Abdelrahman Said
2641 lines
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2641 lines
108 KiB
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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-Cliques"></a>Chapter 19. Cliques and independent vertex sets</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-Cliques.html#cliques">1. Cliques</a></span></dt>
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<dt><span class="section"><a href="igraph-Cliques.html#weighted-cliques">2. Weighted cliques</a></span></dt>
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<dt><span class="section"><a href="igraph-Cliques.html#independent-vertex-sets">3. Independent vertex sets</a></span></dt>
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</dl></div>
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<p>
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These functions calculate various graph properties related
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to cliques and independent vertex sets.
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</p>
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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="cliques"></a>1. Cliques</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-Cliques.html#igraph_is_complete">1.1. <code class="function">igraph_is_complete</code> — Decides whether the graph is complete.</a></span></dt>
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<dt><span class="section"><a href="igraph-Cliques.html#igraph_is_clique">1.2. <code class="function">igraph_is_clique</code> — Does a set of vertices form a clique?</a></span></dt>
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<dt><span class="section"><a href="igraph-Cliques.html#igraph_cliques">1.3. <code class="function">igraph_cliques</code> — Finds all or some cliques in a graph.</a></span></dt>
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<dt><span class="section"><a href="igraph-Cliques.html#igraph_clique_size_hist">1.4. <code class="function">igraph_clique_size_hist</code> — Counts cliques of each size in the graph.</a></span></dt>
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<dt><span class="section"><a href="igraph-Cliques.html#igraph_cliques_callback">1.5. <code class="function">igraph_cliques_callback</code> — Calls a function for each clique in the graph.</a></span></dt>
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<dt><span class="section"><a href="igraph-Cliques.html#igraph_clique_handler_t">1.6. <code class="function">igraph_clique_handler_t</code> — Type of clique handler functions.</a></span></dt>
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<dt><span class="section"><a href="igraph-Cliques.html#igraph_largest_cliques">1.7. <code class="function">igraph_largest_cliques</code> — Finds the largest clique(s) in a graph.</a></span></dt>
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<dt><span class="section"><a href="igraph-Cliques.html#igraph_maximal_cliques">1.8. <code class="function">igraph_maximal_cliques</code> — Finds all maximal cliques in a graph.</a></span></dt>
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<dt><span class="section"><a href="igraph-Cliques.html#igraph_maximal_cliques_count">1.9. <code class="function">igraph_maximal_cliques_count</code> — Count the number of maximal cliques in a graph.</a></span></dt>
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<dt><span class="section"><a href="igraph-Cliques.html#igraph_maximal_cliques_file">1.10. <code class="function">igraph_maximal_cliques_file</code> — Find maximal cliques and write them to a file.</a></span></dt>
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<dt><span class="section"><a href="igraph-Cliques.html#igraph_maximal_cliques_subset">1.11. <code class="function">igraph_maximal_cliques_subset</code> — Maximal cliques for a subset of initial vertices.</a></span></dt>
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<dt><span class="section"><a href="igraph-Cliques.html#igraph_maximal_cliques_hist">1.12. <code class="function">igraph_maximal_cliques_hist</code> — Counts the number of maximal cliques of each size in a graph.</a></span></dt>
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<dt><span class="section"><a href="igraph-Cliques.html#igraph_maximal_cliques_callback">1.13. <code class="function">igraph_maximal_cliques_callback</code> — Finds maximal cliques in a graph and calls a function for each one.</a></span></dt>
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<dt><span class="section"><a href="igraph-Cliques.html#igraph_clique_number">1.14. <code class="function">igraph_clique_number</code> — Finds the clique number of the graph.</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_is_complete"></a>1.1. <code class="function">igraph_is_complete</code> — Decides whether the graph is complete.</h3></div></div></div>
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<a class="indexterm" name="id-1.20.3.2.2"></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_is_complete(const igraph_t *graph, igraph_bool_t *res);
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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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A graph is considered complete if all pairs of different vertices are
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adjacent.
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</p>
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<p>
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The null graph and the singleton graph are considered complete.
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</p>
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<p><b>Arguments: </b>
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</p>
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<div class="variablelist"><table border="0" class="variablelist">
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<colgroup>
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<col align="left" valign="top">
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<col>
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</colgroup>
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<tbody>
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<tr>
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<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
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<td><p>
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The graph object to analyze.
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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>res</code></em>:</span></p></td>
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<td><p>
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Pointer to a Boolean variable, the result will be stored here.</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|) at worst.
