenforceable under
|
||||
any particular circumstance, the balance of the section is intended to
|
||||
apply and the section as a whole is intended to apply in other
|
||||
circumstances.
|
||||
</p>
|
||||
<p>
|
||||
It is not the purpose of this section to induce you to infringe any
|
||||
patents or other property right claims or to contest validity of any
|
||||
such claims; this section has the sole purpose of protecting the
|
||||
integrity of the free software distribution system, which is
|
||||
implemented by public license practices. Many people have made
|
||||
generous contributions to the wide range of software distributed
|
||||
through that system in reliance on consistent application of that
|
||||
system; it is up to the author/donor to decide if he or she is willing
|
||||
to distribute software through any other system and a licensee cannot
|
||||
impose that choice.
|
||||
</p>
|
||||
<p>
|
||||
This section is intended to make thoroughly clear what is believed to
|
||||
be a consequence of the rest of this License.
|
||||
</p>
|
||||
<p>
|
||||
8. If the distribution and/or use of the Program is restricted in
|
||||
certain countries either by patents or by copyrighted interfaces, the
|
||||
original copyright holder who places the Program under this License
|
||||
may add an explicit geographical distribution limitation excluding
|
||||
those countries, so that distribution is permitted only in or among
|
||||
countries not thus excluded. In such case, this License incorporates
|
||||
the limitation as if written in the body of this License.
|
||||
</p>
|
||||
<p>
|
||||
9. The Free Software Foundation may publish revised and/or new versions
|
||||
of the General Public License from time to time. Such new versions will
|
||||
be similar in spirit to the present version, but may differ in detail to
|
||||
address new problems or concerns.
|
||||
</p>
|
||||
<p>
|
||||
Each version is given a distinguishing version number. If the Program
|
||||
specifies a version number of this License which applies to it and "any
|
||||
later version", you have the option of following the terms and conditions
|
||||
either of that version or of any later version published by the Free
|
||||
Software Foundation. If the Program does not specify a version number of
|
||||
this License, you may choose any version ever published by the Free Software
|
||||
Foundation.
|
||||
</p>
|
||||
<p>
|
||||
10. If you wish to incorporate parts of the Program into other free
|
||||
programs whose distribution conditions are different, write to the author
|
||||
to ask for permission. For software which is copyrighted by the Free
|
||||
Software Foundation, write to the Free Software Foundation; we sometimes
|
||||
make exceptions for this. Our decision will be guided by the two goals
|
||||
of preserving the free status of all derivatives of our free software and
|
||||
of promoting the sharing and reuse of software generally.
|
||||
</p>
|
||||
<p>
|
||||
NO WARRANTY
|
||||
</p>
|
||||
<p>
|
||||
11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY
|
||||
FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN
|
||||
OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES
|
||||
PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED
|
||||
OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
|
||||
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS
|
||||
TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE
|
||||
PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING,
|
||||
REPAIR OR CORRECTION.
|
||||
</p>
|
||||
<p>
|
||||
12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
|
||||
WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR
|
||||
REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES,
|
||||
INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING
|
||||
OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED
|
||||
TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY
|
||||
YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER
|
||||
PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE
|
||||
POSSIBILITY OF SUCH DAMAGES.
|
||||
</p>
|
||||
<p>
|
||||
END OF TERMS AND CONDITIONS
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="id-1.37.2.5"></a>1.3. How to Apply These Terms to Your New Programs</h3></div></div></div>
|
||||
<p>
|
||||
If you develop a new program, and you want it to be of the greatest
|
||||
possible use to the public, the best way to achieve this is to make it
|
||||
free software which everyone can redistribute and change under these terms.
|
||||
</p>
|
||||
<p>
|
||||
To do so, attach the following notices to the program. It is safest
|
||||
to attach them to the start of each source file to most effectively
|
||||
convey the exclusion of warranty; and each file should have at least
|
||||
the "copyright" line and a pointer to where the full notice is found.
|
||||
</p>
|
||||
<div class="literallayout"><p><br>
|
||||
<one line to give the program's name and a brief idea of what it does.><br>
|
||||
Copyright (C) <year> <name of author><br>
|
||||
<br>
|
||||
This program is free software; you can redistribute it and/or modify<br>
|
||||
it under the terms of the GNU General Public License as published by<br>
|
||||
the Free Software Foundation; either version 2 of the License, or<br>
|
||||
(at your option) any later version.<br>
|
||||
<br>
|
||||
This program is distributed in the hope that it will be useful,<br>
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of<br>
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the<br>
|
||||
GNU General Public License for more details.<br>
|
||||
<br>
|
||||
You should have received a copy of the GNU General Public License<br>
|
||||
along with this program; if not, write to the Free Software<br>
|
||||
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA<br>
|
||||
</p></div>
|
||||
<p>
|
||||
Also add information on how to contact you by electronic and paper mail.
|
||||
</p>
|
||||
<p>
|
||||
If the program is interactive, make it output a short notice like this
|
||||
when it starts in an interactive mode:
|
||||
</p>
|
||||
<div class="literallayout"><p><br>
|
||||
Gnomovision version 69, Copyright (C) year name of author<br>
|
||||
Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'.<br>
|
||||
This is free software, and you are welcome to redistribute it<br>
|
||||
under certain conditions; type `show c' for details.<br>
|
||||
</p></div>
|
||||
<p>
|
||||
The hypothetical commands `show w' and `show c' should show the appropriate
|
||||
parts of the General Public License. Of course, the commands you use may
|
||||
be called something other than `show w' and `show c'; they could even be
|
||||
mouse-clicks or menu items--whatever suits your program.
|
||||
</p>
|
||||
<p>
|
||||
You should also get your employer (if you work as a programmer) or your
|
||||
school, if any, to sign a "copyright disclaimer" for the program, if
|
||||
necessary. Here is a sample; alter the names:
|
||||
</p>
|
||||
<div class="literallayout"><p><br>
|
||||
Yoyodyne, Inc., hereby disclaims all copyright interest in the program<br>
|
||||
`Gnomovision' (which makes passes at compilers) written by James Hacker.<br>
|
||||
<br>
|
||||
<signature of Ty Coon>, 1 April 1989<br>
|
||||
Ty Coon, President of Vice<br>
|
||||
</p></div>
|
||||
<p>
|
||||
This General Public License does not permit incorporating your program into
|
||||
proprietary programs. If your program is a subroutine library, you may
|
||||
consider it more useful to permit linking proprietary applications with the
|
||||
library. If this is what you want to do, use the GNU Library General
|
||||
Public License instead of this License.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div>
|
||||
<div><h2 class="title" style="clear: both">
|
||||
<a name="igraph-fdl"></a>2. The GNU Free Documentation License</h2></div>
|
||||
<div><p class="copyright">Copyright © 2000, 2001, 2002 Free Software Foundation, Inc.
|
||||
51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
</p></div>
|
||||
<div><div class="legalnotice">
|
||||
<a name="id-1.37.3.1.3"></a><p>
|
||||
Everyone is permitted to copy and distribute verbatim copies
|
||||
of this license document, but changing it is not allowed.
|
||||
</p>
|
||||
</div></div>
|
||||
</div></div>
|
||||
<div class="toc"><dl class="toc">
|
||||
<dt><span class="section"><a href="igraph-Licenses.html#id-1.37.3.3">2.1. 0. PREAMBLE</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Licenses.html#id-1.37.3.4">2.2. 1. APPLICABILITY AND DEFINITIONS</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Licenses.html#id-1.37.3.5">2.3. 2. VERBATIM COPYING</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Licenses.html#id-1.37.3.6">2.4. 3. COPYING IN QUANTITY</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Licenses.html#id-1.37.3.7">2.5. 4. MODIFICATIONS</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Licenses.html#id-1.37.3.8">2.6. 5. COMBINING DOCUMENTS</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Licenses.html#id-1.37.3.9">2.7. 6. COLLECTIONS OF DOCUMENTS</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Licenses.html#id-1.37.3.10">2.8. 7. AGGREGATION WITH INDEPENDENT WORKS</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Licenses.html#id-1.37.3.11">2.9. 8. TRANSLATION</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Licenses.html#id-1.37.3.12">2.10. 9. TERMINATION</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Licenses.html#id-1.37.3.13">2.11. 10. FUTURE REVISIONS OF THIS LICENSE</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Licenses.html#id-1.37.3.14">2.12. G.1.1 ADDENDUM: How to use this License for your documents</a></span></dt>
|
||||
</dl></div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="id-1.37.3.3"></a>2.1. 0. PREAMBLE</h3></div></div></div>
|
||||
<p>
|
||||
The purpose of this License is to make a manual, textbook, or other
|
||||
functional and useful document "free" in the sense of freedom: to
|
||||
assure everyone the effective freedom to copy and redistribute it,
|
||||
with or without modifying it, either commercially or noncommercially.
|
||||
Secondarily, this License preserves for the author and publisher a way
|
||||
to get credit for their work, while not being considered responsible
|
||||
for modifications made by others.
|
||||
</p>
|
||||
<p>
|
||||
This License is a kind of "copyleft", which means that derivative
|
||||
works of the document must themselves be free in the same sense. It
|
||||
complements the GNU General Public License, which is a copyleft
|
||||
license designed for free software.
|
||||
</p>
|
||||
<p>
|
||||
We have designed this License in order to use it for manuals for free
|
||||
software, because free software needs free documentation: a free
|
||||
program should come with manuals providing the same freedoms that the
|
||||
software does. But this License is not limited to software manuals;
|
||||
it can be used for any textual work, regardless of subject matter or
|
||||
whether it is published as a printed book. We recommend this License
|
||||
principally for works whose purpose is instruction or reference.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="id-1.37.3.4"></a>2.2. 1. APPLICABILITY AND DEFINITIONS</h3></div></div></div>
|
||||
<p>
|
||||
This License applies to any manual or other work, in any medium, that
|
||||
contains a notice placed by the copyright holder saying it can be
|
||||
distributed under the terms of this License. Such a notice grants a
|
||||
world-wide, royalty-free license, unlimited in duration, to use that
|
||||
work under the conditions stated herein. The "Document", below,
|
||||
refers to any such manual or work. Any member of the public is a
|
||||
licensee, and is addressed as "you". You accept the license if you
|
||||
copy, modify or distribute the work in a way requiring permission
|
||||
under copyright law.
|
||||
</p>
|
||||
<p>
|
||||
A "Modified Version" of the Document means any work containing the
|
||||
Document or a portion of it, either copied verbatim, or with
|
||||
modifications and/or translated into another language.
|
||||
</p>
|
||||
<p>
|
||||
A "Secondary Section" is a named appendix or a front-matter section of
|
||||
the Document that deals exclusively with the relationship of the
|
||||
publishers or authors of the Document to the Document's overall subject
|
||||
(or to related matters) and contains nothing that could fall directly
|
||||
within that overall subject. (Thus, if the Document is in part a
|
||||
textbook of mathematics, a Secondary Section may not explain any
|
||||
mathematics.) The relationship could be a matter of historical
|
||||
connection with the subject or with related matters, or of legal,
|
||||
commercial, philosophical, ethical or political position regarding
|
||||
them.
|
||||
</p>
|
||||
<p>
|
||||
The "Invariant Sections" are certain Secondary Sections whose titles
|
||||
are designated, as being those of Invariant Sections, in the notice
|
||||
that says that the Document is released under this License. If a
|
||||
section does not fit the above definition of Secondary then it is not
|
||||
allowed to be designated as Invariant. The Document may contain zero
|
||||
Invariant Sections. If the Document does not identify any Invariant
|
||||
Sections then there are none.
|
||||
</p>
|
||||
<p>
|
||||
The "Cover Texts" are certain short passages of text that are listed,
|
||||
as Front-Cover Texts or Back-Cover Texts, in the notice that says that
|
||||
the Document is released under this License. A Front-Cover Text may
|
||||
be at most 5 words, and a Back-Cover Text may be at most 25 words.
|
||||
</p>
|
||||
<p>
|
||||
A "Transparent" copy of the Document means a machine-readable copy,
|
||||
represented in a format whose specification is available to the
|
||||
general public, that is suitable for revising the document
|
||||
straightforwardly with generic text editors or (for images composed of
|
||||
pixels) generic paint programs or (for drawings) some widely available
|
||||
drawing editor, and that is suitable for input to text formatters or
|
||||
for automatic translation to a variety of formats suitable for input
|
||||
to text formatters. A copy made in an otherwise Transparent file
|
||||
format whose markup, or absence of markup, has been arranged to thwart
|
||||
or discourage subsequent modification by readers is not Transparent.
|
||||
An image format is not Transparent if used for any substantial amount
|
||||
of text. A copy that is not "Transparent" is called "Opaque".
|
||||
</p>
|
||||
<p>
|
||||
Examples of suitable formats for Transparent copies include plain
|
||||
ASCII without markup, Texinfo input format, LaTeX input format, SGML
|
||||
or XML using a publicly available DTD, and standard-conforming simple
|
||||
HTML, PostScript or PDF designed for human modification. Examples of
|
||||
transparent image formats include PNG, XCF and JPG. Opaque formats
|
||||
include proprietary formats that can be read and edited only by
|
||||
proprietary word processors, SGML or XML for which the DTD and/or
|
||||
processing tools are not generally available, and the
|
||||
machine-generated HTML, PostScript or PDF produced by some word
|
||||
processors for output purposes only.
|
||||
</p>
|
||||
<p>
|
||||
The "Title Page" means, for a printed book, the title page itself,
|
||||
plus such following pages as are needed to hold, legibly, the material
|
||||
this License requires to appear in the title page. For works in
|
||||
formats which do not have any title page as such, "Title Page" means
|
||||
the text near the most prominent appearance of the work's title,
|
||||
preceding the beginning of the body of the text.
|
||||
</p>
|
||||
<p>
|
||||
A section "Entitled XYZ" means a named subunit of the Document whose
|
||||
title either is precisely XYZ or contains XYZ in parentheses following
|
||||
text that translates XYZ in another language. (Here XYZ stands for a
|
||||
specific section name mentioned below, such as "Acknowledgements",
|
||||
"Dedications", "Endorsements", or "History".) To "Preserve the Title"
|
||||
of such a section when you modify the Document means that it remains a
|
||||
section "Entitled XYZ" according to this definition.
|
||||
</p>
|
||||
<p>
|
||||
The Document may include Warranty Disclaimers next to the notice which
|
||||
states that this License applies to the Document. These Warranty
|
||||
Disclaimers are considered to be included by reference in this
|
||||
License, but only as regards disclaiming warranties: any other
|
||||
implication that these Warranty Disclaimers may have is void and has
|
||||
no effect on the meaning of this License.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="id-1.37.3.5"></a>2.3. 2. VERBATIM COPYING</h3></div></div></div>
|
||||
<p>
|
||||
You may copy and distribute the Document in any medium, either
|
||||
commercially or noncommercially, provided that this License, the
|
||||
copyright notices, and the license notice saying this License applies
|
||||
to the Document are reproduced in all copies, and that you add no other
|
||||
conditions whatsoever to those of this License. You may not use
|
||||
technical measures to obstruct or control the reading or further
|
||||
copying of the copies you make or distribute. However, you may accept
|
||||
compensation in exchange for copies. If you distribute a large enough
|
||||
number of copies you must also follow the conditions in section 3.
|
||||
</p>
|
||||
<p>
|
||||
You may also lend copies, under the same conditions stated above, and
|
||||
you may publicly display copies.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="id-1.37.3.6"></a>2.4. 3. COPYING IN QUANTITY</h3></div></div></div>
|
||||
<p>
|
||||
If you publish printed copies (or copies in media that commonly have
|
||||
printed covers) of the Document, numbering more than 100, and the
|
||||
Document's license notice requires Cover Texts, you must enclose the
|
||||
copies in covers that carry, clearly and legibly, all these Cover
|
||||
Texts: Front-Cover Texts on the front cover, and Back-Cover Texts on
|
||||
the back cover. Both covers must also clearly and legibly identify
|
||||
you as the publisher of these copies. The front cover must present
|
||||
the full title with all words of the title equally prominent and
|
||||
visible. You may add other material on the covers in addition.
|
||||
Copying with changes limited to the covers, as long as they preserve
|
||||
the title of the Document and satisfy these conditions, can be treated
|
||||
as verbatim copying in other respects.
|
||||
</p>
|
||||
<p>
|
||||
If the required texts for either cover are too voluminous to fit
|
||||
legibly, you should put the first ones listed (as many as fit
|
||||
reasonably) on the actual cover, and continue the rest onto adjacent
|
||||
pages.
|
||||
</p>
|
||||
<p>
|
||||
If you publish or distribute Opaque copies of the Document numbering
|
||||
more than 100, you must either include a machine-readable Transparent
|
||||
copy along with each Opaque copy, or state in or with each Opaque copy
|
||||
a computer-network location from which the general network-using
|
||||
public has access to download using public-standard network protocols
|
||||
a complete Transparent copy of the Document, free of added material.
|
||||
If you use the latter option, you must take reasonably prudent steps,
|
||||
when you begin distribution of Opaque copies in quantity, to ensure
|
||||
that this Transparent copy will remain thus accessible at the stated
|
||||
location until at least one year after the last time you distribute an
|
||||
Opaque copy (directly or through your agents or retailers) of that
|
||||
edition to the public.
|
||||
</p>
|
||||
<p>
|
||||
It is requested, but not required, that you contact the authors of the
|
||||
Document well before redistributing any large number of copies, to give
|
||||
them a chance to provide you with an updated version of the Document.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="id-1.37.3.7"></a>2.5. 4. MODIFICATIONS</h3></div></div></div>
|
||||
<p>
|
||||
You may copy and distribute a Modified Version of the Document under
|
||||
the conditions of sections 2 and 3 above, provided that you release
|
||||
the Modified Version under precisely this License, with the Modified
|
||||
Version filling the role of the Document, thus licensing distribution
|
||||
and modification of the Modified Version to whoever possesses a copy
|
||||
of it. In addition, you must do these things in the Modified Version:
|
||||
</p>
|
||||
<p>
|
||||
</p>
|
||||
<div class="orderedlist"><ol class="orderedlist" type="A">
|
||||
<li class="listitem"><p>
|
||||
Use in the Title Page (and on the covers, if any) a title distinct
|
||||
from that of the Document, and from those of previous versions
|
||||
(which should, if there were any, be listed in the History section
|
||||
of the Document). You may use the same title as a previous version
|
||||
if the original publisher of that version gives permission.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
List on the Title Page, as authors, one or more persons or entities
|
||||
responsible for authorship of the modifications in the Modified
|
||||
Version, together with at least five of the principal authors of the
|
||||
Document (all of its principal authors, if it has fewer than five),
|
||||
unless they release you from this requirement.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
State on the Title page the name of the publisher of the
|
||||
Modified Version, as the publisher.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
Preserve all the copyright notices of the Document.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
Add an appropriate copyright notice for your modifications
|
||||
adjacent to the other copyright notices.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
Include, immediately after the copyright notices, a license notice
|
||||
giving the public permission to use the Modified Version under the
|
||||
terms of this License, in the form shown in the Addendum below.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
Preserve in that license notice the full lists of Invariant Sections
|
||||
and required Cover Texts given in the Document's license notice.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
Include an unaltered copy of this License.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
Preserve the section Entitled "History", Preserve its Title, and add
|
||||
to it an item stating at least the title, year, new authors, and
|
||||
publisher of the Modified Version as given on the Title Page. If
|
||||
there is no section Entitled "History" in the Document, create one
|
||||
stating the title, year, authors, and publisher of the Document as
|
||||
given on its Title Page, then add an item describing the Modified
|
||||
Version as stated in the previous sentence.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
Preserve the network location, if any, given in the Document for
|
||||
public access to a Transparent copy of the Document, and likewise
|
||||
the network locations given in the Document for previous versions
|
||||
it was based on. These may be placed in the "History" section.
