Abdelrahman Said
521 lines
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521 lines
36 KiB
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<title>Chapter 3. Tutorial</title>
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<link rel="prev" href="igraph-Installation.html" title="Chapter 2. Installation">
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<link rel="chapter" href="igraph-Introduction.html" title="Chapter 1. Introduction">
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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">
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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-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">
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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">
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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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<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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</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-Tutorial"></a>Chapter 3. Tutorial</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-Tutorial.html#tut-lesson-1">1. Compiling programs using igraph</a></span></dt>
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<dt><span class="section"><a href="igraph-Tutorial.html#tut-lesson-2">2. Creating your first graphs</a></span></dt>
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<dt><span class="section"><a href="igraph-Tutorial.html#tut-lesson-3">3. Calculating various properties of 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="tut-lesson-1"></a>1. Compiling programs using igraph</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-Tutorial.html#tut-lesson-1-compiling-with-cmake">1.1. Compiling with CMake</a></span></dt>
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<dt><span class="section"><a href="igraph-Tutorial.html#tut-lesson-1-compiling-without-cmake">1.2. Compiling without CMake</a></span></dt>
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<dt><span class="section"><a href="igraph-Tutorial.html#tut-lesson-1-running-the-program">1.3. Running the program</a></span></dt>
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</dl></div>
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<p>
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The following short example program demonstrates the basic usage of
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the <span class="command"><strong>igraph</strong></span> library. Save it into a file named
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<code class="filename">igraph_test.c</code>.
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</p>
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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_int_t num_vertices = 1000;
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igraph_int_t num_edges = 1000;
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igraph_real_t diameter, mean_degree;
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igraph_t graph;
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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>/* Ensure identical results across runs. */</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="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>(
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&graph, num_vertices, num_edges,
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IGRAPH_UNDIRECTED, IGRAPH_SIMPLE_SW, IGRAPH_EDGE_UNLABELED);
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<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>(
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&graph, <span class="emphasis"><em>/* weights = */</em></span> NULL,
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&diameter,
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<span class="emphasis"><em>/* from = */</em></span> NULL, <span class="emphasis"><em>/* to = */</em></span> NULL,
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<span class="emphasis"><em>/* vertex_path = */</em></span> NULL, <span class="emphasis"><em>/* edge_path = */</em></span> NULL,
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IGRAPH_UNDIRECTED, <span class="emphasis"><em>/* unconn= */</em></span> true);
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<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);
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<span class="strong"><strong>printf</strong></span>("Diameter of a random graph with average degree %g: %g\n",
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mean_degree, diameter);
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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>
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</p>
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<p>
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This example illustrates a couple of points:
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</p>
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<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
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<li class="listitem"><p>
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First, programs
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using the <span class="command"><strong>igraph</strong></span> library should include the
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<code class="filename">igraph.h</code> header
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file. Note that while igraph installs several sub-headers, the organization of these may change
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without notice. Only use <code class="filename">igraph.h</code> in your projects, not any of the sub-headers.
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</p></li>
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<li class="listitem"><p>
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Second, the library must be initialized using
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<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>
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before use.
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</p></li>
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<li class="listitem"><p>
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Third, <span class="command"><strong>igraph</strong></span> uses the
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<span class="type">igraph_int_t</span> type for integers instead of
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<span class="type">int</span> or <span class="type">long int</span>, and it also uses the
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<span class="type">igraph_real_t</span> type for real numbers instead of
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<span class="type">double</span>. Depending on how <span class="command"><strong>igraph</strong></span> was compiled, and whether you are
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using a 32-bit or 64-bit system, <span class="type">igraph_int_t</span> may be a 32-bit
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or 64-bit integer.
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</p></li>
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<li class="listitem"><p>
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Fourth, <span class="command"><strong>igraph</strong></span> graph objects are represented by the <span class="type">igraph_t</span> data
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type.
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</p></li>
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<li class="listitem"><p>
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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>
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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>
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destroys it, i.e. deallocates the memory associated to it.
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</p></li>
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</ul></div>
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<p>
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For compiling this program you need a C compiler. Optionally,
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<a class="ulink" href="https://cmake.org" target="_top">CMake</a> can be used to automate the compilation.
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</p>
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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="tut-lesson-1-compiling-with-cmake"></a>1.1. Compiling with CMake</h3></div></div></div>
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<p>
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It is convenient to use CMake because it can automatically discover the
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necessary compilation flags on all operating systems. Many IDEs support
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CMake, and can work with CMake projects directly. To create a CMake project
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for this example program, create a file name <code class="filename">CMakeLists.txt</code> with the
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following contents:
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</p>
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<pre class="programlisting">
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cmake_minimum_required(VERSION 3.18)
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project(igraph_test)
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find_package(igraph REQUIRED)
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add_executable(igraph_test igraph_test.c)
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target_link_libraries(igraph_test PUBLIC igraph::igraph)
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</pre>
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<p>
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</p>
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<p>
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To compile the project, create a new directory called <code class="filename">build</code> in
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the root of the <span class="command"><strong>igraph</strong></span> source tree, and switch to it:
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</p>
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<pre class="programlisting">
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mkdir build
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cd build
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</pre>
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<p>
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</p>
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<p>
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Run CMake to configure the project:
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</p>
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<pre class="programlisting">
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cmake ..
