Abdelrahman Said
1597 lines
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1597 lines
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<link rel="chapter" href="igraph-Iterators.html" title="Chapter 9. Vertex and edge selectors and sequences, iterators">
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<link rel="chapter" href="igraph-Bipartite.html" title="Chapter 13. Bipartite, i.e. two-mode graphs">
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<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">
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<link rel="chapter" href="igraph-Visitors.html" title="Chapter 16. Graph visitors">
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<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">
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<link rel="chapter" href="igraph-Motifs.html" title="Chapter 20. Graph motifs, dyad census and triad census">
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<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">
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<link rel="chapter" href="igraph-Separators.html" title="Chapter 24. Vertex separators">
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<link rel="chapter" href="igraph-Community.html" title="Chapter 25. Detecting community structure">
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<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">
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<link rel="chapter" href="igraph-Embedding.html" title="Chapter 28. Embedding of graphs">
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<link rel="chapter" href="igraph-Layout.html" title="Chapter 29. Generating layouts for graph drawing">
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<link rel="chapter" href="igraph-Processes.html" title="Chapter 30. Processes on graphs">
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<link rel="chapter" href="igraph-Foreign.html" title="Chapter 31. Reading and writing graphs from and to files">
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<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">
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<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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</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-Bipartite"></a>Chapter 13. Bipartite, i.e. two-mode graphs</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-Bipartite.html#about-bipartite">1. Bipartite networks in igraph</a></span></dt>
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<dt><span class="section"><a href="igraph-Bipartite.html#create-two-mode-networks">2. Create two-mode networks</a></span></dt>
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<dt><span class="section"><a href="igraph-Bipartite.html#bipartite-adjacency-matrices">3. Bipartite adjacency matrices</a></span></dt>
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<dt><span class="section"><a href="igraph-Bipartite.html#project-two-mode-graphs">4. Project two-mode graphs</a></span></dt>
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<dt><span class="section"><a href="igraph-Bipartite.html#other-operations-on-bipartite-graphs">5. Other operations on bipartite graphs</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="about-bipartite"></a>1. Bipartite networks in igraph</h2></div></div></div>
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<p>
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A bipartite network contains two kinds of vertices and connections
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are only possible between two vertices of different kinds. There are
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many natural examples, e.g. movies and actors as vertices and a
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movie is connected to all participating actors, etc.
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</p>
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<p>
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igraph does not have direct support for bipartite networks, at
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least not at the C language level. In other words the igraph_t
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structure does not contain information about the vertex types.
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The C functions for bipartite networks usually have an additional
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input argument to graph, called <code class="constant">types</code>, a boolean vector giving
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the vertex types.
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</p>
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<p>
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Most functions creating bipartite networks are able to create this
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extra vector, you just need to supply an initialized boolean vector
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to them.</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="create-two-mode-networks"></a>2. Create two-mode networks</h2></div></div></div>
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<div class="toc"><dl class="toc">
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<dt><span class="section"><a href="igraph-Bipartite.html#igraph_create_bipartite">2.1. <code class="function">igraph_create_bipartite</code> — Create a bipartite graph.</a></span></dt>
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<dt><span class="section"><a href="igraph-Bipartite.html#igraph_full_bipartite">2.2. <code class="function">igraph_full_bipartite</code> — Creates a complete bipartite graph.</a></span></dt>
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<dt><span class="section"><a href="igraph-Bipartite.html#igraph_bipartite_game_gnm">2.3. <code class="function">igraph_bipartite_game_gnm</code> — Generate a random bipartite graph with a fixed number of edges.</a></span></dt>
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<dt><span class="section"><a href="igraph-Bipartite.html#igraph_bipartite_game_gnp">2.4. <code class="function">igraph_bipartite_game_gnp</code> — Generates a random bipartite graph with a fixed connection probability.</a></span></dt>
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<dt><span class="section"><a href="igraph-Bipartite.html#igraph_bipartite_iea_game">2.5. <code class="function">igraph_bipartite_iea_game</code> — Generates a random bipartite multigraph through independent edge assignment.</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><h3 class="title">
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<a name="igraph_create_bipartite"></a>2.1. <code class="function">igraph_create_bipartite</code> — Create a bipartite graph.</h3></div></div></div>
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<a class="indexterm" name="id-1.14.3.2.2"></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_create_bipartite(igraph_t *graph, const igraph_vector_bool_t *types,
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const igraph_vector_int_t *edges,
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igraph_bool_t directed);
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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 is a simple wrapper function to create a bipartite graph. It
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does a little more than <a class="link" href="igraph-Generators.html#igraph_create" title="2.1. igraph_create — Creates a graph with the specified edges."><code class="function">igraph_create()</code></a>, e.g. it checks that
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the graph is indeed bipartite with respect to the given <em class="parameter"><code>types</code></em>
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vector. If there is an edge connecting two vertices of the same
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kind, then an error is reported.