|
||||
You may omit a network location for a work that was published at
|
||||
least four years before the Document itself, or if the original
|
||||
publisher of the version it refers to gives permission.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
For any section Entitled "Acknowledgements" or "Dedications",
|
||||
Preserve the Title of the section, and preserve in the section all
|
||||
the substance and tone of each of the contributor acknowledgements
|
||||
and/or dedications given therein.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
Preserve all the Invariant Sections of the Document,
|
||||
unaltered in their text and in their titles. Section numbers
|
||||
or the equivalent are not considered part of the section titles.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
Delete any section Entitled "Endorsements". Such a section
|
||||
may not be included in the Modified Version.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
Do not retitle any existing section to be Entitled "Endorsements"
|
||||
or to conflict in title with any Invariant Section.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
Preserve any Warranty Disclaimers.
|
||||
</p></li>
|
||||
</ol></div>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
If the Modified Version includes new front-matter sections or
|
||||
appendices that qualify as Secondary Sections and contain no material
|
||||
copied from the Document, you may at your option designate some or all
|
||||
of these sections as invariant. To do this, add their titles to the
|
||||
list of Invariant Sections in the Modified Version's license notice.
|
||||
These titles must be distinct from any other section titles.
|
||||
</p>
|
||||
<p>
|
||||
You may add a section Entitled "Endorsements", provided it contains
|
||||
nothing but endorsements of your Modified Version by various
|
||||
parties--for example, statements of peer review or that the text has
|
||||
been approved by an organization as the authoritative definition of a
|
||||
standard.
|
||||
</p>
|
||||
<p>
|
||||
You may add a passage of up to five words as a Front-Cover Text, and a
|
||||
passage of up to 25 words as a Back-Cover Text, to the end of the list
|
||||
of Cover Texts in the Modified Version. Only one passage of
|
||||
Front-Cover Text and one of Back-Cover Text may be added by (or
|
||||
through arrangements made by) any one entity. If the Document already
|
||||
includes a cover text for the same cover, previously added by you or
|
||||
by arrangement made by the same entity you are acting on behalf of,
|
||||
you may not add another; but you may replace the old one, on explicit
|
||||
permission from the previous publisher that added the old one.
|
||||
</p>
|
||||
<p>
|
||||
The author(s) and publisher(s) of the Document do not by this License
|
||||
give permission to use their names for publicity for or to assert or
|
||||
imply endorsement of any Modified Version.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="id-1.37.3.8"></a>2.6. 5. COMBINING DOCUMENTS</h3></div></div></div>
|
||||
<p>
|
||||
You may combine the Document with other documents released under this
|
||||
License, under the terms defined in section 4 above for modified
|
||||
versions, provided that you include in the combination all of the
|
||||
Invariant Sections of all of the original documents, unmodified, and
|
||||
list them all as Invariant Sections of your combined work in its
|
||||
license notice, and that you preserve all their Warranty Disclaimers.
|
||||
</p>
|
||||
<p>
|
||||
The combined work need only contain one copy of this License, and
|
||||
multiple identical Invariant Sections may be replaced with a single
|
||||
copy. If there are multiple Invariant Sections with the same name but
|
||||
different contents, make the title of each such section unique by
|
||||
adding at the end of it, in parentheses, the name of the original
|
||||
author or publisher of that section if known, or else a unique number.
|
||||
Make the same adjustment to the section titles in the list of
|
||||
Invariant Sections in the license notice of the combined work.
|
||||
</p>
|
||||
<p>
|
||||
In the combination, you must combine any sections Entitled "History"
|
||||
in the various original documents, forming one section Entitled
|
||||
"History"; likewise combine any sections Entitled "Acknowledgements",
|
||||
and any sections Entitled "Dedications". You must delete all sections
|
||||
Entitled "Endorsements".
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="id-1.37.3.9"></a>2.7. 6. COLLECTIONS OF DOCUMENTS</h3></div></div></div>
|
||||
<p>
|
||||
You may make a collection consisting of the Document and other documents
|
||||
released under this License, and replace the individual copies of this
|
||||
License in the various documents with a single copy that is included in
|
||||
the collection, provided that you follow the rules of this License for
|
||||
verbatim copying of each of the documents in all other respects.
|
||||
</p>
|
||||
<p>
|
||||
You may extract a single document from such a collection, and distribute
|
||||
it individually under this License, provided you insert a copy of this
|
||||
License into the extracted document, and follow this License in all
|
||||
other respects regarding verbatim copying of that document.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="id-1.37.3.10"></a>2.8. 7. AGGREGATION WITH INDEPENDENT WORKS</h3></div></div></div>
|
||||
<p>
|
||||
A compilation of the Document or its derivatives with other separate
|
||||
and independent documents or works, in or on a volume of a storage or
|
||||
distribution medium, is called an "aggregate" if the copyright
|
||||
resulting from the compilation is not used to limit the legal rights
|
||||
of the compilation's users beyond what the individual works permit.
|
||||
When the Document is included in an aggregate, this License does not
|
||||
apply to the other works in the aggregate which are not themselves
|
||||
derivative works of the Document.
|
||||
</p>
|
||||
<p>
|
||||
If the Cover Text requirement of section 3 is applicable to these
|
||||
copies of the Document, then if the Document is less than one half of
|
||||
the entire aggregate, the Document's Cover Texts may be placed on
|
||||
covers that bracket the Document within the aggregate, or the
|
||||
electronic equivalent of covers if the Document is in electronic form.
|
||||
Otherwise they must appear on printed covers that bracket the whole
|
||||
aggregate.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="id-1.37.3.11"></a>2.9. 8. TRANSLATION</h3></div></div></div>
|
||||
<p>
|
||||
Translation is considered a kind of modification, so you may
|
||||
distribute translations of the Document under the terms of section 4.
|
||||
Replacing Invariant Sections with translations requires special
|
||||
permission from their copyright holders, but you may include
|
||||
translations of some or all Invariant Sections in addition to the
|
||||
original versions of these Invariant Sections. You may include a
|
||||
translation of this License, and all the license notices in the
|
||||
Document, and any Warranty Disclaimers, provided that you also include
|
||||
the original English version of this License and the original versions
|
||||
of those notices and disclaimers. In case of a disagreement between
|
||||
the translation and the original version of this License or a notice
|
||||
or disclaimer, the original version will prevail.
|
||||
</p>
|
||||
<p>
|
||||
If a section in the Document is Entitled "Acknowledgements",
|
||||
"Dedications", or "History", the requirement (section 4) to Preserve
|
||||
its Title (section 1) will typically require changing the actual
|
||||
title.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="id-1.37.3.12"></a>2.10. 9. TERMINATION</h3></div></div></div>
|
||||
<p>
|
||||
You may not copy, modify, sublicense, or distribute the Document except
|
||||
as expressly provided for under this License. Any other attempt to
|
||||
copy, modify, sublicense or distribute the Document is void, and will
|
||||
automatically terminate your rights under this License. However,
|
||||
parties who have received copies, or rights, from you under this
|
||||
License will not have their licenses terminated so long as such
|
||||
parties remain in full compliance.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="id-1.37.3.13"></a>2.11. 10. FUTURE REVISIONS OF THIS LICENSE</h3></div></div></div>
|
||||
<p>
|
||||
The Free Software Foundation may publish new, revised versions
|
||||
of the GNU Free Documentation License from time to time. Such new
|
||||
versions will be similar in spirit to the present version, but may
|
||||
differ in detail to address new problems or concerns. See
|
||||
http://www.gnu.org/copyleft/.
|
||||
</p>
|
||||
<p>
|
||||
Each version of the License is given a distinguishing version number.
|
||||
If the Document specifies that a particular numbered version of this
|
||||
License "or any later version" applies to it, you have the option of
|
||||
following the terms and conditions either of that specified version or
|
||||
of any later version that has been published (not as a draft) by the
|
||||
Free Software Foundation. If the Document does not specify a version
|
||||
number of this License, you may choose any version ever published (not
|
||||
as a draft) by the Free Software Foundation.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="id-1.37.3.14"></a>2.12. G.1.1 ADDENDUM: How to use this License for your documents</h3></div></div></div>
|
||||
<p>
|
||||
To use this License in a document you have written, include a copy of
|
||||
the License in the document and put the following copyright and
|
||||
license notices just after the title page:
|
||||
</p>
|
||||
<div class="literallayout"><p><br>
|
||||
Copyright (c) YEAR YOUR NAME.<br>
|
||||
Permission is granted to copy, distribute and/or modify this document<br>
|
||||
under the terms of the GNU Free Documentation License, Version 1.2<br>
|
||||
or any later version published by the Free Software Foundation;<br>
|
||||
with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.<br>
|
||||
A copy of the license is included in the section entitled "GNU<br>
|
||||
Free Documentation License".<br>
|
||||
</p></div>
|
||||
<p>
|
||||
If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts,
|
||||
replace the "with...Texts." line with this:
|
||||
</p>
|
||||
<div class="literallayout"><p><br>
|
||||
with the Invariant Sections being LIST THEIR TITLES, with the<br>
|
||||
Front-Cover Texts being LIST, and with the Back-Cover Texts being LIST.<br>
|
||||
</p></div>
|
||||
<p>
|
||||
If you have Invariant Sections without Cover Texts, or some other
|
||||
combination of the three, merge those two alternatives to suit the
|
||||
situation.
|
||||
</p>
|
||||
<p>
|
||||
If your document contains nontrivial examples of program code, we
|
||||
recommend releasing these examples in parallel under your choice of
|
||||
free software license, such as the GNU General Public License,
|
||||
to permit their use in free software.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<table class="navigation-footer" width="100%" summary="Navigation footer" cellpadding="2" cellspacing="0"><tr valign="middle">
|
||||
<td align="left"><a accesskey="p" href="igraph-Glossary.html"><b>← Chapter 35. Glossary</b></a></td>
|
||||
<td align="right"><a accesskey="n" href="ix01.html"><b>Index →</b></a></td>
|
||||
</tr></table>
|
||||
</body>
|
||||
</html>
|
||||
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|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
|
||||
<title>Chapter 6. Memory (de)allocation</title>
|
||||
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot">
|
||||
<link rel="home" href="index.html" title="igraph Reference Manual">
|
||||
<link rel="up" href="index.html" title="igraph Reference Manual">
|
||||
<link rel="prev" href="igraph-Error.html" title="Chapter 5. Error handling">
|
||||
<link rel="next" href="igraph-Data-structures.html" title="Chapter 7. Data structure library: vector, matrix, other data types">
|
||||
<script type="text/javascript" src="toggle.js"></script><link rel="stylesheet" href="style.css" type="text/css">
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||||
<link rel="stylesheet" href="https://stackpath.bootstrapcdn.com/font-awesome/4.7.0/css/font-awesome.min.css" type="text/css">
|
||||
<link rel="chapter" href="igraph-Introduction.html" title="Chapter 1. Introduction">
|
||||
<link rel="chapter" href="igraph-Installation.html" title="Chapter 2. Installation">
|
||||
<link rel="chapter" href="igraph-Tutorial.html" title="Chapter 3. Tutorial">
|
||||
<link rel="chapter" href="igraph-Basic.html" title="Chapter 4. Basic data types and interface">
|
||||
<link rel="chapter" href="igraph-Error.html" title="Chapter 5. Error handling">
|
||||
<link rel="chapter" href="igraph-Memory.html" title="Chapter 6. Memory (de)allocation">
|
||||
<link rel="chapter" href="igraph-Data-structures.html" title="Chapter 7. Data structure library: vector, matrix, other data types">
|
||||
<link rel="chapter" href="igraph-Random.html" title="Chapter 8. Random numbers">
|
||||
<link rel="chapter" href="igraph-Iterators.html" title="Chapter 9. Vertex and edge selectors and sequences, iterators">
|
||||
<link rel="chapter" href="igraph-Attributes.html" title="Chapter 10. Graph, vertex and edge attributes">
|
||||
<link rel="chapter" href="igraph-Generators.html" title="Chapter 11. Deterministic graph generators">
|
||||
<link rel="chapter" href="igraph-Games.html" title='Chapter 12. Stochastic graph generators ("games")'>
|
||||
<link rel="chapter" href="igraph-Bipartite.html" title="Chapter 13. Bipartite, i.e. two-mode graphs">
|
||||
<link rel="chapter" href="igraph-Spatial.html" title="Chapter 14. Spatial graphs">
|
||||
<link rel="chapter" href="igraph-Operators.html" title="Chapter 15. Graph operators">
|
||||
<link rel="chapter" href="igraph-Visitors.html" title="Chapter 16. Graph visitors">
|
||||
<link rel="chapter" href="igraph-Structural.html" title="Chapter 17. Structural properties of graphs">
|
||||
<link rel="chapter" href="igraph-Cycles.html" title="Chapter 18. Graph cycles">
|
||||
<link rel="chapter" href="igraph-Cliques.html" title="Chapter 19. Cliques and independent vertex sets">
|
||||
<link rel="chapter" href="igraph-Motifs.html" title="Chapter 20. Graph motifs, dyad census and triad census">
|
||||
<link rel="chapter" href="igraph-Isomorphism.html" title="Chapter 21. Graph isomorphism">
|
||||
<link rel="chapter" href="igraph-Coloring.html" title="Chapter 22. Graph coloring">
|
||||
<link rel="chapter" href="igraph-Flows.html" title="Chapter 23. Maximum flows, minimum cuts and related measures">
|
||||
<link rel="chapter" href="igraph-Separators.html" title="Chapter 24. Vertex separators">
|
||||
<link rel="chapter" href="igraph-Community.html" title="Chapter 25. Detecting community structure">
|
||||
<link rel="chapter" href="igraph-Graphlets.html" title="Chapter 26. Graphlets">
|
||||
<link rel="chapter" href="igraph-HRG.html" title="Chapter 27. Hierarchical random graphs">
|
||||
<link rel="chapter" href="igraph-Embedding.html" title="Chapter 28. Embedding of graphs">
|
||||
<link rel="chapter" href="igraph-Layout.html" title="Chapter 29. Generating layouts for graph drawing">
|
||||
<link rel="chapter" href="igraph-Processes.html" title="Chapter 30. Processes on graphs">
|
||||
<link rel="chapter" href="igraph-Foreign.html" title="Chapter 31. Reading and writing graphs from and to files">
|
||||
<link rel="chapter" href="igraph-Linalg.html" title="Chapter 32. Using BLAS, LAPACK and ARPACK for igraph matrices and graphs">
|
||||
<link rel="chapter" href="igraph-Nongraph.html" title="Chapter 33. Non-graph related functions">
|
||||
<link rel="chapter" href="igraph-Advanced.html" title="Chapter 34. Advanced igraph programming">
|
||||
<link rel="chapter" href="igraph-Glossary.html" title="Chapter 35. Glossary">
|
||||
<link rel="chapter" href="igraph-Licenses.html" title="Chapter 36. Licenses for igraph and this manual">
|
||||
<link rel="index" href="ix01.html" title="Index">
|
||||
</head>
|
||||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
||||
<div class="navigation-header mb-4" width="100%" summary="Navigation header"><div class="btn-group">
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<a accesskey="p" class="btn btn-light" href="igraph-Error.html"><i class="fa fa-chevron-left"></i>
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Previous
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</a><a accesskey="h" class="btn btn-light" href="index.html"><i class="fa fa-home"></i>
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Home
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</a><a accesskey="n" class="btn btn-light" href="igraph-Data-structures.html"><i class="fa fa-chevron-right"></i>
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Next
|
||||
</a>
|
||||
</div></div>
|
||||
<div class="chapter">
|
||||
<div class="titlepage"><div><div><h1 class="title">
|
||||
<a name="igraph-Memory"></a>Chapter 6. Memory (de)allocation</h1></div></div></div>
|
||||
<div class="toc"><dl class="toc">
|
||||
<dt><span class="section"><a href="igraph-Memory.html#about-alloc-funcs">1. About allocation functions</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Memory.html#available-alloc-funcs">2. Available allocation functions</a></span></dt>
|
||||
</dl></div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="about-alloc-funcs"></a>1. About allocation functions</h2></div></div></div>
|
||||
<p>
|
||||
Some igraph functions return a pointer vector (<span class="type">igraph_vector_ptr_t</span>)
|
||||
containing pointers to other igraph or other data types. These data
|
||||
types are dynamically allocated and have to be deallocated
|
||||
manually when the user does not need them any more. <span class="type">igraph_vector_ptr_t</span>
|
||||
has functions to deallocate the contained pointers on its own, but in this
|
||||
case it has to be ensured that these pointers are allocated by a function
|
||||
that corresponds to the deallocator function that igraph uses.
|
||||
</p>
|
||||
<p>
|
||||
To this end, igraph exports the memory allocation functions that are used
|
||||
internally so the user of the library can ensure that the proper functions
|
||||
are used when pointers are moved between the code written by the user and
|
||||
the code of the igraph library.
|
||||
</p>
|
||||
<p>
|
||||
Additionally, the memory allocator functions used by igraph work around the
|
||||
quirks of classical <code class="constant">malloc</code>(), <code class="constant">realloc</code>() and <code class="constant">calloc</code>() implementations
|
||||
where the behaviour of allocating zero bytes is undefined. igraph allocator
|
||||
functions will always allocate at least one byte.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="available-alloc-funcs"></a>2. Available allocation functions</h2></div></div></div>
|
||||
<div class="toc"><dl class="toc">
|
||||
<dt><span class="section"><a href="igraph-Memory.html#igraph_malloc">2.1. <code class="function">igraph_malloc</code> — Allocates memory that can be safely deallocated by igraph functions.</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Memory.html#igraph_calloc">2.2. <code class="function">igraph_calloc</code> — Allocates memory that can be safely deallocated by igraph functions.</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Memory.html#igraph_realloc">2.3. <code class="function">igraph_realloc</code> — Reallocate memory that can be safely deallocated by igraph functions.</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Memory.html#igraph_free">2.4. <code class="function">igraph_free</code> — Deallocates memory that was allocated by igraph functions.</a></span></dt>
|
||||
</dl></div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="igraph_malloc"></a>2.1. <code class="function">igraph_malloc</code> — Allocates memory that can be safely deallocated by igraph functions.</h3></div></div></div>
|
||||
<a class="indexterm" name="id-1.7.3.2.2"></a><p>
|
||||
</p>
|
||||
<div class="informalexample"><pre class="programlisting">
|
||||
void *igraph_malloc(size_t size);
|
||||
</pre></div>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
|
||||
|
||||
|
||||
This function behaves like <code class="constant">malloc</code>(), but it ensures that at least one
|
||||
byte is allocated even when the caller asks for zero bytes.