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</pre>
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<p>
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</p>
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<p>
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If <span class="command"><strong>igraph</strong></span> was installed at a non-standard location, specify its prefix
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using the <code class="option">-DCMAKE_PREFIX_PATH=...</code> option. The prefix must be
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the same directory that was specified as the <code class="option">CMAKE_INSTALL_PREFIX</code>
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when compiling igraph.
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</p>
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<p>
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If configuration has succeeded, build the program using
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</p>
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<pre class="programlisting">
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cmake --build .
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</pre>
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<p>
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</p>
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<div class="note" style="margin-left: 0.5in; margin-right: 0.5in;">
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<h3 class="title">C++ must be enabled in igraph projects</h3>
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<p>Parts of <span class="command"><strong>igraph</strong></span> are implemented in C++; therefore, any CMake target that
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depends on <span class="command"><strong>igraph</strong></span> should use the C++ linker. Furthermore, OpenMP support in
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igraph works correctly only if C++ is enabled in the CMake project. The script
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that finds <span class="command"><strong>igraph</strong></span> on the host machine will throw an error if C++ support is
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not enabled in the CMake project.</p>
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<p>C++ support is enabled by default when no languages are explicitly
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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>
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command, e.g. <code class="code">project(igraph_test)</code>. If you do specify some languages explicitly,
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make sure to also include <code class="code">CXX</code>, e.g. <code class="code">project(igraph_test C CXX)</code>.
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</p>
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</div>
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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="tut-lesson-1-compiling-without-cmake"></a>1.2. Compiling without CMake</h3></div></div></div>
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<p>
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On most Unix-like systems, the default C compiler is called <span class="command"><strong>cc</strong></span>.
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To compile the test program, you will need a command similar to the following:
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</p>
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<pre class="programlisting">
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cc igraph_test.c -I/usr/local/include/igraph -L/usr/local/lib -ligraph -o igraph_test
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</pre>
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<p>
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</p>
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<p>
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The exact form depends on where <span class="command"><strong>igraph</strong></span> was installed on your
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system, whether it was compiled as a shared or static library, and the external
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libraries it was linked to. The directory after the <code class="option">-I</code> switch
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is the one containing the <code class="filename">igraph.h</code> file, while the one
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following <code class="option">-L</code> should contain the library file itself, usually a
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file called <code class="filename">libigraph.a</code> (static library on macOS and
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Linux), <code class="filename">libigraph.so</code> (shared library on Linux),
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<code class="filename">libigraph.dylib</code> (shared library on macOS),
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<code class="filename">igraph.lib</code> (static library on Windows) or
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<code class="filename">igraph.dll</code> (shared library on Windows). If
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<span class="command"><strong>igraph</strong></span> was compiled as a static library, it is also
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necessary to manually link to all of its dependencies.
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</p>
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<p>
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If your system has the <span class="command"><strong>pkg-config</strong></span> utility you are
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likely to get the necessary compile options by issuing the command
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</p>
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<pre class="programlisting">
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pkg-config --libs --cflags igraph
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</pre>
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<p>
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(if <span class="command"><strong>igraph</strong></span> was built as a shared library) or
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</p>
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<pre class="programlisting">
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pkg-config --static --libs --cflags igraph
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</pre>
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<p>
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(if <span class="command"><strong>igraph</strong></span> was built as a static library).
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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="tut-lesson-1-running-the-program"></a>1.3. Running the program</h3></div></div></div>
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<p>
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On most systems, the executable can be run by simply typing its name like this:
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</p>
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<pre class="programlisting">
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./igraph_test
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</pre>
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<p>
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If you use dynamic linking and the <span class="command"><strong>igraph</strong></span>
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library is not installed in a standard place, you may need to add its location to the
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<code class="envar">LD_LIBRARY_PATH</code> (Linux), <code class="envar">DYLD_LIBRARY_PATH</code> (macOS)
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or <code class="envar">PATH</code> (Windows) environment variables. This is typically necessary
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on Windows systems.
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</p>
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</div>
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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="tut-lesson-2"></a>2. Creating your first graphs</h2></div></div></div>
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<p>
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The functions generating graph objects are called graph
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generators. Stochastic (i.e. randomized) graph generators are called
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<span class="quote">“<span class="quote">games</span>”</span>.
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</p>
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<p>
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<span class="command"><strong>igraph</strong></span> can handle directed and undirected graphs. Most graph
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generators are able to create both types of graphs and most other
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functions are usually also capable of handling
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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>,
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which calculates shortest paths from a vertex to other vertices, can calculate
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directed or undirected paths.
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</p>
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<p>
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<span class="command"><strong>igraph</strong></span> has sophisticated ways for creating graphs. The simplest
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graphs are deterministic regular structures like star graphs
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(<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>),
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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
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(<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
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(<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.
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</p>
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<p>
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The following example creates an undirected regular circular lattice,
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adds some random edges to it and calculates the average length of
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shortest paths between all pairs of vertices in the graph before and
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after adding the random edges. (The message is that some random edges
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can reduce path lengths a lot.)
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</p>
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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 dimvector;
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igraph_vector_int_t edges;
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igraph_vector_bool_t periodic;
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igraph_real_t avg_path_len;
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<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>
|
||
</html>
|