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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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Pointer to an uninitialized graph object, the result is
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created 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>types</code></em>:</span></p></td>
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<td><p>
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Boolean vector giving the vertex types. The length of
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the vector defines the number of vertices in the 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>edges</code></em>:</span></p></td>
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<td><p>
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Vector giving the edges of the graph. The highest
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vertex ID in this vector must be smaller than the length of the
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<em class="parameter"><code>types</code></em> vector.
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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>directed</code></em>:</span></p></td>
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<td><p>
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Boolean, whether to create a directed graph.
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</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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</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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Time complexity: O(|V|+|E|), linear in the number of vertices and
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edges.
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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-1.14.3.2.8.1"></a><p class="title"><b>Example 13.1. File <code class="code">examples/simple/igraph_bipartite_create.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 g;
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igraph_int_t edges_array[] = {0, 1, 1, 2, 3, 4, 5, 6, 6, 5, 1, 4, 1, 6, 0, 3 };
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igraph_vector_int_t edges =
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<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]));
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igraph_vector_bool_t types;
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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="strong"><strong>igraph_vector_bool_init</strong></span>(&types, <span class="strong"><strong>igraph_vector_int_max</strong></span>(&edges) + 1);
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<span class="strong"><strong>for</strong></span> (igraph_int_t i = 0; i < <span class="strong"><strong>igraph_vector_bool_size</strong></span>(&types); i++) {
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<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>(types)[i] = i % 2;
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}
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<span class="strong"><strong><a class="link" href="igraph-Bipartite.html#igraph_create_bipartite" title="2.1. igraph_create_bipartite — Create a bipartite graph.">igraph_create_bipartite</a></strong></span>(&g, &types, &edges, IGRAPH_DIRECTED);
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<span class="strong"><strong><a class="link" href="igraph-Foreign.html#igraph_write_graph_edgelist" title="1.2. igraph_write_graph_edgelist — Writes the edge list of a graph to a file.">igraph_write_graph_edgelist</a></strong></span>(&g, stdout);
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<span class="strong"><strong>igraph_vector_bool_destroy</strong></span>(&types);
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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>(&g);
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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><h3 class="title">
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<a name="igraph_full_bipartite"></a>2.2. <code class="function">igraph_full_bipartite</code> — Creates a complete bipartite graph.</h3></div></div></div>
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<a class="indexterm" name="id-1.14.3.3.2"></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_full_bipartite(igraph_t *graph,
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igraph_vector_bool_t *types,
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igraph_int_t n1, igraph_int_t n2,
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igraph_bool_t directed,
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igraph_neimode_t mode);
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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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|
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A bipartite network contains two kinds of vertices and connections
|
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are only possible between two vertices of different kind. There are
|
||
many natural examples, e.g. movies and actors as vertices and a
|
||
movie is connected to all participating actors, etc.
|
||
|
||
</p>
|
||
<p>
|
||
igraph does not have direct support for bipartite networks, at
|
||
least not at the C language level. In other words the <span class="type">igraph_t</span>
|
||
structure does not contain information about the vertex types.
|
||
The C functions for bipartite networks usually have an additional
|
||
input argument to graph, called <em class="parameter"><code>types</code></em>, a boolean vector giving
|
||
the vertex types.
|
||
|
||
</p>
|
||
<p>
|
||
Most functions creating bipartite networks are able to create this
|
||
extra vector, you just need to supply an initialized boolean vector
|
||
to them.
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
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||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
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||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<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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Pointer to an uninitialized graph object, the graph will be
|
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created here.
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||
</p></td>
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||
</tr>
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||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>types</code></em>:</span></p></td>
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<td><p>
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||
Pointer to a boolean vector. If not a null pointer,
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||
then the vertex types will be stored here.
|
||
</p></td>
|
||
</tr>
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||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>n1</code></em>:</span></p></td>
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<td><p>
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Integer, the number of vertices of the first kind.
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</p></td>
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||
</tr>
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||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>n2</code></em>:</span></p></td>
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<td><p>
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Integer, the number of vertices of the second kind.
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</p></td>
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</tr>
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||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>directed</code></em>:</span></p></td>
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<td><p>
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Boolean, whether to create a directed graph.
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||
</p></td>
|
||
</tr>
|
||
<tr>
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<td><p><span class="term"><em class="parameter"><code>mode</code></em>:</span></p></td>
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<td><p>
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A constant that gives the type of connections for
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directed graphs. If <code class="constant">IGRAPH_OUT</code>, then edges point from vertices
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of the first kind to vertices of the second kind; if <code class="constant">IGRAPH_IN</code>, then the opposite direction is realized; if <code class="constant">IGRAPH_ALL</code>, then mutual edges will be created.
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||
</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
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<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>
|
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<td><p>
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Error code.
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||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
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||
|
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Time complexity: O(|V|+|E|), linear in the number of vertices and
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edges.