|
||||
|
||||
</p>
|
||||
<p><b>Arguments: </b>
|
||||
</p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>size</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Number of bytes to be allocated. Zero is treated as one byte.
|
||||
</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
</p>
|
||||
<p><b>Returns: </b></p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||||
<td><p>
|
||||
Pointer to the piece of allocated memory; <code class="constant">NULL</code> if the allocation
|
||||
failed.
|
||||
</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
</p>
|
||||
<p><b>See also: </b></p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||||
<td><p>
|
||||
<a class="link" href="igraph-Memory.html#igraph_calloc" title="2.2. igraph_calloc — Allocates memory that can be safely deallocated by igraph functions."><code class="function">igraph_calloc()</code></a>, <a class="link" href="igraph-Memory.html#igraph_realloc" title="2.3. igraph_realloc — Reallocate memory that can be safely deallocated by igraph functions."><code class="function">igraph_realloc()</code></a>, <a class="link" href="igraph-Memory.html#igraph_free" title="2.4. igraph_free — Deallocates memory that was allocated by igraph functions."><code class="function">igraph_free()</code></a>
|
||||
</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="igraph_calloc"></a>2.2. <code class="function">igraph_calloc</code> — Allocates memory that can be safely deallocated by igraph functions.</h3></div></div></div>
|
||||
<a class="indexterm" name="id-1.7.3.3.2"></a><p>
|
||||
</p>
|
||||
<div class="informalexample"><pre class="programlisting">
|
||||
void *igraph_calloc(size_t count, size_t size);
|
||||
</pre></div>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
|
||||
|
||||
|
||||
This function behaves like <code class="constant">calloc</code>(), but it ensures that at least one
|
||||
byte is allocated even when the caller asks for zero bytes.
|
||||
|
||||
</p>
|
||||
<p><b>Arguments: </b>
|
||||
</p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>count</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Number of items to be allocated.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>size</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Size of a single item to be allocated.
|
||||
</p></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
</p>
|
||||
<p><b>Returns: </b></p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||||
<td><p>
|
||||
Pointer to the piece of allocated memory; <code class="constant">NULL</code> if the allocation
|
||||
failed.
|
||||
</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
</p>
|
||||
<p><b>See also: </b></p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||||
<td><p>
|
||||
<a class="link" href="igraph-Memory.html#igraph_malloc" title="2.1. igraph_malloc — Allocates memory that can be safely deallocated by igraph functions."><code class="function">igraph_malloc()</code></a>, <a class="link" href="igraph-Memory.html#igraph_realloc" title="2.3. igraph_realloc — Reallocate memory that can be safely deallocated by igraph functions."><code class="function">igraph_realloc()</code></a>, <a class="link" href="igraph-Memory.html#igraph_free" title="2.4. igraph_free — Deallocates memory that was allocated by igraph functions."><code class="function">igraph_free()</code></a>
|
||||
</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="igraph_realloc"></a>2.3. <code class="function">igraph_realloc</code> — Reallocate memory that can be safely deallocated by igraph functions.</h3></div></div></div>
|
||||
<a class="indexterm" name="id-1.7.3.4.2"></a><p>
|
||||
</p>
|
||||
<div class="informalexample"><pre class="programlisting">
|
||||
void *igraph_realloc(void *ptr, size_t size);
|
||||
</pre></div>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
|
||||
|
||||
|
||||
This function behaves like <code class="constant">realloc</code>(), but it ensures that at least one
|
||||
byte is allocated even when the caller asks for zero bytes.
|
||||
|
||||
</p>
|
||||
<p><b>Arguments: </b>
|
||||
</p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>ptr</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The pointer to reallocate.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>size</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Number of bytes to be allocated.
|
||||
</p></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
</p>
|
||||
<p><b>Returns: </b></p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||||
<td><p>
|
||||
Pointer to the piece of allocated memory; <code class="constant">NULL</code> if the allocation
|
||||
failed.
|
||||
</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
</p>
|
||||
<p><b>See also: </b></p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||||
<td><p>
|
||||
<a class="link" href="igraph-Memory.html#igraph_free" title="2.4. igraph_free — Deallocates memory that was allocated by igraph functions."><code class="function">igraph_free()</code></a>, <a class="link" href="igraph-Memory.html#igraph_malloc" title="2.1. igraph_malloc — Allocates memory that can be safely deallocated by igraph functions."><code class="function">igraph_malloc()</code></a>
|
||||
</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="igraph_free"></a>2.4. <code class="function">igraph_free</code> — Deallocates memory that was allocated by igraph functions.</h3></div></div></div>
|
||||
<a class="indexterm" name="id-1.7.3.5.2"></a><p>
|
||||
</p>
|
||||
<div class="informalexample"><pre class="programlisting">
|
||||
void igraph_free(void *ptr);
|
||||
</pre></div>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
|
||||
|
||||
|
||||
This function exposes the <code class="constant">free</code>() function used internally by igraph.
|
||||
|
||||
</p>
|
||||
<p><b>Arguments: </b>
|
||||
</p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>ptr</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Pointer to the piece of memory to be deallocated.</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
|
||||
Time complexity: platform dependent, ideally it should be O(1).
|
||||
|
||||
</p>
|
||||
<p><b>See also: </b></p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||||
<td><p>
|
||||
<a class="link" href="igraph-Memory.html#igraph_calloc" title="2.2. igraph_calloc — Allocates memory that can be safely deallocated by igraph functions."><code class="function">igraph_calloc()</code></a>, <a class="link" href="igraph-Memory.html#igraph_malloc" title="2.1. igraph_malloc — Allocates memory that can be safely deallocated by igraph functions."><code class="function">igraph_malloc()</code></a>, <a class="link" href="igraph-Memory.html#igraph_realloc" title="2.3. igraph_realloc — Reallocate memory that can be safely deallocated by igraph functions."><code class="function">igraph_realloc()</code></a>
|
||||
</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<table class="navigation-footer" width="100%" summary="Navigation footer" cellpadding="2" cellspacing="0"><tr valign="middle">
|
||||
<td align="left"><a accesskey="p" href="igraph-Error.html"><b>← Chapter 5. Error handling</b></a></td>
|
||||
<td align="right"><a accesskey="n" href="igraph-Data-structures.html"><b>Chapter 7. Data structure library: vector, matrix, other data types →</b></a></td>
|
||||
</tr></table>
|
||||
</body>
|
||||
</html>
|
||||
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|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
|
||||
<title>Chapter 30. Processes on graphs</title>
|
||||
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot">
|
||||
<link rel="home" href="index.html" title="igraph Reference Manual">
|
||||
<link rel="up" href="index.html" title="igraph Reference Manual">
|
||||
<link rel="prev" href="igraph-Layout.html" title="Chapter 29. Generating layouts for graph drawing">
|
||||
<link rel="next" href="igraph-Foreign.html" title="Chapter 31. Reading and writing graphs from and to files">
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<script type="text/javascript" src="toggle.js"></script><link rel="stylesheet" href="style.css" type="text/css">
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<link rel="stylesheet" href="https://stackpath.bootstrapcdn.com/font-awesome/4.7.0/css/font-awesome.min.css" type="text/css">
|
||||
<link rel="chapter" href="igraph-Introduction.html" title="Chapter 1. Introduction">
|
||||
<link rel="chapter" href="igraph-Installation.html" title="Chapter 2. Installation">
|
||||
<link rel="chapter" href="igraph-Tutorial.html" title="Chapter 3. Tutorial">
|
||||
<link rel="chapter" href="igraph-Basic.html" title="Chapter 4. Basic data types and interface">
|
||||
<link rel="chapter" href="igraph-Error.html" title="Chapter 5. Error handling">
|
||||
<link rel="chapter" href="igraph-Memory.html" title="Chapter 6. Memory (de)allocation">
|
||||
<link rel="chapter" href="igraph-Data-structures.html" title="Chapter 7. Data structure library: vector, matrix, other data types">
|
||||
<link rel="chapter" href="igraph-Random.html" title="Chapter 8. Random numbers">
|
||||
<link rel="chapter" href="igraph-Iterators.html" title="Chapter 9. Vertex and edge selectors and sequences, iterators">
|
||||
<link rel="chapter" href="igraph-Attributes.html" title="Chapter 10. Graph, vertex and edge attributes">
|
||||
<link rel="chapter" href="igraph-Generators.html" title="Chapter 11. Deterministic graph generators">
|
||||
<link rel="chapter" href="igraph-Games.html" title='Chapter 12. Stochastic graph generators ("games")'>
|
||||
<link rel="chapter" href="igraph-Bipartite.html" title="Chapter 13. Bipartite, i.e. two-mode graphs">
|
||||
<link rel="chapter" href="igraph-Spatial.html" title="Chapter 14. Spatial graphs">
|
||||
<link rel="chapter" href="igraph-Operators.html" title="Chapter 15. Graph operators">
|
||||
<link rel="chapter" href="igraph-Visitors.html" title="Chapter 16. Graph visitors">
|
||||
<link rel="chapter" href="igraph-Structural.html" title="Chapter 17. Structural properties of graphs">
|
||||
<link rel="chapter" href="igraph-Cycles.html" title="Chapter 18. Graph cycles">
|
||||
<link rel="chapter" href="igraph-Cliques.html" title="Chapter 19. Cliques and independent vertex sets">
|
||||
<link rel="chapter" href="igraph-Motifs.html" title="Chapter 20. Graph motifs, dyad census and triad census">
|
||||
<link rel="chapter" href="igraph-Isomorphism.html" title="Chapter 21. Graph isomorphism">
|
||||
<link rel="chapter" href="igraph-Coloring.html" title="Chapter 22. Graph coloring">
|
||||
<link rel="chapter" href="igraph-Flows.html" title="Chapter 23. Maximum flows, minimum cuts and related measures">
|
||||
<link rel="chapter" href="igraph-Separators.html" title="Chapter 24. Vertex separators">
|
||||
<link rel="chapter" href="igraph-Community.html" title="Chapter 25. Detecting community structure">
|
||||
<link rel="chapter" href="igraph-Graphlets.html" title="Chapter 26. Graphlets">
|
||||
<link rel="chapter" href="igraph-HRG.html" title="Chapter 27. Hierarchical random graphs">
|
||||
<link rel="chapter" href="igraph-Embedding.html" title="Chapter 28. Embedding of graphs">
|
||||
<link rel="chapter" href="igraph-Layout.html" title="Chapter 29. Generating layouts for graph drawing">
|
||||
<link rel="chapter" href="igraph-Processes.html" title="Chapter 30. Processes on graphs">
|
||||
<link rel="chapter" href="igraph-Foreign.html" title="Chapter 31. Reading and writing graphs from and to files">
|
||||
<link rel="chapter" href="igraph-Linalg.html" title="Chapter 32. Using BLAS, LAPACK and ARPACK for igraph matrices and graphs">
|
||||
<link rel="chapter" href="igraph-Nongraph.html" title="Chapter 33. Non-graph related functions">
|
||||
<link rel="chapter" href="igraph-Advanced.html" title="Chapter 34. Advanced igraph programming">
|
||||
<link rel="chapter" href="igraph-Glossary.html" title="Chapter 35. Glossary">
|
||||
<link rel="chapter" href="igraph-Licenses.html" title="Chapter 36. Licenses for igraph and this manual">
|
||||
<link rel="index" href="ix01.html" title="Index">
|
||||
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||||
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<div class="chapter">
|
||||
<div class="titlepage"><div><div><h1 class="title">
|
||||
<a name="igraph-Processes"></a>Chapter 30. Processes on graphs</h1></div></div></div>
|
||||
<div class="toc"><dl class="toc"><dt><span class="section"><a href="igraph-Processes.html#epidemic-models">1. Epidemic models</a></span></dt></dl></div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="epidemic-models"></a>1. Epidemic models</h2></div></div></div>
|
||||
<div class="toc"><dl class="toc">
|
||||
<dt><span class="section"><a href="igraph-Processes.html#igraph_sir">1.1. <code class="function">igraph_sir</code> — Performs a number of SIR epidemics model runs on a graph.</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Processes.html#igraph_sir_t">1.2. <code class="function">igraph_sir_t</code> — The result of one SIR model simulation.</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Processes.html#igraph_sir_destroy">1.3. <code class="function">igraph_sir_destroy</code> — Deallocates memory associated with a SIR simulation run.</a></span></dt>
|
||||
</dl></div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="igraph_sir"></a>1.1. <code class="function">igraph_sir</code> — Performs a number of SIR epidemics model runs on a graph.</h3></div></div></div>
|
||||
<a class="indexterm" name="id-1.31.2.2.2"></a><p>
|
||||
</p>
|
||||
<div class="informalexample"><pre class="programlisting">
|
||||
igraph_error_t igraph_sir(const igraph_t *graph, igraph_real_t beta,
|
||||
igraph_real_t gamma, igraph_int_t no_sim,
|
||||
igraph_vector_ptr_t *result);
|
||||
</pre></div>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
|
||||
|
||||
|
||||
The SIR model is a simple model from epidemiology. The individuals
|
||||
of the population might be in three states: susceptible, infected
|
||||
and recovered. Recovered people are assumed to be immune to the
|
||||
disease. Susceptibles become infected with a rate that depends on
|
||||
their number of infected neighbors. Infected people become recovered
|
||||
with a constant rate. See these parameters below.
|
||||
|
||||
</p>
|
||||
<p>
|
||||
This function runs multiple simulations, all starting with a
|
||||
single uniformly randomly chosen infected individual. A simulation
|
||||
is stopped when no infected individuals are left.
|
||||
|
||||
</p>
|
||||
<p><b>Arguments: </b>
|
||||
</p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The graph to perform the model on. For directed graphs
|
||||
edge directions are ignored and a warning is given.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>beta</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The rate of infection of an individual that is
|
||||
susceptible and has a single infected neighbor.
|
||||
The infection rate of a susceptible individual with n
|
||||
infected neighbors is n times beta. Formally
|
||||
this is the rate parameter of an exponential distribution.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>gamma</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The rate of recovery of an infected individual.
|
||||
Formally, this is the rate parameter of an exponential
|
||||
distribution.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>no_sim</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The number of simulation runs to perform.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>result</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The result of the simulation is stored here,
|
||||
in a list of <a class="link" href="igraph-Processes.html#igraph_sir_t" title="1.2. igraph_sir_t — The result of one SIR model simulation."><code class="function">igraph_sir_t</code></a> objects. To deallocate
|
||||
memory, the user needs to call <a class="link" href="igraph-Processes.html#igraph_sir_destroy" title="1.3. igraph_sir_destroy — Deallocates memory associated with a SIR simulation run."><code class="function">igraph_sir_destroy</code></a> on
|
||||
each element, before destroying the pointer vector itself
|
||||
using <a class="link" href="igraph-Data-structures.html#igraph_vector_ptr_destroy_all" title="2.17.5. igraph_vector_ptr_destroy_all — Frees all the elements and destroys the pointer vector."><code class="function">igraph_vector_ptr_destroy_all()</code></a>.
|
||||
</p></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
</p>
|
||||
<p><b>Returns: </b></p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||||
<td><p>
|
||||
Error code.
|
||||
</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
Time complexity: O(no_sim * (|V| + |E| log(|V|))).
|
||||
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="igraph_sir_t"></a>1.2. <code class="function">igraph_sir_t</code> — The result of one SIR model simulation.</h3></div></div></div>
|
||||
<a class="indexterm" name="id-1.31.2.3.2"></a><p>
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
typedef struct igraph_sir_t {
|
||||
igraph_vector_t times;
|
||||
igraph_vector_int_t no_s, no_i, no_r;
|
||||
} igraph_sir_t;
|
||||
</pre>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
</p>
|
||||
<p>Data structure to store the results of one simulation
|
||||
of the SIR (susceptible-infected-recovered) model on a graph.
|
||||
|
||||
It has the following members. They are all (real or integer)
|
||||
vectors, and they are of the same length.