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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">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
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||
</colgroup>
|
||
<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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||
<a class="link" href="igraph-Generators.html#igraph_full" title="7.1. igraph_full — Creates a full graph (complete graph)."><code class="function">igraph_full()</code></a> for non-bipartite complete graphs,
|
||
<a class="link" href="igraph-Generators.html#igraph_full_multipartite" title="7.3. igraph_full_multipartite — Creates a full multipartite graph."><code class="function">igraph_full_multipartite()</code></a> for complete multipartite graphs.
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</p></td>
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||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_bipartite_game_gnm"></a>2.3. <code class="function">igraph_bipartite_game_gnm</code> — Generate a random bipartite graph with a fixed number of edges.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.14.3.4.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_bipartite_game_gnm(
|
||
igraph_t *graph,
|
||
igraph_vector_bool_t *types,
|
||
igraph_int_t n1, igraph_int_t n2, igraph_int_t m,
|
||
igraph_bool_t directed, igraph_neimode_t mode,
|
||
igraph_edge_type_sw_t allowed_edge_types,
|
||
igraph_bool_t edge_labeled);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
The <code class="literal">G(n1, n2, m)</code> model uniformly samples bipartite graphs with
|
||
<em class="parameter"><code>n1</code></em> bottom vertices and <em class="parameter"><code>n2</code></em> top vertices, and precisely <em class="parameter"><code>m</code></em> edges.
|
||
|
||
</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>
|
||
Pointer to an uninitialized igraph graph, the result
|
||
is stored here.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>types</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized boolean vector, or a null
|
||
pointer. If not a null pointer, then the vertex types are stored
|
||
here. Bottom vertices come first, <em class="parameter"><code>n1</code></em> of them, then <em class="parameter"><code>n2</code></em> top
|
||
vertices.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>n1</code></em>:</span></p></td>
|
||
<td><p>
|
||
The number of bottom vertices.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>n2</code></em>:</span></p></td>
|
||
<td><p>
|
||
The number of top vertices.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>m</code></em>:</span></p></td>
|
||
<td><p>
|
||
The number of edges.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>directed</code></em>:</span></p></td>
|
||
<td><p>
|
||
Boolean, whether to generate a directed graph. See
|
||
also the <em class="parameter"><code>mode</code></em> argument.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>mode</code></em>:</span></p></td>
|
||
<td><p>
|
||
Specifies how to direct the edges in directed
|
||
graphs. If it is <code class="constant">IGRAPH_OUT</code>, then directed edges point from
|
||
bottom vertices to top vertices. If it is <code class="constant">IGRAPH_IN</code>, edges
|
||
point from top vertices to bottom vertices. <code class="constant">IGRAPH_OUT</code> and
|
||
<code class="constant">IGRAPH_IN</code> do not generate mutual edges. If this argument is
|
||
<code class="constant">IGRAPH_ALL</code>, then each edge direction is considered
|
||
independently and mutual edges might be generated. This
|
||
argument is ignored for undirected graphs.
|
||
* </p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>allowed_edge_types</code></em>:</span></p></td>
|
||
<td>
|
||
<p>
|
||
The types of edges to allow in the graph.
|
||
</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_SIMPLE_SW</code></span></p></td>
|
||
<td><p>
|
||
|
||
simple graph (i.e. no multi-edges allowed).
|
||
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">IGRAPH_MULTI_SW</code></span></p></td>
|
||
<td><p>
|
||
|
||
multi-edges are allowed
|
||
|
||
</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>edge_labeled</code></em>:</span></p></td>
|
||
<td><p>
|
||
If true, the sampling is done uniformly from the set
|
||
of ordered edge lists. See <a class="link" href="igraph-Bipartite.html#igraph_bipartite_iea_game" title="2.5. igraph_bipartite_iea_game — Generates a random bipartite multigraph through independent edge assignment."><code class="function">igraph_bipartite_iea_game()</code></a> for more
|
||
information. Set this to <code class="constant">false</code> to select the classic Erdős-Rényi model.
|
||
The constants <code class="constant">IGRAPH_EDGE_UNLABELED</code> and <code class="constant">IGRAPH_EDGE_LABELED</code>
|
||
may be used instead of <code class="constant">false</code> and <code class="constant">true</code> for better readability.
|
||
</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-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> for the unipartite version,
|
||
<a class="link" href="igraph-Bipartite.html#igraph_bipartite_game_gnp" title="2.4. igraph_bipartite_game_gnp — Generates a random bipartite graph with a fixed connection probability."><code class="function">igraph_bipartite_game_gnp()</code></a> for the <code class="literal">G(n1, n2, p)</code>
|
||
model.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: O(|V|+|E|), linear in the number of vertices and
|
||
edges.
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_bipartite_game_gnp"></a>2.4. <code class="function">igraph_bipartite_game_gnp</code> — Generates a random bipartite graph with a fixed connection probability.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.14.3.5.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_bipartite_game_gnp(
|
||
igraph_t *graph,
|
||
igraph_vector_bool_t *types,
|
||
igraph_int_t n1, igraph_int_t n2, igraph_real_t p,
|
||
igraph_bool_t directed, igraph_neimode_t mode,
|
||
igraph_edge_type_sw_t allowed_edge_types,
|
||
igraph_bool_t edge_labeled);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
In the <code class="literal">G(n1, n2, p)</code> model, every possible edge between the <em class="parameter"><code>n1</code></em>
|
||
bottom vertices and <em class="parameter"><code>n2</code></em> top vertices is realized independently with
|
||
probability <em class="parameter"><code>p</code></em>. This is equivalent to a maximum entropy model with
|
||
a constraint on the <span class="emphasis"><em>expected</em></span> total edge count. This view allows
|
||
a multigraph extension, in which case <em class="parameter"><code>is</code></em> interpreted as the expected
|
||
number of edges between any vertex pair. See <a class="link" href="igraph-Games.html#igraph_erdos_renyi_game_gnp" title="1.2. igraph_erdos_renyi_game_gnp — Generates a random (Erdős-Rényi) graph with fixed edge probabilities."><code class="function">igraph_erdos_renyi_game_gnp()</code></a>
|
||
for more details.
|
||
|
||
</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>
|
||
Pointer to an uninitialized igraph graph, the result
|
||
is stored here.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>types</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized boolean vector, or a null
|
||
pointer. If not <code class="constant">NULL</code>, then the vertex types are stored
|
||
here. Bottom vertices come first, <em class="parameter"><code>n1</code></em> of them, then <em class="parameter"><code>n2</code></em> top
|
||
vertices.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>n1</code></em>:</span></p></td>
|
||
<td><p>
|
||
The number of bottom vertices.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>n2</code></em>:</span></p></td>
|
||
<td><p>
|
||
The number of top vertices.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>p</code></em>:</span></p></td>
|
||
<td><p>
|
||
The expected number of edges between any vertex pair.
|
||
When multi-edges are disallowed, this is equivalent to the probability
|
||
of having a connection between any two vertices.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>directed</code></em>:</span></p></td>
|
||
<td><p>
|
||
Whether to generate a directed graph. See also
|
||
the <em class="parameter"><code>mode</code></em> argument.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>mode</code></em>:</span></p></td>
|
||
<td><p>
|
||
Specifies how to direct the edges in directed
|
||
graphs. If it is <code class="constant">IGRAPH_OUT</code>, then directed edges point from
|
||
bottom vertices to top vertices. If it is <code class="constant">IGRAPH_IN</code>, edges
|
||
point from top vertices to bottom vertices. <code class="constant">IGRAPH_OUT</code> and
|
||
<code class="constant">IGRAPH_IN</code> do not generate mutual edges. If this argument is
|
||
<code class="constant">IGRAPH_ALL</code>, then each edge direction is considered
|
||
independently and mutual edges might be generated. This
|
||
argument is ignored for undirected graphs.
|
||
* </p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>allowed_edge_types</code></em>:</span></p></td>
|
||
<td>
|
||
<p>
|
||
The types of edges to allow in the graph.
|
||
</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_SIMPLE_SW</code></span></p></td>
|
||
<td><p>
|
||
|
||
simple graph (i.e. no multi-edges allowed).
|
||
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><code class="constant">IGRAPH_MULTI_SW</code></span></p></td>
|
||
<td><p>
|
||
|
||
multi-edges are allowed
|
||
|
||
</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>edge_labeled</code></em>:</span></p></td>
|
||
<td><p>
|
||
If true, the model is defined over the set of ordered
|
||
edge lists, i.e. over the set of edge-labeled graphs. Set it to
|
||
<code class="constant">false</code> to select the classic bipartite Erdős-Rényi model.
|
||
The constants <code class="constant">IGRAPH_EDGE_UNLABELED</code> and <code class="constant">IGRAPH_EDGE_LABELED</code>
|
||
may be used instead of <code class="constant">false</code> and <code class="constant">true</code> for better readability.
|
||
</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-Games.html#igraph_erdos_renyi_game_gnp" title="1.2. igraph_erdos_renyi_game_gnp — Generates a random (Erdős-Rényi) graph with fixed edge probabilities."><code class="function">igraph_erdos_renyi_game_gnp()</code></a> for the unipartite version,
|
||
<a class="link" href="igraph-Bipartite.html#igraph_bipartite_game_gnm" title="2.3. igraph_bipartite_game_gnm — Generate a random bipartite graph with a fixed number of edges."><code class="function">igraph_bipartite_game_gnm()</code></a> for the <code class="literal">G(n1, n2, m)</code> model.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: O(|V|+|E|), linear in the number of vertices and
|
||
edges.