|
||||
|
||||
</p>
|
||||
<p><b>Values: </b></p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><p><span class="term"><code class="constant">times</code>:</span></p></td>
|
||||
<td><p>
|
||||
A vector, the times of the events are stored here.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><code class="constant">no_s</code>:</span></p></td>
|
||||
<td><p>
|
||||
An integer vector, the number of susceptibles in
|
||||
each time step is stored here.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><code class="constant">no_i</code>:</span></p></td>
|
||||
<td><p>
|
||||
An integer vector, the number of infected individuals
|
||||
at each time step, is stored here.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><code class="constant">no_r</code>:</span></p></td>
|
||||
<td><p>
|
||||
An integer vector, the number of recovered individuals
|
||||
is stored here at each time step.</p></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="igraph_sir_destroy"></a>1.3. <code class="function">igraph_sir_destroy</code> — Deallocates memory associated with a SIR simulation run.</h3></div></div></div>
|
||||
<a class="indexterm" name="id-1.31.2.4.2"></a><p>
|
||||
</p>
|
||||
<div class="informalexample"><pre class="programlisting">
|
||||
void igraph_sir_destroy(igraph_sir_t *sir);
|
||||
</pre></div>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
|
||||
|
||||
|
||||
</p>
|
||||
<p><b>Arguments: </b>
|
||||
</p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>sir</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The <a class="link" href="igraph-Processes.html#igraph_sir_t" title="1.2. igraph_sir_t — The result of one SIR model simulation."><code class="function">igraph_sir_t</code></a> object storing the simulation.</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<table class="navigation-footer" width="100%" summary="Navigation footer" cellpadding="2" cellspacing="0"><tr valign="middle">
|
||||
<td align="left"><a accesskey="p" href="igraph-Layout.html"><b>← Chapter 29. Generating layouts for graph drawing</b></a></td>
|
||||
<td align="right"><a accesskey="n" href="igraph-Foreign.html"><b>Chapter 31. Reading and writing graphs from and to files →</b></a></td>
|
||||
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|
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<html>
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|
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<link rel="prev" href="igraph-Flows.html" title="Chapter 23. Maximum flows, minimum cuts and related measures">
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<link rel="next" href="igraph-Community.html" title="Chapter 25. Detecting community structure">
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|
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<link rel="chapter" href="igraph-Installation.html" title="Chapter 2. Installation">
|
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<link rel="chapter" href="igraph-Tutorial.html" title="Chapter 3. Tutorial">
|
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<link rel="chapter" href="igraph-Basic.html" title="Chapter 4. Basic data types and interface">
|
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<link rel="chapter" href="igraph-Error.html" title="Chapter 5. Error handling">
|
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<link rel="chapter" href="igraph-Memory.html" title="Chapter 6. Memory (de)allocation">
|
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<link rel="chapter" href="igraph-Data-structures.html" title="Chapter 7. Data structure library: vector, matrix, other data types">
|
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<link rel="chapter" href="igraph-Random.html" title="Chapter 8. Random numbers">
|
||||
<link rel="chapter" href="igraph-Iterators.html" title="Chapter 9. Vertex and edge selectors and sequences, iterators">
|
||||
<link rel="chapter" href="igraph-Attributes.html" title="Chapter 10. Graph, vertex and edge attributes">
|
||||
<link rel="chapter" href="igraph-Generators.html" title="Chapter 11. Deterministic graph generators">
|
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<link rel="chapter" href="igraph-Games.html" title='Chapter 12. Stochastic graph generators ("games")'>
|
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<link rel="chapter" href="igraph-Bipartite.html" title="Chapter 13. Bipartite, i.e. two-mode graphs">
|
||||
<link rel="chapter" href="igraph-Spatial.html" title="Chapter 14. Spatial graphs">
|
||||
<link rel="chapter" href="igraph-Operators.html" title="Chapter 15. Graph operators">
|
||||
<link rel="chapter" href="igraph-Visitors.html" title="Chapter 16. Graph visitors">
|
||||
<link rel="chapter" href="igraph-Structural.html" title="Chapter 17. Structural properties of graphs">
|
||||
<link rel="chapter" href="igraph-Cycles.html" title="Chapter 18. Graph cycles">
|
||||
<link rel="chapter" href="igraph-Cliques.html" title="Chapter 19. Cliques and independent vertex sets">
|
||||
<link rel="chapter" href="igraph-Motifs.html" title="Chapter 20. Graph motifs, dyad census and triad census">
|
||||
<link rel="chapter" href="igraph-Isomorphism.html" title="Chapter 21. Graph isomorphism">
|
||||
<link rel="chapter" href="igraph-Coloring.html" title="Chapter 22. Graph coloring">
|
||||
<link rel="chapter" href="igraph-Flows.html" title="Chapter 23. Maximum flows, minimum cuts and related measures">
|
||||
<link rel="chapter" href="igraph-Separators.html" title="Chapter 24. Vertex separators">
|
||||
<link rel="chapter" href="igraph-Community.html" title="Chapter 25. Detecting community structure">
|
||||
<link rel="chapter" href="igraph-Graphlets.html" title="Chapter 26. Graphlets">
|
||||
<link rel="chapter" href="igraph-HRG.html" title="Chapter 27. Hierarchical random graphs">
|
||||
<link rel="chapter" href="igraph-Embedding.html" title="Chapter 28. Embedding of graphs">
|
||||
<link rel="chapter" href="igraph-Layout.html" title="Chapter 29. Generating layouts for graph drawing">
|
||||
<link rel="chapter" href="igraph-Processes.html" title="Chapter 30. Processes on graphs">
|
||||
<link rel="chapter" href="igraph-Foreign.html" title="Chapter 31. Reading and writing graphs from and to files">
|
||||
<link rel="chapter" href="igraph-Linalg.html" title="Chapter 32. Using BLAS, LAPACK and ARPACK for igraph matrices and graphs">
|
||||
<link rel="chapter" href="igraph-Nongraph.html" title="Chapter 33. Non-graph related functions">
|
||||
<link rel="chapter" href="igraph-Advanced.html" title="Chapter 34. Advanced igraph programming">
|
||||
<link rel="chapter" href="igraph-Glossary.html" title="Chapter 35. Glossary">
|
||||
<link rel="chapter" href="igraph-Licenses.html" title="Chapter 36. Licenses for igraph and this manual">
|
||||
<link rel="index" href="ix01.html" title="Index">
|
||||
</head>
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||||
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<a accesskey="p" class="btn btn-light" href="igraph-Flows.html"><i class="fa fa-chevron-left"></i>
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||||
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|
||||
<div class="chapter">
|
||||
<div class="titlepage"><div><div><h1 class="title">
|
||||
<a name="igraph-Separators"></a>Chapter 24. Vertex separators</h1></div></div></div>
|
||||
<div class="toc"><dl class="toc">
|
||||
<dt><span class="section"><a href="igraph-Separators.html#igraph_is_separator">1. <code class="function">igraph_is_separator</code> — Would removing this set of vertices disconnect the graph?</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Separators.html#igraph_is_minimal_separator">2. <code class="function">igraph_is_minimal_separator</code> — Decides whether a set of vertices is a minimal separator.</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Separators.html#igraph_all_minimal_st_separators">3. <code class="function">igraph_all_minimal_st_separators</code> — List all vertex sets that are minimal (s,t) separators for some s and t.</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Separators.html#igraph_minimum_size_separators">4. <code class="function">igraph_minimum_size_separators</code> — Find all minimum size separating vertex sets.</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Separators.html#igraph_even_tarjan_reduction">5. <code class="function">igraph_even_tarjan_reduction</code> — Even-Tarjan reduction of a graph.</a></span></dt>
|
||||
</dl></div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="igraph_is_separator"></a>1. <code class="function">igraph_is_separator</code> — Would removing this set of vertices disconnect the graph?</h2></div></div></div>
|
||||
<a class="indexterm" name="id-1.25.2.2"></a><p>
|
||||
</p>
|
||||
<div class="informalexample"><pre class="programlisting">
|
||||
igraph_error_t igraph_is_separator(const igraph_t *graph,
|
||||
const igraph_vs_t candidate,
|
||||
igraph_bool_t *res);
|
||||
</pre></div>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
|
||||
|
||||
|
||||
A vertex set <code class="constant">S</code> is a separator if there are vertices <code class="constant">u</code> and <code class="constant">v</code>
|
||||
in the graph such that all paths between <code class="constant">u</code> and <code class="constant">v</code> pass through
|
||||
some vertices in <code class="constant">S</code>.
|
||||
|
||||
</p>
|
||||
<p><b>Arguments: </b>
|
||||
</p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The input graph. It may be directed, but edge
|
||||
directions are ignored.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>candidate</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The candidate separator.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Pointer to a boolean variable, the result is stored here.
|
||||
</p></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
</p>
|
||||
<p><b>Returns: </b></p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||||
<td><p>
|
||||
Error code.
|
||||
</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
Time complexity: O(|V|+|E|), linear in the number vertices and edges.
|
||||
|
||||
</p>
|
||||
<div class="hideshow" onClick="toggle(this, event)">
|
||||
<div class="example">
|
||||
<a name="id-1.25.2.8.1"></a><p class="title"><b>Example 24.1. File <code class="code">examples/simple/igraph_is_separator.c</code></b></p>
|
||||
<div class="example-contents">
|
||||
<pre class="programlisting"><span class="strong"><strong>#include</strong></span> <igraph.h>
|
||||
<span class="strong"><strong>#include</strong></span> <stdio.h>
|
||||
|
||||
<span class="strong"><strong>#define</strong></span> <span class="strong"><strong>FAIL</strong></span>(msg, error) <span class="strong"><strong>do</strong></span> { <span class="strong"><strong>printf</strong></span>(msg "\n") ; <span class="strong"><strong>return</strong></span> error; } <span class="strong"><strong>while</strong></span> (0)
|
||||
|
||||
int <span class="strong"><strong>main</strong></span>(void) {
|
||||
|
||||
igraph_t graph;
|
||||
igraph_vector_int_t sep;
|
||||
igraph_bool_t result;
|
||||
|
||||
<span class="emphasis"><em>/* Initialize the library. */</em></span>
|
||||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_setup" title="4.1. igraph_setup — Initializes the igraph library.">igraph_setup</a></strong></span>();
|
||||
|
||||
<span class="emphasis"><em>/* Simple star graph, remove the center */</em></span>
|
||||
<span class="strong"><strong><a class="link" href="igraph-Generators.html#igraph_star" title="4.1. igraph_star — Creates a star graph, every vertex connects only to the center.">igraph_star</a></strong></span>(&graph, 10, IGRAPH_STAR_UNDIRECTED, 0);
|
||||
<span class="strong"><strong><a class="link" href="igraph-Separators.html#igraph_is_separator" title="1. igraph_is_separator — Would removing this set of vertices disconnect the graph?">igraph_is_separator</a></strong></span>(&graph, <span class="strong"><strong><a class="link" href="igraph-Iterators.html#igraph_vss_1" title="4.3. igraph_vss_1 — Vertex set with a single vertex (immediate version).">igraph_vss_1</a></strong></span>(0), &result);
|
||||
<span class="strong"><strong>if</strong></span> (!result) {
|
||||
<span class="strong"><strong>FAIL</strong></span>("Center of star graph failed.", 1);
|
||||
}
|
||||
|
||||
<span class="emphasis"><em>/* Same graph, but another vertex */</em></span>
|
||||
<span class="strong"><strong><a class="link" href="igraph-Separators.html#igraph_is_separator" title="1. igraph_is_separator — Would removing this set of vertices disconnect the graph?">igraph_is_separator</a></strong></span>(&graph, <span class="strong"><strong><a class="link" href="igraph-Iterators.html#igraph_vss_1" title="4.3. igraph_vss_1 — Vertex set with a single vertex (immediate version).">igraph_vss_1</a></strong></span>(6), &result);
|
||||
<span class="strong"><strong>if</strong></span> (result) {
|
||||
<span class="strong"><strong>FAIL</strong></span>("Non-center of star graph failed.", 2);
|
||||
}
|
||||
|
||||
<span class="emphasis"><em>/* Same graph, all vertices but the center */</em></span>
|
||||
<span class="strong"><strong><a class="link" href="igraph-Separators.html#igraph_is_separator" title="1. igraph_is_separator — Would removing this set of vertices disconnect the graph?">igraph_is_separator</a></strong></span>(&graph, <span class="strong"><strong><a class="link" href="igraph-Iterators.html#igraph_vss_range" title="4.5. igraph_vss_range — An interval of vertices (immediate version).">igraph_vss_range</a></strong></span>(1, 10), &result);
|
||||
<span class="strong"><strong>if</strong></span> (result) {
|
||||
<span class="strong"><strong>FAIL</strong></span>("All non-central vertices of star graph failed.", 5);
|
||||
}
|
||||
|
||||
<span class="emphasis"><em>/* Same graph, all vertices */</em></span>
|
||||
<span class="strong"><strong><a class="link" href="igraph-Separators.html#igraph_is_separator" title="1. igraph_is_separator — Would removing this set of vertices disconnect the graph?">igraph_is_separator</a></strong></span>(&graph, <span class="strong"><strong><a class="link" href="igraph-Iterators.html#igraph_vss_range" title="4.5. igraph_vss_range — An interval of vertices (immediate version).">igraph_vss_range</a></strong></span>(0, 10), &result);
|
||||
<span class="strong"><strong>if</strong></span> (result) {
|
||||
<span class="strong"><strong>FAIL</strong></span>("All vertices of star graph failed.", 6);
|
||||
}
|
||||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_destroy" title="5.1.4. igraph_destroy — Frees the memory allocated for a graph object.">igraph_destroy</a></strong></span>(&graph);
|
||||
|
||||
<span class="emphasis"><em>/* Karate club */</em></span>
|
||||
<span class="strong"><strong><a class="link" href="igraph-Generators.html#igraph_famous" title="8.1. igraph_famous — Create a famous graph by simply providing its name.">igraph_famous</a></strong></span>(&graph, "zachary");
|
||||
<span class="strong"><strong>igraph_vector_int_init</strong></span>(&sep, 0);
|
||||
<span class="strong"><strong>igraph_vector_int_push_back</strong></span>(&sep, 32);
|
||||
<span class="strong"><strong>igraph_vector_int_push_back</strong></span>(&sep, 33);
|
||||
<span class="strong"><strong><a class="link" href="igraph-Separators.html#igraph_is_separator" title="1. igraph_is_separator — Would removing this set of vertices disconnect the graph?">igraph_is_separator</a></strong></span>(&graph, <span class="strong"><strong><a class="link" href="igraph-Iterators.html#igraph_vss_vector" title="4.4. igraph_vss_vector — Vertex set based on a vector (immediate version).">igraph_vss_vector</a></strong></span>(&sep), &result);
|
||||
<span class="strong"><strong>if</strong></span> (!result) {
|
||||
<span class="strong"><strong>FAIL</strong></span>("Karate network (32,33) failed", 3);
|
||||
}
|
||||
|
||||
<span class="strong"><strong>igraph_vector_int_resize</strong></span>(&sep, 5);
|
||||
<span class="strong"><strong><a class="link" href="igraph-Data-structures.html#VECTOR" title="2.4.1. VECTOR — Accessing an element of a vector.">VECTOR</a></strong></span>(sep)[0] = 8;
|
||||
<span class="strong"><strong><a class="link" href="igraph-Data-structures.html#VECTOR" title="2.4.1. VECTOR — Accessing an element of a vector.">VECTOR</a></strong></span>(sep)[1] = 9;
|
||||
<span class="strong"><strong><a class="link" href="igraph-Data-structures.html#VECTOR" title="2.4.1. VECTOR — Accessing an element of a vector.">VECTOR</a></strong></span>(sep)[2] = 19;
|
||||
<span class="strong"><strong><a class="link" href="igraph-Data-structures.html#VECTOR" title="2.4.1. VECTOR — Accessing an element of a vector.">VECTOR</a></strong></span>(sep)[3] = 30;
|
||||
<span class="strong"><strong><a class="link" href="igraph-Data-structures.html#VECTOR" title="2.4.1. VECTOR — Accessing an element of a vector.">VECTOR</a></strong></span>(sep)[4] = 31;
|
||||
<span class="strong"><strong><a class="link" href="igraph-Separators.html#igraph_is_separator" title="1. igraph_is_separator — Would removing this set of vertices disconnect the graph?">igraph_is_separator</a></strong></span>(&graph, <span class="strong"><strong><a class="link" href="igraph-Iterators.html#igraph_vss_vector" title="4.4. igraph_vss_vector — Vertex set based on a vector (immediate version).">igraph_vss_vector</a></strong></span>(&sep), &result);
|
||||
<span class="strong"><strong>if</strong></span> (result) {
|
||||
<span class="strong"><strong>FAIL</strong></span>("Karate network (8,9,19,30,31) failed", 4);
|
||||
}
|
||||
|
||||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_destroy" title="5.1.4. igraph_destroy — Frees the memory allocated for a graph object.">igraph_destroy</a></strong></span>(&graph);
|
||||
<span class="strong"><strong>igraph_vector_int_destroy</strong></span>(&sep);
|
||||
|
||||
<span class="strong"><strong>return</strong></span> 0;
|
||||
}
|
||||
</pre>
|
||||
<p></p>
|
||||
</div>
|
||||
</div>
|
||||
<br class="example-break">
|
||||
</div>
|
||||
<p>
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="igraph_is_minimal_separator"></a>2. <code class="function">igraph_is_minimal_separator</code> — Decides whether a set of vertices is a minimal separator.</h2></div></div></div>
|
||||
<a class="indexterm" name="id-1.25.3.2"></a><p>
|
||||
</p>
|
||||
<div class="informalexample"><pre class="programlisting">
|
||||
igraph_error_t igraph_is_minimal_separator(const igraph_t *graph,
|
||||
const igraph_vs_t candidate,
|
||||
igraph_bool_t *res);
|
||||
</pre></div>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
|
||||
|
||||
|
||||
A vertex separator <code class="constant">S</code> is minimal is no proper subset of <code class="constant">S</code>
|
||||
is also a separator.
|
||||
|
||||
</p>
|
||||
<p><b>Arguments: </b>
|
||||
</p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The input graph. It may be directed, but edge
|
||||
directions are ignored.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>candidate</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The candidate minimal separators.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Pointer to a boolean variable, the result is stored
|
||||
here.
|
||||
</p></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
</p>
|
||||
<p><b>Returns: </b></p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||||
<td><p>
|
||||
Error code.
|
||||
</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
Time complexity: O(|V|+|E|), linear in the number vertices and edges.