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_bipartite_iea_game"></a>2.5. <code class="function">igraph_bipartite_iea_game</code> — Generates a random bipartite multigraph through independent edge assignment.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.14.3.6.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_bipartite_iea_game(
|
||
igraph_t *graph, igraph_vector_bool_t *types,
|
||
igraph_int_t n1, igraph_int_t n2, igraph_int_t m,
|
||
igraph_bool_t directed, igraph_neimode_t mode);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
</p>
|
||
<div class="warning" style="margin-left: 0.5in; margin-right: 0.5in;">
|
||
<h3 class="title">Warning</h3>
|
||
<p>This function is experimental and its signature is not considered final yet.
|
||
We reserve the right to change the function signature without changing the
|
||
major version of igraph. Use it at your own risk.</p>
|
||
</div>
|
||
<p>This model generates random multigraphs with <em class="parameter"><code>n1</code></em> bottom vertices,
|
||
<em class="parameter"><code>n2</code></em> top vertices and <em class="parameter"><code>m</code></em> edges through independent edge assignment (IEA).
|
||
Each of the <em class="parameter"><code>m</code></em> edges is assigned uniformly at random to a vertex pair,
|
||
independently of each other.
|
||
|
||
</p>
|
||
<p>
|
||
This model does not sample multigraphs uniformly. Undirected graphs are
|
||
generated with probability proportional to
|
||
|
||
</p>
|
||
<p>
|
||
<code class="literal">(prod_(i<j) A_ij !)^(-1)</code>,
|
||
|
||
</p>
|
||
<p>
|
||
where <code class="constant">A</code> denotes the adjacency matrix. The corresponding expression for
|
||
directed graphs is
|
||
|
||
</p>
|
||
<p>
|
||
<code class="literal">(prod_(i,j) A_ij !)^(-1)</code>.
|
||
|
||
</p>
|
||
<p>
|
||
Thus the probability of all simple graphs (which only have 0s and 1s in the
|
||
adjacency matrix) is the same, while that of non-simple ones depends on
|
||
their edge and self-loop multiplicities.
|
||
|
||
</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>
|
||
Pointer to an uninitialized igraph graph, the result
|
||
is stored here.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>types</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized boolean vector, or a <code class="constant">NULL</code>
|
||
pointer. If not <code class="constant">NULL</code>, then the vertex types are stored
|
||
here. Bottom vertices come first, <em class="parameter"><code>n1</code></em> of them, then <em class="parameter"><code>n2</code></em> top
|
||
vertices.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>n1</code></em>:</span></p></td>
|
||
<td><p>
|
||
The number of bottom vertices.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>n2</code></em>:</span></p></td>
|
||
<td><p>
|
||
The number of top vertices.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>m</code></em>:</span></p></td>
|
||
<td><p>
|
||
The number of edges.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>directed</code></em>:</span></p></td>
|
||
<td><p>
|
||
Whether to generate a directed graph. See
|
||
also the <em class="parameter"><code>mode</code></em> argument.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>mode</code></em>:</span></p></td>
|
||
<td><p>
|
||
Specifies how to direct the edges in directed
|
||
graphs. If it is <code class="constant">IGRAPH_OUT</code>, then directed edges point from
|
||
bottom vertices to top vertices. If it is <code class="constant">IGRAPH_IN</code>, edges
|
||
point from top vertices to bottom vertices. <code class="constant">IGRAPH_OUT</code> and
|
||
<code class="constant">IGRAPH_IN</code> do not generate mutual edges. If this argument is
|
||
<code class="constant">IGRAPH_ALL</code>, then each edge direction is considered
|
||
independently and mutual edges might be generated. This
|
||
argument is ignored for undirected graphs.
|
||
</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-Games.html#igraph_iea_game" title="1.3. igraph_iea_game — Generates a random multigraph through independent edge assignment."><code class="function">igraph_iea_game()</code></a> for the unipartite version;
|
||
<a class="link" href="igraph-Bipartite.html#igraph_bipartite_game_gnm" title="2.3. igraph_bipartite_game_gnm — Generate a random bipartite graph with a fixed number of edges."><code class="function">igraph_bipartite_game_gnm()</code></a> to uniformly sample bipartite graphs
|
||
with a given number of vertices and edges.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: O(|V|+|E|), linear in the number of vertices and
|
||
edges.
|
||
|
||
</p>
|
||
</div>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||
<a name="bipartite-adjacency-matrices"></a>3. Bipartite adjacency matrices</h2></div></div></div>
|
||
<div class="toc"><dl class="toc">
|
||
<dt><span class="section"><a href="igraph-Bipartite.html#igraph_biadjacency">3.1. <code class="function">igraph_biadjacency</code> — Creates a bipartite graph from a bipartite adjacency matrix.</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-Bipartite.html#igraph_weighted_biadjacency">3.2. <code class="function">igraph_weighted_biadjacency</code> — Creates a bipartite graph from a weighted bipartite adjacency matrix.</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-Bipartite.html#igraph_get_biadjacency">3.3. <code class="function">igraph_get_biadjacency</code> — Converts a bipartite graph into a bipartite adjacency matrix.</a></span></dt>
|
||
</dl></div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_biadjacency"></a>3.1. <code class="function">igraph_biadjacency</code> — Creates a bipartite graph from a bipartite adjacency matrix.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.14.4.2.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_biadjacency(
|
||
igraph_t *graph,
|
||
igraph_vector_bool_t *types,
|
||
const igraph_matrix_t *biadjmatrix,
|
||
igraph_bool_t directed,
|
||
igraph_neimode_t mode,
|
||
igraph_bool_t multiple);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
A bipartite (or two-mode) graph contains two types of vertices and
|
||
edges always connect vertices of different types. A bipartite adjacency
|
||
matrix is an <span class="emphasis"><em>n</em></span> x <span class="emphasis"><em>m</em></span> matrix, <span class="emphasis"><em>n</em></span> and <span class="emphasis"><em>m</em></span> are the number of vertices
|
||
of the two types, respectively. Nonzero elements in the matrix denote
|
||
edges between the two corresponding vertices.