|
||||
|
||||
</p>
|
||||
<div class="hideshow" onClick="toggle(this, event)">
|
||||
<div class="example">
|
||||
<a name="id-1.25.3.8.1"></a><p class="title"><b>Example 24.2. File <code class="code">examples/simple/igraph_is_minimal_separator.c</code></b></p>
|
||||
<div class="example-contents">
|
||||
<pre class="programlisting"><span class="strong"><strong>#include</strong></span> <igraph.h>
|
||||
<span class="strong"><strong>#include</strong></span> <stdio.h>
|
||||
|
||||
<span class="strong"><strong>#define</strong></span> <span class="strong"><strong>FAIL</strong></span>(msg, error) <span class="strong"><strong>do</strong></span> { <span class="strong"><strong>printf</strong></span>(msg "\n") ; <span class="strong"><strong>return</strong></span> error; } <span class="strong"><strong>while</strong></span> (0)
|
||||
|
||||
int <span class="strong"><strong>main</strong></span>(void) {
|
||||
|
||||
igraph_t graph;
|
||||
igraph_vector_int_t sep;
|
||||
igraph_bool_t result;
|
||||
|
||||
<span class="emphasis"><em>/* Initialize the library. */</em></span>
|
||||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_setup" title="4.1. igraph_setup — Initializes the igraph library.">igraph_setup</a></strong></span>();
|
||||
|
||||
<span class="emphasis"><em>/* Simple star graph, remove the center */</em></span>
|
||||
<span class="strong"><strong><a class="link" href="igraph-Generators.html#igraph_star" title="4.1. igraph_star — Creates a star graph, every vertex connects only to the center.">igraph_star</a></strong></span>(&graph, 10, IGRAPH_STAR_UNDIRECTED, 0);
|
||||
<span class="strong"><strong><a class="link" href="igraph-Separators.html#igraph_is_minimal_separator" title="2. igraph_is_minimal_separator — Decides whether a set of vertices is a minimal separator.">igraph_is_minimal_separator</a></strong></span>(&graph, <span class="strong"><strong><a class="link" href="igraph-Iterators.html#igraph_vss_1" title="4.3. igraph_vss_1 — Vertex set with a single vertex (immediate version).">igraph_vss_1</a></strong></span>(0), &result);
|
||||
<span class="strong"><strong>if</strong></span> (!result) {
|
||||
<span class="strong"><strong>FAIL</strong></span>("Center of star graph failed.", 1);
|
||||
}
|
||||
|
||||
<span class="emphasis"><em>/* Same graph, but another vertex */</em></span>
|
||||
<span class="strong"><strong><a class="link" href="igraph-Separators.html#igraph_is_minimal_separator" title="2. igraph_is_minimal_separator — Decides whether a set of vertices is a minimal separator.">igraph_is_minimal_separator</a></strong></span>(&graph, <span class="strong"><strong><a class="link" href="igraph-Iterators.html#igraph_vss_1" title="4.3. igraph_vss_1 — Vertex set with a single vertex (immediate version).">igraph_vss_1</a></strong></span>(6), &result);
|
||||
<span class="strong"><strong>if</strong></span> (result) {
|
||||
<span class="strong"><strong>FAIL</strong></span>("Non-center of star graph failed.", 2);
|
||||
}
|
||||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_destroy" title="5.1.4. igraph_destroy — Frees the memory allocated for a graph object.">igraph_destroy</a></strong></span>(&graph);
|
||||
|
||||
<span class="emphasis"><em>/* Karate club */</em></span>
|
||||
<span class="strong"><strong><a class="link" href="igraph-Generators.html#igraph_famous" title="8.1. igraph_famous — Create a famous graph by simply providing its name.">igraph_famous</a></strong></span>(&graph, "zachary");
|
||||
<span class="strong"><strong>igraph_vector_int_init</strong></span>(&sep, 0);
|
||||
<span class="strong"><strong>igraph_vector_int_push_back</strong></span>(&sep, 32);
|
||||
<span class="strong"><strong>igraph_vector_int_push_back</strong></span>(&sep, 33);
|
||||
<span class="strong"><strong><a class="link" href="igraph-Separators.html#igraph_is_minimal_separator" title="2. igraph_is_minimal_separator — Decides whether a set of vertices is a minimal separator.">igraph_is_minimal_separator</a></strong></span>(&graph, <span class="strong"><strong><a class="link" href="igraph-Iterators.html#igraph_vss_vector" title="4.4. igraph_vss_vector — Vertex set based on a vector (immediate version).">igraph_vss_vector</a></strong></span>(&sep), &result);
|
||||
<span class="strong"><strong>if</strong></span> (!result) {
|
||||
<span class="strong"><strong>FAIL</strong></span>("Karate network (32,33) failed", 3);
|
||||
}
|
||||
|
||||
<span class="strong"><strong>igraph_vector_int_resize</strong></span>(&sep, 5);
|
||||
<span class="strong"><strong><a class="link" href="igraph-Data-structures.html#VECTOR" title="2.4.1. VECTOR — Accessing an element of a vector.">VECTOR</a></strong></span>(sep)[0] = 8;
|
||||
<span class="strong"><strong><a class="link" href="igraph-Data-structures.html#VECTOR" title="2.4.1. VECTOR — Accessing an element of a vector.">VECTOR</a></strong></span>(sep)[1] = 9;
|
||||
<span class="strong"><strong><a class="link" href="igraph-Data-structures.html#VECTOR" title="2.4.1. VECTOR — Accessing an element of a vector.">VECTOR</a></strong></span>(sep)[2] = 19;
|
||||
<span class="strong"><strong><a class="link" href="igraph-Data-structures.html#VECTOR" title="2.4.1. VECTOR — Accessing an element of a vector.">VECTOR</a></strong></span>(sep)[3] = 30;
|
||||
<span class="strong"><strong><a class="link" href="igraph-Data-structures.html#VECTOR" title="2.4.1. VECTOR — Accessing an element of a vector.">VECTOR</a></strong></span>(sep)[4] = 31;
|
||||
<span class="strong"><strong><a class="link" href="igraph-Separators.html#igraph_is_minimal_separator" title="2. igraph_is_minimal_separator — Decides whether a set of vertices is a minimal separator.">igraph_is_minimal_separator</a></strong></span>(&graph, <span class="strong"><strong><a class="link" href="igraph-Iterators.html#igraph_vss_vector" title="4.4. igraph_vss_vector — Vertex set based on a vector (immediate version).">igraph_vss_vector</a></strong></span>(&sep), &result);
|
||||
<span class="strong"><strong>if</strong></span> (result) {
|
||||
<span class="strong"><strong>FAIL</strong></span>("Karate network (8,9,19,30,31) failed", 4);
|
||||
}
|
||||
|
||||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_destroy" title="5.1.4. igraph_destroy — Frees the memory allocated for a graph object.">igraph_destroy</a></strong></span>(&graph);
|
||||
<span class="strong"><strong>igraph_vector_int_destroy</strong></span>(&sep);
|
||||
|
||||
<span class="strong"><strong>return</strong></span> 0;
|
||||
}
|
||||
</pre>
|
||||
<p></p>
|
||||
</div>
|
||||
</div>
|
||||
<br class="example-break">
|
||||
</div>
|
||||
<p>
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="igraph_all_minimal_st_separators"></a>3. <code class="function">igraph_all_minimal_st_separators</code> — List all vertex sets that are minimal (s,t) separators for some s and t.</h2></div></div></div>
|
||||
<a class="indexterm" name="id-1.25.4.2"></a><p>
|
||||
</p>
|
||||
<div class="informalexample"><pre class="programlisting">
|
||||
igraph_error_t igraph_all_minimal_st_separators(
|
||||
const igraph_t *graph, igraph_vector_int_list_t *separators
|
||||
);
|
||||
</pre></div>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
|
||||
|
||||
|
||||
This function lists all vertex sets that are minimal (s,t)
|
||||
separators for some (s,t) vertex pair.
|
||||
|
||||
</p>
|
||||
<p>
|
||||
Note that some vertex sets returned by this function may not be minimal
|
||||
with respect to disconnecting the graph (or increasing the number of
|
||||
connected components). Take for example the 5-vertex graph with edges
|
||||
<code class="literal">0-1-2-3-4-1</code>. This function returns the vertex sets
|
||||
<code class="literal">{1}</code>, <code class="literal">{2,4}</code> and <code class="literal">{1,3}</code>.
|
||||
Notice that <code class="literal">{1,3}</code> is not minimal with respect to disconnecting
|
||||
the graph, as <code class="literal">{1}</code> would be sufficient for that. However, it is
|
||||
minimal with respect to separating vertices <code class="constant">2</code> and <code class="constant">4</code>.
|
||||
|
||||
</p>
|
||||
<p>
|
||||
See more about the implemented algorithm in
|
||||
Anne Berry, Jean-Paul Bordat and Olivier Cogis: Generating All the
|
||||
Minimal Separators of a Graph, In: Peter Widmayer, Gabriele Neyer
|
||||
and Stephan Eidenbenz (editors): Graph-theoretic concepts in
|
||||
computer science, 1665, 167--172, 1999. Springer.
|
||||
<a class="ulink" href="https://doi.org/10.1007/3-540-46784-X_17" target="_top">https://doi.org/10.1007/3-540-46784-X_17</a>
|
||||
|
||||
</p>
|
||||
<p><b>Arguments: </b>
|
||||
</p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The input graph. It may be directed, but edge
|
||||
directions are ignored.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>separators</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Pointer to a list of integer vectors, the separators
|
||||
will be stored here.
|
||||
</p></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
</p>
|
||||
<p><b>Returns: </b></p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||||
<td><p>
|
||||
Error code.
|
||||
</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
</p>
|
||||
<p><b>See also: </b></p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||||
<td><p>
|
||||
<a class="link" href="igraph-Separators.html#igraph_minimum_size_separators" title="4. igraph_minimum_size_separators — Find all minimum size separating vertex sets."><code class="function">igraph_minimum_size_separators()</code></a>
|
||||
</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
Time complexity: O(n|V|^3), |V| is the number of vertices, n is the
|
||||
number of separators.
|
||||
|
||||
</p>
|
||||
<div class="hideshow" onClick="toggle(this, event)">
|
||||
<div class="example">
|
||||
<a name="id-1.25.4.12.1"></a><p class="title"><b>Example 24.3. File <code class="code">examples/simple/igraph_minimal_separators.c</code></b></p>
|
||||
<div class="example-contents">
|
||||
<pre class="programlisting"><span class="strong"><strong>#include</strong></span> <igraph.h>
|
||||
<span class="strong"><strong>#include</strong></span> <stdio.h>
|
||||
|
||||
int <span class="strong"><strong>main</strong></span>(void) {
|
||||
igraph_t graph;
|
||||
igraph_vector_int_list_t separators;
|
||||
igraph_int_t i, n;
|
||||
|
||||
<span class="emphasis"><em>/* Initialize the library. */</em></span>
|
||||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_setup" title="4.1. igraph_setup — Initializes the igraph library.">igraph_setup</a></strong></span>();
|
||||
|
||||
<span class="strong"><strong><a class="link" href="igraph-Generators.html#igraph_famous" title="8.1. igraph_famous — Create a famous graph by simply providing its name.">igraph_famous</a></strong></span>(&graph, "zachary");
|
||||
<span class="strong"><strong>igraph_vector_int_list_init</strong></span>(&separators, 0);
|
||||
<span class="strong"><strong><a class="link" href="igraph-Separators.html#igraph_all_minimal_st_separators" title="3. igraph_all_minimal_st_separators — List all vertex sets that are minimal (s,t) separators for some s and t.">igraph_all_minimal_st_separators</a></strong></span>(&graph, &separators);
|
||||
|
||||
n = <span class="strong"><strong>igraph_vector_int_list_size</strong></span>(&separators);
|
||||
<span class="strong"><strong>for</strong></span> (i = 0; i < n; i++) {
|
||||
igraph_bool_t res;
|
||||
igraph_vector_int_t *sep = <span class="strong"><strong>igraph_vector_int_list_get_ptr</strong></span>(&separators, i);
|
||||
|
||||
<span class="strong"><strong><a class="link" href="igraph-Separators.html#igraph_is_separator" title="1. igraph_is_separator — Would removing this set of vertices disconnect the graph?">igraph_is_separator</a></strong></span>(&graph, <span class="strong"><strong><a class="link" href="igraph-Iterators.html#igraph_vss_vector" title="4.4. igraph_vss_vector — Vertex set based on a vector (immediate version).">igraph_vss_vector</a></strong></span>(sep), &res);
|
||||
<span class="strong"><strong>if</strong></span> (!res) {
|
||||
<span class="strong"><strong>printf</strong></span>("Vertex set %" IGRAPH_PRId " is not a separator!\n", i);
|
||||
<span class="strong"><strong>igraph_vector_int_print</strong></span>(sep);
|
||||
<span class="strong"><strong>return</strong></span> 1;
|
||||
}
|
||||
}
|
||||
|
||||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_destroy" title="5.1.4. igraph_destroy — Frees the memory allocated for a graph object.">igraph_destroy</a></strong></span>(&graph);
|
||||
<span class="strong"><strong>igraph_vector_int_list_destroy</strong></span>(&separators);
|
||||
|
||||
<span class="strong"><strong>return</strong></span> 0;
|
||||
}
|
||||
</pre>
|
||||
<p></p>
|
||||
</div>
|
||||
</div>
|
||||
<br class="example-break">
|
||||
</div>
|
||||
<p>
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="igraph_minimum_size_separators"></a>4. <code class="function">igraph_minimum_size_separators</code> — Find all minimum size separating vertex sets.</h2></div></div></div>
|
||||
<a class="indexterm" name="id-1.25.5.2"></a><p>
|
||||
</p>
|
||||
<div class="informalexample"><pre class="programlisting">
|
||||
igraph_error_t igraph_minimum_size_separators(
|
||||
const igraph_t *graph, igraph_vector_int_list_t *separators
|
||||
);
|
||||
</pre></div>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
|
||||
|
||||
|
||||
This function lists all separator vertex sets of minimum size.
|
||||
A vertex set is a separator if its removal disconnects the graph.
|
||||
|
||||
</p>
|
||||
<p>
|
||||
If the graph is already disconnected, no separators are returned.
|
||||
Note that this convention differs from that used by some other
|
||||
funtions such as <a class="link" href="igraph-Separators.html#igraph_all_minimal_st_separators" title="3. igraph_all_minimal_st_separators — List all vertex sets that are minimal (s,t) separators for some s and t."><code class="function">igraph_all_minimal_st_separators()</code></a>.
|
||||
|
||||
</p>
|
||||
<p>
|
||||
Complete graphs have no vertex separators.
|
||||
|
||||
</p>
|
||||
<p>
|
||||
The implementation is based on the following paper:
|
||||
Arkady Kanevsky: Finding all minimum-size separating vertex sets in
|
||||
a graph, Networks 23, 533--541, 1993.
|
||||
<a class="ulink" href="https://doi.org/10.1002/net.3230230604" target="_top">https://doi.org/10.1002/net.3230230604</a>
|
||||
|
||||
</p>
|
||||
<p><b>Arguments: </b>
|
||||
</p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
The input graph, which must be undirected.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>separators</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
An initialized list of integer vectors, the separators
|
||||
are stored here. It is a list of pointers to <span class="type">igraph_vector_int_t</span>
|
||||
objects. Each vector will contain the IDs of the vertices in
|
||||
the separator. The separators are returned in an arbitrary order.
|
||||
</p></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
</p>
|
||||
<p><b>Returns: </b></p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||||
<td><p>
|
||||
Error code.
|
||||
</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
Time complexity: TODO.
|
||||
|
||||
</p>
|
||||
<div class="hideshow" onClick="toggle(this, event)">
|
||||
<div class="example">
|
||||
<a name="id-1.25.5.11.1"></a><p class="title"><b>Example 24.4. File <code class="code">examples/simple/igraph_minimum_size_separators.c</code></b></p>
|
||||
<div class="example-contents">
|
||||
<pre class="programlisting"><span class="strong"><strong>#include</strong></span> <igraph.h>
|
||||
|
||||
int <span class="strong"><strong>main</strong></span>(void) {
|
||||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_setup" title="4.1. igraph_setup — Initializes the igraph library.">igraph_setup</a></strong></span>();
|
||||
igraph_t g;
|
||||
igraph_vector_int_list_t sep;
|
||||
|
||||
<span class="strong"><strong><a class="link" href="igraph-Generators.html#igraph_small" title="2.2. igraph_small — Shorthand to create a small graph, giving the edges as arguments.">igraph_small</a></strong></span>(&g, 7, IGRAPH_UNDIRECTED,
|
||||
1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0,
|
||||
-1);
|
||||
<span class="strong"><strong>igraph_vector_int_list_init</strong></span>(&sep, 0);
|
||||
<span class="strong"><strong><a class="link" href="igraph-Separators.html#igraph_minimum_size_separators" title="4. igraph_minimum_size_separators — Find all minimum size separating vertex sets.">igraph_minimum_size_separators</a></strong></span>(&g, &sep);
|
||||
|
||||
<span class="strong"><strong>for</strong></span> (igraph_int_t i = 0; i < <span class="strong"><strong>igraph_vector_int_list_size</strong></span>(&sep); i++) {
|
||||
igraph_vector_int_t* v = <span class="strong"><strong>igraph_vector_int_list_get_ptr</strong></span>(&sep, i);
|
||||
<span class="strong"><strong>igraph_vector_int_print</strong></span>(v);
|
||||
}
|
||||
|
||||
<span class="strong"><strong>igraph_vector_int_list_destroy</strong></span>(&sep);
|
||||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_destroy" title="5.1.4. igraph_destroy — Frees the memory allocated for a graph object.">igraph_destroy</a></strong></span>(&g);
|
||||
|
||||
<span class="strong"><strong>return</strong></span> 0;
|
||||
}
|
||||
</pre>
|
||||
<p></p>
|
||||
</div>
|
||||
</div>
|
||||
<br class="example-break">
|
||||
</div>
|
||||
<p>
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="igraph_even_tarjan_reduction"></a>5. <code class="function">igraph_even_tarjan_reduction</code> — Even-Tarjan reduction of a graph.</h2></div></div></div>
|
||||
<a class="indexterm" name="id-1.25.6.2"></a><p>
|
||||
</p>
|
||||
<div class="informalexample"><pre class="programlisting">
|
||||
igraph_error_t igraph_even_tarjan_reduction(const igraph_t *graph, igraph_t *graphbar,
|
||||
igraph_vector_t *capacity);
|
||||
</pre></div>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
|
||||
|
||||
|
||||
A digraph is created with twice as many vertices and edges. For each
|
||||
original vertex <code class="constant">i</code>, two vertices <code class="literal">i' = i</code> and
|
||||
<code class="literal">i'' = i' + n</code> are created,
|
||||
with a directed edge from <code class="literal">i'</code> to <code class="literal">i''</code>.
|
||||
For each original directed edge from <code class="constant">i</code> to <code class="constant">j</code>, two new edges are created,
|
||||
from <code class="literal">i'</code> to <code class="literal">j''</code> and from <code class="literal">i''</code>
|
||||
to <code class="literal">j'</code>.
|
||||
|
||||
</p>
|
||||
<p>This reduction is used in the paper (observation 2):
|
||||
Arkady Kanevsky: Finding all minimum-size separating vertex sets in
|
||||
a graph, Networks 23, 533--541, 1993.
|
||||
|
||||
</p>
|
||||
<p>The original paper where this reduction was conceived is
|
||||
Shimon Even and R. Endre Tarjan: Network Flow and Testing Graph
|
||||
Connectivity, SIAM J. Comput., 4(4), 507–518.
|
||||
<a class="ulink" href="https://doi.org/10.1137/0204043" target="_top">https://doi.org/10.1137/0204043</a>
|
||||
|
||||
</p>
|
||||
<p><b>Arguments: </b>
|
||||
</p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
A graph. Although directness is not checked, this function
|
||||
is commonly used only on directed graphs.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>graphbar</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Pointer to a new directed graph that will contain the
|
||||
reduction, with twice as many vertices and edges.
|
||||
</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p><span class="term"><em class="parameter"><code>capacity</code></em>:</span></p></td>
|
||||
<td><p>
|
||||
Pointer to an initialized vector or a null pointer. If
|
||||
not a null pointer, then it will be filled the capacity from
|
||||
the reduction: the first |E| elements are 1, the remaining |E|
|
||||
are equal to |V| (which is used to indicate infinity).
|
||||
</p></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
</p>
|
||||
<p><b>Returns: </b></p>
|
||||
<div class="variablelist"><table border="0" class="variablelist">
|
||||
<colgroup>
|
||||
<col align="left" valign="top">
|
||||
<col>
|
||||
</colgroup>
|
||||
<tbody><tr>
|
||||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||||
<td><p>
|
||||
Error code.
|
||||
</p></td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
|
||||
Time complexity: O(|E|+|V|).
|
||||
|
||||
</p>
|
||||
<div class="hideshow" onClick="toggle(this, event)">
|
||||
<div class="example">
|
||||
<a name="id-1.25.6.10.1"></a><p class="title"><b>Example 24.5. File <code class="code">examples/simple/even_tarjan.c</code></b></p>
|
||||
<div class="example-contents">
|
||||
<pre class="programlisting"><span class="strong"><strong>#include</strong></span> <igraph.h>
|
||||
<span class="strong"><strong>#include</strong></span> <limits.h>
|
||||
|
||||
int <span class="strong"><strong>main</strong></span>(void) {
|
||||
|
||||
igraph_t g, gbar;
|
||||
igraph_int_t k1, k2 = INT_MAX;
|
||||
igraph_real_t tmpk;
|
||||
igraph_int_t i, j, n;
|
||||
<a class="link" href="igraph-Flows.html#igraph_maxflow_stats_t" title="1.4. igraph_maxflow_stats_t — Data structure holding statistics from the push-relabel maximum flow solver.">igraph_maxflow_stats_t</a> stats;
|
||||
|
||||
<span class="emphasis"><em>/* Initialize the library. */</em></span>
|
||||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_setup" title="4.1. igraph_setup — Initializes the igraph library.">igraph_setup</a></strong></span>();
|
||||
|
||||
<span class="strong"><strong><a class="link" href="igraph-Generators.html#igraph_famous" title="8.1. igraph_famous — Create a famous graph by simply providing its name.">igraph_famous</a></strong></span>(&g, "meredith");
|
||||
<span class="strong"><strong><a class="link" href="igraph-Separators.html#igraph_even_tarjan_reduction" title="5. igraph_even_tarjan_reduction — Even-Tarjan reduction of a graph.">igraph_even_tarjan_reduction</a></strong></span>(&g, &gbar, <span class="emphasis"><em>/*capacity=*/</em></span> NULL);
|
||||
|
||||
<span class="strong"><strong><a class="link" href="igraph-Flows.html#igraph_vertex_connectivity" title="3.4. igraph_vertex_connectivity — The vertex connectivity of a graph.">igraph_vertex_connectivity</a></strong></span>(&g, &k1, <span class="emphasis"><em>/* checks= */</em></span> false);
|
||||
|
||||
n = <span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_vcount" title="5.2.1. igraph_vcount — The number of vertices in a graph.">igraph_vcount</a></strong></span>(&g);
|
||||
<span class="strong"><strong>for</strong></span> (i = 0; i < n; i++) {
|
||||
<span class="strong"><strong>for</strong></span> (j = i + 1; j < n; j++) {
|
||||
igraph_bool_t conn;
|
||||
<span class="strong"><strong><a class="link" href="igraph-Structural.html#igraph_are_adjacent" title="1.1. igraph_are_adjacent — Decides whether two vertices are adjacent.">igraph_are_adjacent</a></strong></span>(&g, i, j, &conn);
|
||||
<span class="strong"><strong>if</strong></span> (conn) {
|
||||
<span class="strong"><strong>continue</strong></span>;
|
||||
}
|
||||
<span class="strong"><strong><a class="link" href="igraph-Flows.html#igraph_maxflow_value" title="1.2. igraph_maxflow_value — Maximum flow in a network with the push/relabel algorithm.">igraph_maxflow_value</a></strong></span>(&gbar, &tmpk,
|
||||
<span class="emphasis"><em>/* source= */</em></span> i + n,
|
||||
<span class="emphasis"><em>/* target= */</em></span> j,
|
||||
<span class="emphasis"><em>/* capacity= */</em></span> 0,
|
||||
&stats);
|
||||
<span class="strong"><strong>if</strong></span> (tmpk < k2) {
|
||||
k2 = tmpk;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_destroy" title="5.1.4. igraph_destroy — Frees the memory allocated for a graph object.">igraph_destroy</a></strong></span>(&gbar);
|
||||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_destroy" title="5.1.4. igraph_destroy — Frees the memory allocated for a graph object.">igraph_destroy</a></strong></span>(&g);
|
||||
|
||||
<span class="strong"><strong>if</strong></span> (k1 != k2) {
|
||||
<span class="strong"><strong>printf</strong></span>("k1 = %" IGRAPH_PRId " while k2 = %" IGRAPH_PRId "\n", k1, k2);
|
||||
<span class="strong"><strong>return</strong></span> 1;
|
||||
}
|
||||
|
||||
<span class="strong"><strong>return</strong></span> 0;
|
||||
}
|
||||
</pre>
|
||||
<p></p>
|
||||
</div>
|
||||
</div>
|
||||
<br class="example-break">
|
||||
</div>
|
||||
<p>
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
<table class="navigation-footer" width="100%" summary="Navigation footer" cellpadding="2" cellspacing="0"><tr valign="middle">
|
||||
<td align="left"><a accesskey="p" href="igraph-Flows.html"><b>← Chapter 23. Maximum flows, minimum cuts and related measures</b></a></td>
|
||||
<td align="right"><a accesskey="n" href="igraph-Community.html"><b>Chapter 25. Detecting community structure →</b></a></td>
|
||||
</tr></table>
|
||||
</body>
|
||||
</html>
|
||||
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Load Diff
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Load Diff
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|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
|
||||
<title>Chapter 3. Tutorial</title>
|
||||
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot">
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<link rel="home" href="index.html" title="igraph Reference Manual">
|
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<link rel="up" href="index.html" title="igraph Reference Manual">
|
||||
<link rel="prev" href="igraph-Installation.html" title="Chapter 2. Installation">
|
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<link rel="next" href="igraph-Basic.html" title="Chapter 4. Basic data types and interface">
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<link rel="stylesheet" href="https://stackpath.bootstrapcdn.com/font-awesome/4.7.0/css/font-awesome.min.css" type="text/css">
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<link rel="chapter" href="igraph-Introduction.html" title="Chapter 1. Introduction">
|
||||
<link rel="chapter" href="igraph-Installation.html" title="Chapter 2. Installation">
|
||||
<link rel="chapter" href="igraph-Tutorial.html" title="Chapter 3. Tutorial">
|
||||
<link rel="chapter" href="igraph-Basic.html" title="Chapter 4. Basic data types and interface">
|
||||
<link rel="chapter" href="igraph-Error.html" title="Chapter 5. Error handling">
|
||||
<link rel="chapter" href="igraph-Memory.html" title="Chapter 6. Memory (de)allocation">
|
||||
<link rel="chapter" href="igraph-Data-structures.html" title="Chapter 7. Data structure library: vector, matrix, other data types">
|
||||
<link rel="chapter" href="igraph-Random.html" title="Chapter 8. Random numbers">
|
||||
<link rel="chapter" href="igraph-Iterators.html" title="Chapter 9. Vertex and edge selectors and sequences, iterators">
|
||||
<link rel="chapter" href="igraph-Attributes.html" title="Chapter 10. Graph, vertex and edge attributes">
|
||||
<link rel="chapter" href="igraph-Generators.html" title="Chapter 11. Deterministic graph generators">
|
||||
<link rel="chapter" href="igraph-Games.html" title='Chapter 12. Stochastic graph generators ("games")'>
|
||||
<link rel="chapter" href="igraph-Bipartite.html" title="Chapter 13. Bipartite, i.e. two-mode graphs">
|
||||
<link rel="chapter" href="igraph-Spatial.html" title="Chapter 14. Spatial graphs">
|
||||
<link rel="chapter" href="igraph-Operators.html" title="Chapter 15. Graph operators">
|
||||
<link rel="chapter" href="igraph-Visitors.html" title="Chapter 16. Graph visitors">
|
||||
<link rel="chapter" href="igraph-Structural.html" title="Chapter 17. Structural properties of graphs">
|
||||
<link rel="chapter" href="igraph-Cycles.html" title="Chapter 18. Graph cycles">
|
||||
<link rel="chapter" href="igraph-Cliques.html" title="Chapter 19. Cliques and independent vertex sets">
|
||||
<link rel="chapter" href="igraph-Motifs.html" title="Chapter 20. Graph motifs, dyad census and triad census">
|
||||
<link rel="chapter" href="igraph-Isomorphism.html" title="Chapter 21. Graph isomorphism">
|
||||
<link rel="chapter" href="igraph-Coloring.html" title="Chapter 22. Graph coloring">
|
||||
<link rel="chapter" href="igraph-Flows.html" title="Chapter 23. Maximum flows, minimum cuts and related measures">
|
||||
<link rel="chapter" href="igraph-Separators.html" title="Chapter 24. Vertex separators">
|
||||
<link rel="chapter" href="igraph-Community.html" title="Chapter 25. Detecting community structure">
|
||||
<link rel="chapter" href="igraph-Graphlets.html" title="Chapter 26. Graphlets">
|
||||
<link rel="chapter" href="igraph-HRG.html" title="Chapter 27. Hierarchical random graphs">
|
||||
<link rel="chapter" href="igraph-Embedding.html" title="Chapter 28. Embedding of graphs">
|
||||
<link rel="chapter" href="igraph-Layout.html" title="Chapter 29. Generating layouts for graph drawing">
|
||||
<link rel="chapter" href="igraph-Processes.html" title="Chapter 30. Processes on graphs">
|
||||
<link rel="chapter" href="igraph-Foreign.html" title="Chapter 31. Reading and writing graphs from and to files">
|
||||
<link rel="chapter" href="igraph-Linalg.html" title="Chapter 32. Using BLAS, LAPACK and ARPACK for igraph matrices and graphs">
|
||||
<link rel="chapter" href="igraph-Nongraph.html" title="Chapter 33. Non-graph related functions">
|
||||
<link rel="chapter" href="igraph-Advanced.html" title="Chapter 34. Advanced igraph programming">
|
||||
<link rel="chapter" href="igraph-Glossary.html" title="Chapter 35. Glossary">
|
||||
<link rel="chapter" href="igraph-Licenses.html" title="Chapter 36. Licenses for igraph and this manual">
|
||||
<link rel="index" href="ix01.html" title="Index">
|
||||
</head>
|
||||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
||||
<div class="navigation-header mb-4" width="100%" summary="Navigation header"><div class="btn-group">
|
||||
<a accesskey="p" class="btn btn-light" href="igraph-Installation.html"><i class="fa fa-chevron-left"></i>
|
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Previous
|
||||
</a><a accesskey="h" class="btn btn-light" href="index.html"><i class="fa fa-home"></i>
|
||||
Home
|
||||
</a><a accesskey="n" class="btn btn-light" href="igraph-Basic.html"><i class="fa fa-chevron-right"></i>
|
||||
Next
|
||||
</a>
|
||||
</div></div>
|
||||
<div class="chapter">
|
||||
<div class="titlepage"><div><div><h1 class="title">
|
||||
<a name="igraph-Tutorial"></a>Chapter 3. Tutorial</h1></div></div></div>
|
||||
<div class="toc"><dl class="toc">
|
||||
<dt><span class="section"><a href="igraph-Tutorial.html#tut-lesson-1">1. Compiling programs using igraph</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Tutorial.html#tut-lesson-2">2. Creating your first graphs</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Tutorial.html#tut-lesson-3">3. Calculating various properties of graphs</a></span></dt>
|
||||
</dl></div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="tut-lesson-1"></a>1. Compiling programs using igraph</h2></div></div></div>
|
||||
<div class="toc"><dl class="toc">
|
||||
<dt><span class="section"><a href="igraph-Tutorial.html#tut-lesson-1-compiling-with-cmake">1.1. Compiling with CMake</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Tutorial.html#tut-lesson-1-compiling-without-cmake">1.2. Compiling without CMake</a></span></dt>
|
||||
<dt><span class="section"><a href="igraph-Tutorial.html#tut-lesson-1-running-the-program">1.3. Running the program</a></span></dt>
|
||||
</dl></div>
|
||||
<p>
|
||||
The following short example program demonstrates the basic usage of
|
||||
the <span class="command"><strong>igraph</strong></span> library. Save it into a file named
|
||||
<code class="filename">igraph_test.c</code>.
|
||||
</p>
|
||||
<pre class="programlisting"><span class="strong"><strong>#include</strong></span> <igraph.h>
|
||||
|
||||
int <span class="strong"><strong>main</strong></span>(void) {
|
||||
igraph_int_t num_vertices = 1000;
|
||||
igraph_int_t num_edges = 1000;
|
||||
igraph_real_t diameter, mean_degree;
|
||||
igraph_t graph;
|
||||
|
||||
<span class="emphasis"><em>/* Initialize the library. */</em></span>
|
||||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_setup" title="4.1. igraph_setup — Initializes the igraph library.">igraph_setup</a></strong></span>();
|
||||
|
||||
<span class="emphasis"><em>/* Ensure identical results across runs. */</em></span>
|
||||
<span class="strong"><strong><a class="link" href="igraph-Random.html#igraph_rng_seed" title="3.3. igraph_rng_seed — Seeds a random number generator.">igraph_rng_seed</a></strong></span>(<span class="strong"><strong><a class="link" href="igraph-Random.html#igraph_rng_default" title="2.1. igraph_rng_default — Query the default random number generator.">igraph_rng_default</a></strong></span>(), 42);
|
||||
|
||||
<span class="strong"><strong><a class="link" href="igraph-Games.html#igraph_erdos_renyi_game_gnm" title="1.1. igraph_erdos_renyi_game_gnm — Generates a random (Erdős-Rényi) graph with a fixed number of edges.">igraph_erdos_renyi_game_gnm</a></strong></span>(
|
||||
&graph, num_vertices, num_edges,
|
||||
IGRAPH_UNDIRECTED, IGRAPH_SIMPLE_SW, IGRAPH_EDGE_UNLABELED);
|
||||
|
||||
<span class="strong"><strong><a class="link" href="igraph-Structural.html#igraph_diameter" title="3.22. igraph_diameter — Calculates the weighted diameter of a graph using Dijkstra's algorithm.">igraph_diameter</a></strong></span>(
|
||||
&graph, <span class="emphasis"><em>/* weights = */</em></span> NULL,
|
||||
&diameter,
|
||||
<span class="emphasis"><em>/* from = */</em></span> NULL, <span class="emphasis"><em>/* to = */</em></span> NULL,
|
||||
<span class="emphasis"><em>/* vertex_path = */</em></span> NULL, <span class="emphasis"><em>/* edge_path = */</em></span> NULL,
|
||||
IGRAPH_UNDIRECTED, <span class="emphasis"><em>/* unconn= */</em></span> true);
|
||||
|
||||
<span class="strong"><strong><a class="link" href="igraph-Structural.html#igraph_mean_degree" title="26.2. igraph_mean_degree — The mean degree of a graph.">igraph_mean_degree</a></strong></span>(&graph, &mean_degree, IGRAPH_LOOPS);
|
||||
<span class="strong"><strong>printf</strong></span>("Diameter of a random graph with average degree %g: %g\n",
|
||||
mean_degree, diameter);
|
||||
|
||||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_destroy" title="5.1.4. igraph_destroy — Frees the memory allocated for a graph object.">igraph_destroy</a></strong></span>(&graph);
|
||||
|
||||
<span class="strong"><strong>return</strong></span> 0;
|
||||
}
|
||||
</pre>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
This example illustrates a couple of points:
|
||||
</p>
|
||||
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
|
||||
<li class="listitem"><p>
|
||||
First, programs
|
||||
using the <span class="command"><strong>igraph</strong></span> library should include the
|
||||
<code class="filename">igraph.h</code> header
|
||||
file. Note that while igraph installs several sub-headers, the organization of these may change
|
||||
without notice. Only use <code class="filename">igraph.h</code> in your projects, not any of the sub-headers.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
Second, the library must be initialized using
|
||||
<a class="link" href="igraph-Basic.html#igraph_setup" title="4.1. igraph_setup — Initializes the igraph library."><code class="function">igraph_setup()</code></a>
|
||||
before use.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
Third, <span class="command"><strong>igraph</strong></span> uses the
|
||||
<span class="type">igraph_int_t</span> type for integers instead of
|
||||
<span class="type">int</span> or <span class="type">long int</span>, and it also uses the
|
||||
<span class="type">igraph_real_t</span> type for real numbers instead of
|
||||
<span class="type">double</span>. Depending on how <span class="command"><strong>igraph</strong></span> was compiled, and whether you are
|
||||
using a 32-bit or 64-bit system, <span class="type">igraph_int_t</span> may be a 32-bit
|
||||
or 64-bit integer.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
Fourth, <span class="command"><strong>igraph</strong></span> graph objects are represented by the <span class="type">igraph_t</span> data
|
||||
type.
|
||||
</p></li>
|
||||
<li class="listitem"><p>
|
||||
Fifth, the <a class="link" href="igraph-Games.html#igraph_erdos_renyi_game_gnm" title="1.1. igraph_erdos_renyi_game_gnm — Generates a random (Erdős-Rényi) graph with a fixed number of edges."><code class="function">igraph_erdos_renyi_game_gnm()</code></a>
|
||||
creates a graph and <a class="link" href="igraph-Basic.html#igraph_destroy" title="5.1.4. igraph_destroy — Frees the memory allocated for a graph object."><code class="function">igraph_destroy()</code></a>
|
||||
destroys it, i.e. deallocates the memory associated to it.
|
||||
</p></li>
|
||||
</ul></div>
|
||||
<p>
|
||||
For compiling this program you need a C compiler. Optionally,
|
||||
<a class="ulink" href="https://cmake.org" target="_top">CMake</a> can be used to automate the compilation.
|
||||
</p>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="tut-lesson-1-compiling-with-cmake"></a>1.1. Compiling with CMake</h3></div></div></div>
|
||||
<p>
|
||||
It is convenient to use CMake because it can automatically discover the
|
||||
necessary compilation flags on all operating systems. Many IDEs support
|
||||
CMake, and can work with CMake projects directly. To create a CMake project
|
||||
for this example program, create a file name <code class="filename">CMakeLists.txt</code> with the
|
||||
following contents:
|
||||
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
cmake_minimum_required(VERSION 3.18)
|
||||
project(igraph_test)
|
||||
|
||||
find_package(igraph REQUIRED)
|
||||
|
||||
add_executable(igraph_test igraph_test.c)
|
||||
target_link_libraries(igraph_test PUBLIC igraph::igraph)
|
||||
</pre>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
To compile the project, create a new directory called <code class="filename">build</code> in
|
||||
the root of the <span class="command"><strong>igraph</strong></span> source tree, and switch to it:
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
mkdir build
|
||||
cd build
|
||||
</pre>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
Run CMake to configure the project:
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
cmake ..
|
||||
</pre>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
If <span class="command"><strong>igraph</strong></span> was installed at a non-standard location, specify its prefix
|
||||
using the <code class="option">-DCMAKE_PREFIX_PATH=...</code> option. The prefix must be
|
||||
the same directory that was specified as the <code class="option">CMAKE_INSTALL_PREFIX</code>
|
||||
when compiling igraph.
|
||||
</p>
|
||||
<p>
|
||||
If configuration has succeeded, build the program using
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
cmake --build .