|
||
|
||
</p>
|
||
<p>
|
||
This function can operate in two modes, depending on the
|
||
<em class="parameter"><code>multiple</code></em> argument. If it is <code class="constant">false</code>, then a single edge is
|
||
created for every non-zero element in the bipartite adjacency matrix. If
|
||
<em class="parameter"><code>multiple</code></em> is <code class="constant">true</code>, then as many edges are created between two
|
||
vertices as the corresponding matrix element. When <em class="parameter"><code>multiple</code></em>
|
||
is set to <code class="constant">true</code>, matrix elements should be whole numbers.
|
||
Otherwise their fractional part will be discarded.
|
||
|
||
</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>
|
||
Pointer to an uninitialized graph object.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>types</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized boolean vector, or a null
|
||
pointer. If not a null pointer, then the vertex types are stored
|
||
here. It is resized as needed.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>biadjmatrix</code></em>:</span></p></td>
|
||
<td><p>
|
||
The bipartite adjacency matrix that serves as an input
|
||
to this function.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>directed</code></em>:</span></p></td>
|
||
<td><p>
|
||
Specifies whether to create an undirected or a directed
|
||
graph.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>mode</code></em>:</span></p></td>
|
||
<td><p>
|
||
Specifies the direction of the edges in a directed
|
||
graph. If <code class="constant">IGRAPH_OUT</code>, then edges point from vertices
|
||
of the first kind (corresponding to rows) to vertices of the
|
||
second kind (corresponding to columns); if <code class="constant">IGRAPH_IN</code>,
|
||
then the opposite direction is realized; if <code class="constant">IGRAPH_ALL</code>,
|
||
then mutual edges will be created.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>multiple</code></em>:</span></p></td>
|
||
<td><p>
|
||
Whether to interpret matrix entries as edge multiplicities,
|
||
see details above.
|
||
</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*m), the size of the bipartite adjacency matrix.
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_weighted_biadjacency"></a>3.2. <code class="function">igraph_weighted_biadjacency</code> — Creates a bipartite graph from a weighted bipartite adjacency matrix.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.14.4.3.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_weighted_biadjacency(
|
||
igraph_t *graph,
|
||
igraph_vector_bool_t *types,
|
||
igraph_vector_t *weights,
|
||
const igraph_matrix_t *biadjmatrix,
|
||
igraph_bool_t directed,
|
||
igraph_neimode_t mode);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
A bipartite (or two-mode) graph contains two types of vertices and
|
||
edges always connect vertices of different types. A bipartite adjacency
|
||
matrix is an <span class="emphasis"><em>n</em></span> x <span class="emphasis"><em>m</em></span> matrix, <span class="emphasis"><em>n</em></span> and <span class="emphasis"><em>m</em></span> are the number of vertices
|
||
of the two types, respectively. Nonzero elements in the matrix denote
|
||
edges between the two corresponding vertices.
|
||
|
||
</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>
|
||
Pointer to an uninitialized graph object.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>types</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized boolean vector, or a null
|
||
pointer. If not a null pointer, then the vertex types are stored
|
||
here. It is resized as needed.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>weights</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized vector, the weights will be stored here.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>biadjmatrix</code></em>:</span></p></td>
|
||
<td><p>
|
||
The bipartite adjacency matrix that serves as an input
|
||
to this function.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>directed</code></em>:</span></p></td>
|
||
<td><p>
|
||
Specifies whether to create an undirected or a directed
|
||
graph.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>mode</code></em>:</span></p></td>
|
||
<td><p>
|
||
Specifies the direction of the edges in a directed
|
||
graph. If <code class="constant">IGRAPH_OUT</code>, then edges point from vertices
|
||
of the first kind (corresponding to rows) to vertices of the
|
||
second kind (corresponding to columns); if <code class="constant">IGRAPH_IN</code>,
|
||
then the opposite direction is realized; if <code class="constant">IGRAPH_ALL</code>,
|
||
then mutual edges will be created.
|
||
</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*m), the size of the bipartite adjacency matrix.