|
||||
</pre>
|
||||
<p>
|
||||
</p>
|
||||
<div class="note" style="margin-left: 0.5in; margin-right: 0.5in;">
|
||||
<h3 class="title">C++ must be enabled in igraph projects</h3>
|
||||
<p>Parts of <span class="command"><strong>igraph</strong></span> are implemented in C++; therefore, any CMake target that
|
||||
depends on <span class="command"><strong>igraph</strong></span> should use the C++ linker. Furthermore, OpenMP support in
|
||||
igraph works correctly only if C++ is enabled in the CMake project. The script
|
||||
that finds <span class="command"><strong>igraph</strong></span> on the host machine will throw an error if C++ support is
|
||||
not enabled in the CMake project.</p>
|
||||
<p>C++ support is enabled by default when no languages are explicitly
|
||||
specified in CMake's <a class="ulink" href="https://cmake.org/cmake/help/latest/command/project.html" target="_top"><code class="code">project</code></a>
|
||||
command, e.g. <code class="code">project(igraph_test)</code>. If you do specify some languages explicitly,
|
||||
make sure to also include <code class="code">CXX</code>, e.g. <code class="code">project(igraph_test C CXX)</code>.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="tut-lesson-1-compiling-without-cmake"></a>1.2. Compiling without CMake</h3></div></div></div>
|
||||
<p>
|
||||
On most Unix-like systems, the default C compiler is called <span class="command"><strong>cc</strong></span>.
|
||||
To compile the test program, you will need a command similar to the following:
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
cc igraph_test.c -I/usr/local/include/igraph -L/usr/local/lib -ligraph -o igraph_test
|
||||
</pre>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
The exact form depends on where <span class="command"><strong>igraph</strong></span> was installed on your
|
||||
system, whether it was compiled as a shared or static library, and the external
|
||||
libraries it was linked to. The directory after the <code class="option">-I</code> switch
|
||||
is the one containing the <code class="filename">igraph.h</code> file, while the one
|
||||
following <code class="option">-L</code> should contain the library file itself, usually a
|
||||
file called <code class="filename">libigraph.a</code> (static library on macOS and
|
||||
Linux), <code class="filename">libigraph.so</code> (shared library on Linux),
|
||||
<code class="filename">libigraph.dylib</code> (shared library on macOS),
|
||||
<code class="filename">igraph.lib</code> (static library on Windows) or
|
||||
<code class="filename">igraph.dll</code> (shared library on Windows). If
|
||||
<span class="command"><strong>igraph</strong></span> was compiled as a static library, it is also
|
||||
necessary to manually link to all of its dependencies.
|
||||
</p>
|
||||
<p>
|
||||
If your system has the <span class="command"><strong>pkg-config</strong></span> utility you are
|
||||
likely to get the necessary compile options by issuing the command
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
pkg-config --libs --cflags igraph
|
||||
</pre>
|
||||
<p>
|
||||
(if <span class="command"><strong>igraph</strong></span> was built as a shared library) or
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
pkg-config --static --libs --cflags igraph
|
||||
</pre>
|
||||
<p>
|
||||
(if <span class="command"><strong>igraph</strong></span> was built as a static library).
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="tut-lesson-1-running-the-program"></a>1.3. Running the program</h3></div></div></div>
|
||||
<p>
|
||||
On most systems, the executable can be run by simply typing its name like this:
|
||||
</p>
|
||||
<pre class="programlisting">
|
||||
./igraph_test
|
||||
</pre>
|
||||
<p>
|
||||
If you use dynamic linking and the <span class="command"><strong>igraph</strong></span>
|
||||
library is not installed in a standard place, you may need to add its location to the
|
||||
<code class="envar">LD_LIBRARY_PATH</code> (Linux), <code class="envar">DYLD_LIBRARY_PATH</code> (macOS)
|
||||
or <code class="envar">PATH</code> (Windows) environment variables. This is typically necessary
|
||||
on Windows systems.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="tut-lesson-2"></a>2. Creating your first graphs</h2></div></div></div>
|
||||
<p>
|
||||
The functions generating graph objects are called graph
|
||||
generators. Stochastic (i.e. randomized) graph generators are called
|
||||
<span class="quote">“<span class="quote">games</span>”</span>.
|
||||
</p>
|
||||
<p>
|
||||
<span class="command"><strong>igraph</strong></span> can handle directed and undirected graphs. Most graph
|
||||
generators are able to create both types of graphs and most other
|
||||
functions are usually also capable of handling
|
||||
both. E.g., <a class="link" href="igraph-Structural.html#igraph_get_shortest_paths" title="3.8. igraph_get_shortest_paths — Shortest paths from a vertex."><code class="function">igraph_get_shortest_paths()</code></a>,
|
||||
which calculates shortest paths from a vertex to other vertices, can calculate
|
||||
directed or undirected paths.
|
||||
</p>
|
||||
<p>
|
||||
<span class="command"><strong>igraph</strong></span> has sophisticated ways for creating graphs. The simplest
|
||||
graphs are deterministic regular structures like star graphs
|
||||
(<a class="link" href="igraph-Generators.html#igraph_star" title="4.1. igraph_star — Creates a star graph, every vertex connects only to the center."><code class="function">igraph_star()</code></a>),
|
||||
cycle graphs (<a class="link" href="igraph-Generators.html#igraph_cycle_graph" title="4.9. igraph_cycle_graph — A cycle graph C_n."><code class="function">igraph_cycle_graph()</code></a>), lattices
|
||||
(<a class="link" href="igraph-Generators.html#igraph_square_lattice" title="4.4. igraph_square_lattice — Arbitrary dimensional square lattices."><code class="function">igraph_square_lattice()</code></a>) or trees
|
||||
(<a class="link" href="igraph-Generators.html#igraph_kary_tree" title="5.1. igraph_kary_tree — Creates a k-ary tree in which almost all vertices have k children."><code class="function">igraph_kary_tree()</code></a>), and many more.
|
||||
</p>
|
||||
<p>
|
||||
The following example creates an undirected regular circular lattice,
|
||||
adds some random edges to it and calculates the average length of
|
||||
shortest paths between all pairs of vertices in the graph before and
|
||||
after adding the random edges. (The message is that some random edges
|
||||
can reduce path lengths a lot.)
|
||||
</p>
|
||||
<pre class="programlisting"><span class="strong"><strong>#include</strong></span> <igraph.h>
|
||||
|
||||
int <span class="strong"><strong>main</strong></span>(void) {
|
||||
igraph_t graph;
|
||||
igraph_vector_int_t dimvector;
|
||||
igraph_vector_int_t edges;
|
||||
igraph_vector_bool_t periodic;
|
||||
igraph_real_t avg_path_len;
|
||||
|
||||
<span class="emphasis"><em>/* Initialize the library. */</em></span>
|
||||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_setup" title="4.1. igraph_setup — Initializes the igraph library.">igraph_setup</a></strong></span>();
|
||||
|
||||
<span class="strong"><strong>igraph_vector_int_init</strong></span>(&dimvector, 2);
|
||||
<span class="strong"><strong><a class="link" href="igraph-Data-structures.html#VECTOR" title="2.4.1. VECTOR — Accessing an element of a vector.">VECTOR</a></strong></span>(dimvector)[0] = 30;
|
||||
<span class="strong"><strong><a class="link" href="igraph-Data-structures.html#VECTOR" title="2.4.1. VECTOR — Accessing an element of a vector.">VECTOR</a></strong></span>(dimvector)[1] = 30;
|
||||
|
||||
<span class="strong"><strong>igraph_vector_bool_init</strong></span>(&periodic, 2);
|
||||
<span class="strong"><strong>igraph_vector_bool_fill</strong></span>(&periodic, true);
|
||||
<span class="strong"><strong><a class="link" href="igraph-Generators.html#igraph_square_lattice" title="4.4. igraph_square_lattice — Arbitrary dimensional square lattices.">igraph_square_lattice</a></strong></span>(&graph, &dimvector, 0, IGRAPH_UNDIRECTED,
|
||||
<span class="emphasis"><em>/* mutual= */</em></span> false, &periodic);
|
||||
|
||||
<span class="strong"><strong><a class="link" href="igraph-Structural.html#igraph_average_path_length" title="3.20. igraph_average_path_length — The average shortest path length between all vertex pairs.">igraph_average_path_length</a></strong></span>(&graph, NULL, &avg_path_len, NULL,
|
||||
IGRAPH_UNDIRECTED, <span class="emphasis"><em>/* unconn= */</em></span> true);
|
||||
<span class="strong"><strong>printf</strong></span>("Average path length (lattice): %g\n", (double) avg_path_len);
|
||||
|
||||
<span class="emphasis"><em>/* Seed the RNG to ensure identical results across runs. */</em></span>
|
||||
<span class="strong"><strong><a class="link" href="igraph-Random.html#igraph_rng_seed" title="3.3. igraph_rng_seed — Seeds a random number generator.">igraph_rng_seed</a></strong></span>(<span class="strong"><strong><a class="link" href="igraph-Random.html#igraph_rng_default" title="2.1. igraph_rng_default — Query the default random number generator.">igraph_rng_default</a></strong></span>(), 42);
|
||||
|
||||
<span class="strong"><strong>igraph_vector_int_init</strong></span>(&edges, 20);
|
||||
<span class="strong"><strong>for</strong></span> (igraph_int_t i = 0; i < <span class="strong"><strong>igraph_vector_int_size</strong></span>(&edges); i++) {
|
||||
<span class="strong"><strong><a class="link" href="igraph-Data-structures.html#VECTOR" title="2.4.1. VECTOR — Accessing an element of a vector.">VECTOR</a></strong></span>(edges)[i] = <span class="strong"><strong>RNG_INTEGER</strong></span>(0, <span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_vcount" title="5.2.1. igraph_vcount — The number of vertices in a graph.">igraph_vcount</a></strong></span>(&graph) - 1);
|
||||
}
|
||||
|
||||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_add_edges" title="5.3.2. igraph_add_edges — Adds edges to a graph object.">igraph_add_edges</a></strong></span>(&graph, &edges, NULL);
|
||||
<span class="strong"><strong><a class="link" href="igraph-Structural.html#igraph_average_path_length" title="3.20. igraph_average_path_length — The average shortest path length between all vertex pairs.">igraph_average_path_length</a></strong></span>(&graph, NULL, &avg_path_len, NULL,
|
||||
IGRAPH_UNDIRECTED, <span class="emphasis"><em>/* unconn= */</em></span> true);
|
||||
<span class="strong"><strong>printf</strong></span>("Average path length (randomized lattice): %g\n", (double) avg_path_len);
|
||||
|
||||
<span class="strong"><strong>igraph_vector_bool_destroy</strong></span>(&periodic);
|
||||
<span class="strong"><strong>igraph_vector_int_destroy</strong></span>(&dimvector);
|
||||
<span class="strong"><strong>igraph_vector_int_destroy</strong></span>(&edges);
|
||||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_destroy" title="5.1.4. igraph_destroy — Frees the memory allocated for a graph object.">igraph_destroy</a></strong></span>(&graph);
|
||||
|
||||
<span class="strong"><strong>return</strong></span> 0;
|
||||
}
|
||||
</pre>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
This example illustrates some new points. <span class="command"><strong>igraph</strong></span> uses
|
||||
<a class="link" href="igraph-Data-structures.html#igraph_vector_t" title="2.1. About igraph_vector_t objects"><span class="type">igraph_vector_t</span></a>
|
||||
and its related types (<span class="type">igraph_vector_int_t</span>, <span class="type">igraph_vector_bool_t</span>
|
||||
and so on) instead of plain C arrays. <span class="type">igraph_vector_t</span> is superior to
|
||||
regular arrays in almost every sense. Vectors are created by the
|
||||
<a class="link" href="igraph-Data-structures.html#igraph_vector_init" title="2.2.1. igraph_vector_init — Initializes a vector object (constructor)."><code class="function">igraph_vector_init()</code></a>
|
||||
function and, like graphs, they should be destroyed if not
|
||||
needed any more by calling
|
||||
<a class="link" href="igraph-Data-structures.html#igraph_vector_destroy" title="2.2.5. igraph_vector_destroy — Destroys a vector object."><code class="function">igraph_vector_destroy()</code></a>
|
||||
on them. A vector can be indexed by the
|
||||
<a class="link" href="igraph-Data-structures.html#VECTOR" title="2.4.1. VECTOR — Accessing an element of a vector."><code class="function">VECTOR()</code></a> function
|
||||
(right now it is a macro). The elements of a vector are of type <span class="type">igraph_real_t</span>
|
||||
for <a class="link" href="igraph-Data-structures.html#igraph_vector_t" title="2.1. About igraph_vector_t objects"><span class="type">igraph_vector_t</span></a>,
|
||||
and of type <span class="type">igraph_int_t</span> for <span class="type">igraph_vector_int_t</span>.
|
||||
As you might expect, <span class="type">igraph_vector_bool_t</span> holds
|
||||
<span class="type">igraph_bool_t</span> values. Vectors can be resized and most <span class="command"><strong>igraph</strong></span>
|
||||
functions returning the result in a vector automatically resize it to the size they need.
|
||||
</p>
|
||||
<p>
|
||||
<a class="link" href="igraph-Generators.html#igraph_square_lattice" title="4.4. igraph_square_lattice — Arbitrary dimensional square lattices."><code class="function">igraph_square_lattice()</code></a>
|
||||
takes an integer vector argument specifying the dimensions of
|
||||
the lattice. In this example we generate a 30x30 two dimensional
|
||||
periodic lattice. See the documentation of
|
||||
<a class="link" href="igraph-Generators.html#igraph_square_lattice" title="4.4. igraph_square_lattice — Arbitrary dimensional square lattices."><code class="function">igraph_square_lattice()</code></a> in
|
||||
the reference manual for the other arguments.
|
||||
</p>
|
||||
<p>
|
||||
The vertices in a graph are identified by a <span class="emphasis"><em>vertex ID</em></span>, an integer between
|
||||
<code class="code">0</code> and <code class="code">n - 1</code>, where <code class="code">n</code> is the number of vertices in the graph.
|
||||
The vertex count can be retrieved using <a class="link" href="igraph-Basic.html#igraph_vcount" title="5.2.1. igraph_vcount — The number of vertices in a graph."><code class="function">igraph_vcount()</code></a>,
|
||||
as in the example.
|
||||
</p>
|
||||
<p>
|
||||
The <a class="link" href="igraph-Basic.html#igraph_add_edges" title="5.3.2. igraph_add_edges — Adds edges to a graph object."><code class="function">igraph_add_edges()</code></a>
|
||||
function simply takes a graph and a vector of
|
||||
vertex IDs defining the new edges. The first edge is between the first
|
||||
two vertex IDs in the vector, the second edge is between the second
|
||||
two, etc. This way we add ten random edges to the lattice.
|
||||
</p>
|
||||
<p>
|
||||
Note that this example program may add <span class="emphasis"><em>loop edges</em></span>, edges
|
||||
pointing a vertex to itself, or <span class="emphasis"><em>multiple edges</em></span>, more than one edge
|
||||
between the same pair of vertices.
|
||||
<span class="type">igraph_t</span> can of course represent loops and multiple edges, although some
|
||||
routines expect simple graphs, i.e. graphs which contain neither of these. This is because some
|
||||
structural properties are ill-defined for non-simple graphs. Loop and multi-edges can be removed by calling
|
||||
<a class="link" href="igraph-Operators.html#igraph_simplify" title="3.11. igraph_simplify — Removes loop and/or multiple edges from the graph."><code class="function">igraph_simplify()</code></a>.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="tut-lesson-3"></a>3. Calculating various properties of graphs</h2></div></div></div>
|
||||
<p>
|
||||
In our next example we will calculate various centrality measures in a
|
||||
friendship graph. The friendship graph is from the famous Zachary karate
|
||||
club study. (Do a web search on "Zachary karate" if you want to know more about
|
||||
this.) Centrality measures quantify how central is the position of
|
||||
individual vertices in the graph.
|
||||
</p>
|
||||
<pre class="programlisting"><span class="strong"><strong>#include</strong></span> <igraph.h>
|
||||
|
||||
int <span class="strong"><strong>main</strong></span>(void) {
|
||||
igraph_t graph;
|
||||
igraph_vector_int_t result;
|
||||
<a class="link" href="igraph-Data-structures.html#igraph_vector_t" title="2.1. About igraph_vector_t objects">igraph_vector_t</a> result_real;
|
||||
igraph_int_t edges_array[] = {
|
||||
0,1, 0,2, 0,3, 0,4, 0,5, 0,6, 0,7, 0,8,
|
||||
0,10, 0,11, 0,12, 0,13, 0,17, 0,19, 0,21, 0,31,
|
||||
1, 2, 1, 3, 1, 7, 1,13, 1,17, 1,19, 1,21, 1,30,
|
||||
2, 3, 2, 7, 2,27, 2,28, 2,32, 2, 9, 2, 8, 2,13,
|
||||
3, 7, 3,12, 3,13, 4, 6, 4,10, 5, 6, 5,10, 5,16,
|
||||
6,16, 8,30, 8,32, 8,33, 9,33, 13,33, 14,32, 14,33,
|
||||
15,32, 15,33, 18,32, 18,33, 19,33, 20,32, 20,33,
|
||||
22,32, 22,33, 23,25, 23,27, 23,32, 23,33, 23,29,
|
||||
24,25, 24,27, 24,31, 25,31, 26,29, 26,33, 27,33,
|
||||
28,31, 28,33, 29,32, 29,33, 30,32, 30,33, 31,32,
|
||||
31,33, 32,33
|
||||
};
|
||||
igraph_vector_int_t edges =
|
||||
<span class="strong"><strong>igraph_vector_int_view</strong></span>(edges_array, <span class="strong"><strong>sizeof</strong></span>(edges_array) / <span class="strong"><strong>sizeof</strong></span>(edges_array[0]));
|
||||
|
||||
<span class="emphasis"><em>/* Initialize the library. */</em></span>
|
||||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_setup" title="4.1. igraph_setup — Initializes the igraph library.">igraph_setup</a></strong></span>();
|
||||
|
||||
<span class="strong"><strong><a class="link" href="igraph-Generators.html#igraph_create" title="2.1. igraph_create — Creates a graph with the specified edges.">igraph_create</a></strong></span>(&graph, &edges, 0, IGRAPH_UNDIRECTED);
|
||||
|
||||
<span class="strong"><strong>igraph_vector_int_init</strong></span>(&result, 0);
|
||||
<span class="strong"><strong><a class="link" href="igraph-Data-structures.html#igraph_vector_init" title="2.2.1. igraph_vector_init — Initializes a vector object (constructor).">igraph_vector_init</a></strong></span>(&result_real, 0);
|
||||
|
||||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_degree" title="5.2.14. igraph_degree — The degree of some vertices in a graph.">igraph_degree</a></strong></span>(&graph, &result, <span class="strong"><strong><a class="link" href="igraph-Iterators.html#igraph_vss_all" title="4.1. igraph_vss_all — All vertices of a graph (immediate version).">igraph_vss_all</a></strong></span>(), IGRAPH_ALL, IGRAPH_LOOPS);
|
||||
<span class="strong"><strong>printf</strong></span>("Maximum degree is %10" IGRAPH_PRId ", vertex %2" IGRAPH_PRId ".\n",
|
||||
<span class="strong"><strong>igraph_vector_int_max</strong></span>(&result),
|
||||
<span class="strong"><strong>igraph_vector_int_which_max</strong></span>(&result));
|
||||
|
||||
<span class="strong"><strong><a class="link" href="igraph-Structural.html#igraph_closeness" title="11.1. igraph_closeness — Closeness centrality calculations for some vertices.">igraph_closeness</a></strong></span>(&graph, &result_real, NULL, NULL, <span class="strong"><strong><a class="link" href="igraph-Iterators.html#igraph_vss_all" title="4.1. igraph_vss_all — All vertices of a graph (immediate version).">igraph_vss_all</a></strong></span>(),
|
||||
IGRAPH_ALL, <span class="emphasis"><em>/* weights= */</em></span> NULL, <span class="emphasis"><em>/* normalized= */</em></span> false);
|
||||
<span class="strong"><strong>printf</strong></span>("Maximum closeness is %10g, vertex %2" IGRAPH_PRId ".\n",
|
||||
(double) <span class="strong"><strong><a class="link" href="igraph-Data-structures.html#igraph_vector_max" title="2.10.2. igraph_vector_max — Largest element of a vector.">igraph_vector_max</a></strong></span>(&result_real),
|
||||
<span class="strong"><strong><a class="link" href="igraph-Data-structures.html#igraph_vector_which_max" title="2.10.4. igraph_vector_which_max — Gives the index of the maximum element of the vector.">igraph_vector_which_max</a></strong></span>(&result_real));
|
||||
|
||||
<span class="strong"><strong><a class="link" href="igraph-Structural.html#igraph_betweenness" title="11.3. igraph_betweenness — Betweenness centrality of some vertices.">igraph_betweenness</a></strong></span>(&graph, <span class="emphasis"><em>/* weights= */</em></span> NULL, &result_real, <span class="strong"><strong><a class="link" href="igraph-Iterators.html#igraph_vss_all" title="4.1. igraph_vss_all — All vertices of a graph (immediate version).">igraph_vss_all</a></strong></span>(),
|
||||
IGRAPH_UNDIRECTED, <span class="emphasis"><em>/* normalized= */</em></span> false);
|
||||
<span class="strong"><strong>printf</strong></span>("Maximum betweenness is %10g, vertex %2" IGRAPH_PRId ".\n",
|
||||
(double) <span class="strong"><strong><a class="link" href="igraph-Data-structures.html#igraph_vector_max" title="2.10.2. igraph_vector_max — Largest element of a vector.">igraph_vector_max</a></strong></span>(&result_real),
|
||||
<span class="strong"><strong><a class="link" href="igraph-Data-structures.html#igraph_vector_which_max" title="2.10.4. igraph_vector_which_max — Gives the index of the maximum element of the vector.">igraph_vector_which_max</a></strong></span>(&result_real));
|
||||
|
||||
<span class="strong"><strong>igraph_vector_int_destroy</strong></span>(&result);
|
||||
<span class="strong"><strong><a class="link" href="igraph-Data-structures.html#igraph_vector_destroy" title="2.2.5. igraph_vector_destroy — Destroys a vector object.">igraph_vector_destroy</a></strong></span>(&result_real);
|
||||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_destroy" title="5.1.4. igraph_destroy — Frees the memory allocated for a graph object.">igraph_destroy</a></strong></span>(&graph);
|
||||
|
||||
<span class="strong"><strong>return</strong></span> 0;
|
||||
}
|
||||
</pre>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
This example demonstrates some new operations. First of all, it shows a
|
||||
way to create a graph a list of edges stored in a plain C array.
|
||||
Function <a class="link" href="igraph-Data-structures.html#igraph_vector_view" title="2.5.1. igraph_vector_view — Handle a regular C array as a igraph_vector_t."><code class="function">igraph_vector_view()</code></a>
|
||||
creates a <span class="emphasis"><em>view</em></span> of a C array. It does not copy any data,
|
||||
which means that you must not call
|
||||
<a class="link" href="igraph-Data-structures.html#igraph_vector_destroy" title="2.2.5. igraph_vector_destroy — Destroys a vector object."><code class="function">igraph_vector_destroy()</code></a>
|
||||
on a vector created this way. This vector is then used to create the
|
||||
undirected graph.
|
||||
</p>
|
||||
<p>
|
||||
Then the degree, closeness and betweenness centrality of the vertices
|
||||
is calculated and the highest values are printed. Note that the vector
|
||||
<code class="varname">result</code>, into which these functions will write their
|
||||
result, must be initialized first, and also that the functions resize
|
||||
it to be able to hold the result.
|
||||
</p>
|
||||
<p>
|
||||
Notice that in order to print values of type <span class="type">igraph_int_t</span>,
|
||||
we used the <code class="constant">IGRAPH_PRId</code> format macro constant. This
|
||||
macro is similar to the standard <code class="constant">PRI</code> constants defined
|
||||
in <code class="code">stdint.h</code>, and expands to the correct <code class="code">printf</code>
|
||||
format specifier on each platform that <span class="command"><strong>igraph</strong></span> supports.
|
||||
</p>
|
||||
<p>
|
||||
The <a class="link" href="igraph-Iterators.html#igraph_vss_all" title="4.1. igraph_vss_all — All vertices of a graph (immediate version)."><code class="function">igraph_vss_all()</code></a> argument
|
||||
tells the functions to calculate the property for every vertex in the graph.
|
||||
It is shorthand for a <span class="emphasis"><em>vertex selector</em></span>, represented by type
|
||||
<span class="type">igraph_vs_t</span>.
|
||||
Vertex selectors help perform operations on a subset of vertices.
|
||||
You can read more about them in <a class="link" href="igraph-Iterators.html" title="Chapter 9. Vertex and edge selectors and sequences, iterators">one
|
||||
of the following chapters</a>.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
<table class="navigation-footer" width="100%" summary="Navigation footer" cellpadding="2" cellspacing="0"><tr valign="middle">
|
||||
<td align="left"><a accesskey="p" href="igraph-Installation.html"><b>← Chapter 2. Installation</b></a></td>
|
||||
<td align="right"><a accesskey="n" href="igraph-Basic.html"><b>Chapter 4. Basic data types and interface →</b></a></td>
|
||||
</tr></table>
|
||||
</body>
|
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</html>
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|
||||
<link rel="chapter" href="igraph-Error.html" title="Chapter 5. Error handling">
|
||||
<link rel="chapter" href="igraph-Memory.html" title="Chapter 6. Memory (de)allocation">
|
||||
<link rel="chapter" href="igraph-Data-structures.html" title="Chapter 7. Data structure library: vector, matrix, other data types">
|
||||
<link rel="chapter" href="igraph-Random.html" title="Chapter 8. Random numbers">
|
||||
<link rel="chapter" href="igraph-Iterators.html" title="Chapter 9. Vertex and edge selectors and sequences, iterators">
|
||||
<link rel="chapter" href="igraph-Attributes.html" title="Chapter 10. Graph, vertex and edge attributes">
|
||||
<link rel="chapter" href="igraph-Generators.html" title="Chapter 11. Deterministic graph generators">
|
||||
<link rel="chapter" href="igraph-Games.html" title='Chapter 12. Stochastic graph generators ("games")'>
|
||||
<link rel="chapter" href="igraph-Bipartite.html" title="Chapter 13. Bipartite, i.e. two-mode graphs">
|
||||
<link rel="chapter" href="igraph-Spatial.html" title="Chapter 14. Spatial graphs">
|
||||
<link rel="chapter" href="igraph-Operators.html" title="Chapter 15. Graph operators">
|
||||
<link rel="chapter" href="igraph-Visitors.html" title="Chapter 16. Graph visitors">
|
||||
<link rel="chapter" href="igraph-Structural.html" title="Chapter 17. Structural properties of graphs">
|
||||
<link rel="chapter" href="igraph-Cycles.html" title="Chapter 18. Graph cycles">
|
||||
<link rel="chapter" href="igraph-Cliques.html" title="Chapter 19. Cliques and independent vertex sets">
|
||||
<link rel="chapter" href="igraph-Motifs.html" title="Chapter 20. Graph motifs, dyad census and triad census">
|
||||
<link rel="chapter" href="igraph-Isomorphism.html" title="Chapter 21. Graph isomorphism">
|
||||
<link rel="chapter" href="igraph-Coloring.html" title="Chapter 22. Graph coloring">
|
||||
<link rel="chapter" href="igraph-Flows.html" title="Chapter 23. Maximum flows, minimum cuts and related measures">
|
||||
<link rel="chapter" href="igraph-Separators.html" title="Chapter 24. Vertex separators">
|
||||
<link rel="chapter" href="igraph-Community.html" title="Chapter 25. Detecting community structure">
|
||||
<link rel="chapter" href="igraph-Graphlets.html" title="Chapter 26. Graphlets">
|
||||
<link rel="chapter" href="igraph-HRG.html" title="Chapter 27. Hierarchical random graphs">
|
||||
<link rel="chapter" href="igraph-Embedding.html" title="Chapter 28. Embedding of graphs">
|
||||
<link rel="chapter" href="igraph-Layout.html" title="Chapter 29. Generating layouts for graph drawing">
|
||||
<link rel="chapter" href="igraph-Processes.html" title="Chapter 30. Processes on graphs">
|
||||
<link rel="chapter" href="igraph-Foreign.html" title="Chapter 31. Reading and writing graphs from and to files">
|
||||
<link rel="chapter" href="igraph-Linalg.html" title="Chapter 32. Using BLAS, LAPACK and ARPACK for igraph matrices and graphs">
|
||||
<link rel="chapter" href="igraph-Nongraph.html" title="Chapter 33. Non-graph related functions">
|
||||
<link rel="chapter" href="igraph-Advanced.html" title="Chapter 34. Advanced igraph programming">
|
||||
<link rel="chapter" href="igraph-Glossary.html" title="Chapter 35. Glossary">
|
||||
<link rel="chapter" href="igraph-Licenses.html" title="Chapter 36. Licenses for igraph and this manual">
|
||||
<link rel="index" href="ix01.html" title="Index">
|
||||
</head>
|
||||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
||||
<div class="book">
|
||||
<div class="titlepage">
|
||||
<div>
|
||||
<div></div>
|
||||
<div><div class="authorgroup">
|
||||
<div class="author">
|
||||
<h3 class="author">
|
||||
<span class="firstname">Gábor</span> <span class="surname">Csárdi</span>
|
||||
</h3>
|
||||
<div class="affiliation">
|
||||
<span class="orgname">Department of Statistics, Harvard University<br></span><div class="address"><p>1 Oxford street, Cambridge, MA, 02138 USA</p></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="author">
|
||||
<h3 class="author">
|
||||
<span class="firstname">Tamás</span> <span class="surname">Nepusz</span>
|
||||
</h3>
|
||||
<div class="affiliation">
|
||||
<span class="orgname">Department of Biological Physics, Eötvös Loránd University<br></span><div class="address"><p>1/a Pázmány Péter sétány, 1117 Budapest, Hungary</p></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="author">
|
||||
<h3 class="author">
|
||||
<span class="firstname">Vincent</span> <span class="surname">Traag</span>
|
||||
</h3>
|
||||
<div class="affiliation">
|
||||
<span class="orgname">Centre for Science and Technology Studies, Leiden University<br></span><div class="address"><p>Room B5.31, Kolffpad 1, 2333 BN Leiden, Netherlands</p></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="author">
|
||||
<h3 class="author">
|
||||
<span class="firstname">Szabolcs</span> <span class="surname">Horvát</span>
|
||||
</h3>
|
||||
<div class="affiliation">
|
||||
<span class="orgname">Department of Computer Science, Reykjavik University<br></span><div class="address"><p>Menntavegur 1, 102 Reykjavík, Iceland</p></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="author">
|
||||
<h3 class="author">
|
||||
<span class="firstname">Fabio</span> <span class="surname">Zanini</span>
|
||||
</h3>
|
||||
<div class="affiliation">
|
||||
<span class="orgname">Lowy Cancer Research Centre, University of New South Wales<br></span><div class="address"><p>Room 211, Botany and High St, Kensington, NSW, 2033, Australia</p></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="author">
|
||||
<h3 class="author">
|
||||
<span class="firstname">Daniel</span> <span class="surname">Noom</span>
|
||||
</h3>
|
||||
<div class="affiliation">
|
||||
<span class="orgname">jitjit software development<br></span><div class="address"><p>Amsterdam, Netherlands</p></div>
|
||||
</div>
|
||||
</div>
|
||||
</div></div>
|
||||
<div><p class="releaseinfo">1.0.1</p></div>
|
||||
<div><div class="legalnotice">
|
||||
<a name="id-1.1.4"></a><p>This manual is for igraph, version 1.0.1.</p>
|
||||
<p>
|
||||
Copyright (C) 2005-2019 Gábor Csárdi and Tamás Nepusz.
|
||||
Copyright (C) 2020-2025 igraph development team.
|
||||
Permission is granted to copy, distribute and/or modify this document
|
||||
under the terms of the GNU Free Documentation License, Version 1.2
|
||||
or any later version published by the Free Software Foundation;
|
||||
with no Invariant Sections, no Front-Cover Texts, and no Back-Cover
|
||||
Texts. A copy of the license is included in the section entitled
|
||||
<span class="quote">“<span class="quote">GNU Free Documentation License</span>”</span>.
|
||||
</p>
|
||||
</div></div>
|
||||
</div>
|
||||
<hr>
|
||||
</div>
|
||||
<div class="toc"><dl class="toc">
|
||||
<dt><span class="chapter"><a href="igraph-Introduction.html">1. Introduction</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Installation.html">2. Installation</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Tutorial.html">3. Tutorial</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Basic.html">4. Basic data types and interface</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Error.html">5. Error handling</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Memory.html">6. Memory (de)allocation</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Data-structures.html">7. Data structure library: vector, matrix, other data types</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Random.html">8. Random numbers</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Iterators.html">9. Vertex and edge selectors and sequences, iterators</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Attributes.html">10. Graph, vertex and edge attributes</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Generators.html">11. Deterministic graph generators</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Games.html">12. Stochastic graph generators ("games")</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Bipartite.html">13. Bipartite, i.e. two-mode graphs</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Spatial.html">14. Spatial graphs</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Operators.html">15. Graph operators</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Visitors.html">16. Graph visitors</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Structural.html">17. Structural properties of graphs</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Cycles.html">18. Graph cycles</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Cliques.html">19. Cliques and independent vertex sets</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Motifs.html">20. Graph motifs, dyad census and triad census</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Isomorphism.html">21. Graph isomorphism</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Coloring.html">22. Graph coloring</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Flows.html">23. Maximum flows, minimum cuts and related measures</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Separators.html">24. Vertex separators</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Community.html">25. Detecting community structure</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Graphlets.html">26. Graphlets</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-HRG.html">27. Hierarchical random graphs</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Embedding.html">28. Embedding of graphs</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Layout.html">29. Generating layouts for graph drawing</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Processes.html">30. Processes on graphs</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Foreign.html">31. Reading and writing graphs from and to files</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Linalg.html">32. Using BLAS, LAPACK and ARPACK for igraph matrices and graphs</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Nongraph.html">33. Non-graph related functions </a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Advanced.html">34. Advanced igraph programming</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Glossary.html">35. Glossary</a></span></dt>
|
||||
<dt><span class="chapter"><a href="igraph-Licenses.html">36. Licenses for igraph and this manual</a></span></dt>
|
||||
<dt><span class="index"><a href="ix01.html">Index</a></span></dt>
|
||||
</dl></div>
|
||||
</div>
|
||||
<table class="navigation-footer" width="100%" summary="Navigation footer" cellpadding="2" cellspacing="0"><tr valign="middle">
|
||||
<td align="left"></td>
|
||||
<td align="right"><a accesskey="n" href="igraph-Introduction.html"><b>Chapter 1. Introduction →</b></a></td>
|
||||
</tr></table>
|
||||
</body>
|
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</html>
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}
|
||||
ul li.item-links {
|
||||
background: url(images/icon_links.png) no-repeat 0px 3px;
|
||||
}
|
||||
ul li.item-license {
|
||||
background: url(images/icon_license.png) no-repeat 0px 3px;
|
||||
}
|
||||
|
||||
/* Forms */
|
||||
label {
|
||||
display: block;
|
||||
float: left;
|
||||
width: 130px;
|
||||
font-weight: bold;
|
||||
}
|
||||
label.normal {
|
||||
color: #444;
|
||||
}
|
||||
div.explanation {
|
||||
border-left: 130px solid white;
|
||||
font-size: 0.8em;
|
||||
color: #888;
|
||||
}
|
||||
div.example-contents {
|
||||
display: none;
|
||||
}
|
||||
|
||||
.example p.title {
|
||||
color: blue;
|
||||
font-size:0.8em;
|
||||
}
|
||||
.example p.title b:before {
|
||||
content: '\25B6\00a0';
|
||||
}
|
||||
.example p.title:hover {
|
||||
color: #00f;
|
||||
text-decoration: underline;
|
||||
cursor: hand;
|
||||
}
|
||||
|
||||
.warning {
|
||||
background-color: #ffc;
|
||||
padding: 0.2em 1em;
|
||||
border: 1px solid #f80;
|
||||
}
|
||||
.warning .title {
|
||||
color: #f80;
|
||||
}
|
||||
@@ -0,0 +1,23 @@
|
||||
function getElementByClass(element, className) {
|
||||
tc = element.childNodes;
|
||||
for (var i = 0; i < tc.length; i++) {
|
||||
if (tc[i].className == className) { return tc[i]; }
|
||||
}
|
||||
return null;
|
||||
}
|
||||
|
||||
function toggle(target, event) {
|
||||
exdiv = getElementByClass(target, "example");
|
||||
excdiv = getElementByClass(exdiv, "example-contents");
|
||||
titlediv = getElementByClass(exdiv, "title");
|
||||
|
||||
if (!titlediv || !titlediv.contains(event.target)) {
|
||||
return;
|
||||
}
|
||||
|
||||
if (excdiv.style.display != 'block') {
|
||||
excdiv.style.display = 'block';
|
||||
} else {
|
||||
excdiv.style.display = 'none';
|
||||
}
|
||||
}
|
||||
Binary file not shown.
|
After Width: | Height: | Size: 406 B |
Reference in New Issue
Block a user