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_get_biadjacency"></a>3.3. <code class="function">igraph_get_biadjacency</code> — Converts a bipartite graph into a bipartite adjacency matrix.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.14.4.4.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_get_biadjacency(
|
||
const igraph_t *graph, const igraph_vector_bool_t *types,
|
||
const igraph_vector_t *weights,
|
||
igraph_matrix_t *res, igraph_vector_int_t *row_ids,
|
||
igraph_vector_int_t *col_ids
|
||
);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
In a bipartite adjacency matrix <code class="constant">A</code>, element <code class="literal">A_ij</code>
|
||
gives the number of edges between the <code class="literal">i</code>th vertex of the
|
||
first partition and the <code class="literal">j</code>th vertex of the second partition.
|
||
|
||
</p>
|
||
<p>
|
||
If the graph contains edges within the same partition, this function
|
||
issues a warning.
|
||
|
||
</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, edge directions are ignored.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>types</code></em>:</span></p></td>
|
||
<td><p>
|
||
Boolean vector containing the vertex types. Vertices belonging
|
||
to the first partition have type <code class="constant">false</code>, the one in the second
|
||
partition type <code class="constant">true</code>.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>weights</code></em>:</span></p></td>
|
||
<td><p>
|
||
A vector specifying a weight for each edge or <code class="constant">NULL</code>.
|
||
If <code class="constant">NULL</code>, all edges are assumed to have weight 1.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized matrix, the result is stored
|
||
here. An element of the matrix gives the number of edges
|
||
(irrespectively of their direction), or sum of edge weights,
|
||
between the two corresponding vertices. The rows will correspond
|
||
to vertices with type <code class="constant">false</code>, the columns correspond to vertices
|
||
with type <code class="constant">true</code>.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>row_ids</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized vector or <code class="constant">NULL</code>.
|
||
If not a null pointer, then the IDs of vertices with type <code class="constant">false</code>
|
||
are stored here, with the same ordering as the rows of the
|
||
biadjacency matrix.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>col_ids</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized vector or <code class="constant">NULL</code>.
|
||
If not a null pointer, then the IDs of vertices with type <code class="constant">true</code>
|
||
are stored here, with the same ordering as the columns of the
|
||
biadjacency matrix.
|
||
</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|) where |E| is 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>
|
||
<a class="link" href="igraph-Bipartite.html#igraph_biadjacency" title="3.1. igraph_biadjacency — Creates a bipartite graph from a bipartite adjacency matrix."><code class="function">igraph_biadjacency()</code></a> for the opposite operation.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
</p>
|
||
</div>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||
<a name="project-two-mode-graphs"></a>4. Project two-mode graphs</h2></div></div></div>
|
||
<div class="toc"><dl class="toc">
|
||
<dt><span class="section"><a href="igraph-Bipartite.html#igraph_bipartite_projection_size">4.1. <code class="function">igraph_bipartite_projection_size</code> — Calculate the number of vertices and edges in the bipartite projections.</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-Bipartite.html#igraph_bipartite_projection">4.2. <code class="function">igraph_bipartite_projection</code> — Create one or both projections of a bipartite (two-mode) network.</a></span></dt>
|
||
</dl></div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_bipartite_projection_size"></a>4.1. <code class="function">igraph_bipartite_projection_size</code> — Calculate the number of vertices and edges in the bipartite projections.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.14.5.2.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_bipartite_projection_size(const igraph_t *graph,
|
||
const igraph_vector_bool_t *types,
|
||
igraph_int_t *vcount1,
|
||
igraph_int_t *ecount1,
|
||
igraph_int_t *vcount2,
|
||
igraph_int_t *ecount2);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
This function calculates the number of vertices and edges in the
|
||
two projections of a bipartite network. This is useful if you have
|
||
a big bipartite network and you want to estimate the amount of
|
||
memory you would need to calculate the projections themselves.
|
||
|
||
</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>
|
||
Boolean vector giving the vertex types of the graph.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>vcount1</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an <code class="constant">igraph_int_t</code>, the number of
|
||
vertices in the first projection is stored here. May be <code class="constant">NULL</code>
|
||
if not needed.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>ecount1</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an <code class="constant">igraph_int_t</code>, the number of
|
||
edges in the first projection is stored here. May be <code class="constant">NULL</code>
|
||
if not needed.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>vcount2</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an <code class="constant">igraph_int_t</code>, the number of
|
||
vertices in the second projection is stored here. May be <code class="constant">NULL</code>
|
||
if not needed.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>ecount2</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an <code class="constant">igraph_int_t</code>, the number of
|
||
edges in the second projection is stored here. May be <code class="constant">NULL</code>
|
||
if not needed.
|
||
</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-Bipartite.html#igraph_bipartite_projection" title="4.2. igraph_bipartite_projection — Create one or both projections of a bipartite (two-mode) network."><code class="function">igraph_bipartite_projection()</code></a> to calculate the actual
|
||
projection.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: O(|V|*d^2+|E|), |V| is the number of vertices, |E|
|
||
is the number of edges, d is the average (total) degree of the
|
||
graphs.
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_bipartite_projection"></a>4.2. <code class="function">igraph_bipartite_projection</code> — Create one or both projections of a bipartite (two-mode) network.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.14.5.3.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_bipartite_projection(const igraph_t *graph,
|
||
const igraph_vector_bool_t *types,
|
||
igraph_t *proj1,
|
||
igraph_t *proj2,
|
||
igraph_vector_int_t *multiplicity1,
|
||
igraph_vector_int_t *multiplicity2,
|
||
igraph_int_t probe1);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
Creates one or both projections of a bipartite graph.
|
||
|
||
</p>
|
||
<p>
|
||
A graph is called bipartite if its vertices can be partitioned into
|
||
two sets, V1 and V2, so that connections only run between V1 and V2,
|
||
but not within V1 or within V2. The <em class="parameter"><code>types</code></em> parameter specifies
|
||
which vertex should be considered a member of one or the other
|
||
partition. The projection to V1 has vertex set V1, and two vertices
|
||
are connected if they have at least one common neighbour in V2.
|
||
The number of common neighbours is returned in <em class="parameter"><code>multiplicity1</code></em>,
|
||
if requested.
|
||
|
||
</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 bipartite input graph. Directedness of the edges
|
||
is ignored.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>types</code></em>:</span></p></td>
|
||
<td><p>
|
||
Boolean vector giving the vertex types of the graph.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>proj1</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an uninitialized graph object, the first
|
||
projection will be created here. It a null pointer, then it is
|
||
ignored, see also the <em class="parameter"><code>probe1</code></em> argument.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>proj2</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an uninitialized graph object, the second
|
||
projection is created here, if it is not a null pointer. See also
|
||
the <em class="parameter"><code>probe1</code></em> argument.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>multiplicity1</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to a vector, or a null pointer. If not
|
||
the latter, then the multiplicity of the edges is stored
|
||
here. E.g. if there is an A-C-B and also an A-D-B triple in the
|
||
bipartite graph (but no more X, such that A-X-B is also in the
|
||
graph), then the multiplicity of the A-B edge in the projection
|
||
will be 2.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>multiplicity2</code></em>:</span></p></td>
|
||
<td><p>
|
||
The same as <code class="constant">multiplicity1</code>, but for the
|
||
other projection.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>probe1</code></em>:</span></p></td>
|
||
<td><p>
|
||
This argument can be used to specify the order of the
|
||
projections in the resulting list. When it is non-negative, then
|
||
it is considered as a vertex ID and the projection containing
|
||
this vertex will be the first one in the result. Setting this
|
||
argument to a non-negative value implies that <code class="constant">proj1</code> must be
|
||
a non-null pointer. If you don't care about the ordering of the
|
||
projections, pass -1 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-Bipartite.html#igraph_bipartite_projection_size" title="4.1. igraph_bipartite_projection_size — Calculate the number of vertices and edges in the bipartite projections."><code class="function">igraph_bipartite_projection_size()</code></a> to calculate the number
|
||
of vertices and edges in the projections, without creating the
|
||
projection graphs themselves.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: O(|V|*d^2+|E|), |V| is the number of vertices, |E|
|
||
is the number of edges, d is the average (total) degree of the
|
||
graphs.
|
||
|
||
</p>
|
||
</div>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||
<a name="other-operations-on-bipartite-graphs"></a>5. Other operations on bipartite graphs</h2></div></div></div>
|
||
<div class="toc"><dl class="toc"><dt><span class="section"><a href="igraph-Bipartite.html#igraph_is_bipartite">5.1. <code class="function">igraph_is_bipartite</code> — Check whether a graph is bipartite.</a></span></dt></dl></div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_is_bipartite"></a>5.1. <code class="function">igraph_is_bipartite</code> — Check whether a graph is bipartite.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.14.6.2.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_is_bipartite(const igraph_t *graph,
|
||
igraph_bool_t *res,
|
||
igraph_vector_bool_t *types);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
This function checks whether a graph is bipartite. It tries
|
||
to find a mapping that gives a possible division of the vertices into two
|
||
classes, such that no two vertices of the same class are connected by an
|
||
edge.
|
||
|
||
</p>
|
||
<p>
|
||
The existence of such a mapping is equivalent of having no circuits of
|
||
odd length in the graph. A graph with loop edges cannot be bipartite.
|
||
|
||
</p>
|
||
<p>
|
||
Note that the mapping is not necessarily unique, e.g. if the graph has
|
||
at least two components, then the vertices in the separate components
|
||
can be mapped independently.
|
||
|
||
</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>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>types</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized boolean vector, or a null
|
||
pointer. If not a null pointer and a mapping was found, then it
|
||
is stored here. If not a null pointer, but no mapping was found,
|
||
the contents of this vector is invalid.
|
||
</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 of vertices and
|
||
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_coloring() to determine if all edges connect
|
||
vertices of different types, given a specific type vector.
|
||
</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-Games.html"><b>← Chapter 12. Stochastic graph generators ("games")</b></a></td>
|
||
<td align="right"><a accesskey="n" href="igraph-Spatial.html"><b>Chapter 14. Spatial graphs →</b></a></td>
|
||
</tr></table>
|
||
</body>
|
||
</html>
|