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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_is_clique"></a>1.2. <code class="function">igraph_is_clique</code> — Does a set of vertices form a clique?</h3></div></div></div>
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<a class="indexterm" name="id-1.20.3.3.2"></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_is_clique(const igraph_t *graph, igraph_vs_t candidate,
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igraph_bool_t directed, igraph_bool_t *res);
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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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Tests if all pairs within a set of vertices are adjacent, i.e. whether they
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form a clique. An empty set and singleton set are considered to be a clique.
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</p>
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<p><b>Arguments: </b>
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</p>
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<div class="variablelist"><table border="0" class="variablelist">
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<colgroup>
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<col align="left" valign="top">
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<col>
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</colgroup>
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<tbody>
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<tr>
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<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
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<td><p>
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The input graph.
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</p></td>
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</tr>
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<tr>
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<td><p><span class="term"><em class="parameter"><code>candidate</code></em>:</span></p></td>
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<td><p>
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The vertex set to test for being a clique.
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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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Whether to take edge directions into account in directed graphs.
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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>res</code></em>:</span></p></td>
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<td><p>
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The result will be stored here.
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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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</p>
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<p><b>See also: </b></p>
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<div class="variablelist"><table border="0" class="variablelist">
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<colgroup>
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<col align="left" valign="top">
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<col>
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</colgroup>
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<tbody><tr>
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<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
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<td><p>
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<a class="link" href="igraph-Cliques.html#igraph_is_complete" title="1.1. igraph_is_complete — Decides whether the graph is complete."><code class="function">igraph_is_complete()</code></a> to test if a graph is complete;
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<a class="link" href="igraph-Cliques.html#igraph_is_independent_vertex_set" title="3.1. igraph_is_independent_vertex_set — Does a set of vertices form an independent set?"><code class="function">igraph_is_independent_vertex_set()</code></a> to test for independent vertex sets;
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<a class="link" href="igraph-Cliques.html#igraph_cliques" title="1.3. igraph_cliques — Finds all or some cliques in a graph."><code class="function">igraph_cliques()</code></a>, <a class="link" href="igraph-Cliques.html#igraph_maximal_cliques" title="1.8. igraph_maximal_cliques — Finds all maximal cliques in a graph."><code class="function">igraph_maximal_cliques()</code></a> and
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<a class="link" href="igraph-Cliques.html#igraph_largest_cliques" title="1.7. igraph_largest_cliques — Finds the largest clique(s) in a graph."><code class="function">igraph_largest_cliques()</code></a> to find cliques.
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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(n^2 log(d)) where n is the number of vertices in the
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candidate set and d is the typical vertex degree.
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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_cliques"></a>1.3. <code class="function">igraph_cliques</code> — Finds all or some cliques in a graph.</h3></div></div></div>
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<a class="indexterm" name="id-1.20.3.4.2"></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_cliques(
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const igraph_t *graph, igraph_vector_int_list_t *res,
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igraph_int_t min_size, igraph_int_t max_size,
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igraph_int_t max_results);
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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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</p>
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<p>
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Cliques are fully connected subgraphs of a graph.
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</p>
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<p>
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If you are only interested in the size of the largest clique in the graph,
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use <a class="link" href="igraph-Cliques.html#igraph_clique_number" title="1.14. igraph_clique_number — Finds the clique number of the graph."><code class="function">igraph_clique_number()</code></a> instead.
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</p>
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<p>The current implementation of this function
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uses version 1.21 of the Cliquer library by Sampo Niskanen and
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Patric R. J. Östergård, <a class="ulink" href="http://users.aalto.fi/~pat/cliquer.html" target="_top">http://users.aalto.fi/~pat/cliquer.html</a>
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</p>
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<p><b>Arguments: </b>
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</p>
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<div class="variablelist"><table border="0" class="variablelist">
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<colgroup>
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<col align="left" valign="top">
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<col>
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||
</colgroup>
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||
<tbody>
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<tr>
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<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
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<td><p>
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The input graph.
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</p></td>
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</tr>
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<tr>
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<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
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<td><p>
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Pointer to an initialized list of integer vectors. The cliques
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will be stored here as vectors of vertex IDs.
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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>min_size</code></em>:</span></p></td>
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<td><p>
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Integer specifying the minimum size of the cliques to be
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returned. If negative or zero, no lower bound will be used.
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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>max_size</code></em>:</span></p></td>
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<td><p>
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Integer specifying the maximum size of the cliques to be
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returned. If negative or zero, no upper bound will be used.
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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>max_results</code></em>:</span></p></td>
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<td><p>
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At most this many cliques will be recorded. If
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negative, or <a class="link" href="igraph-Basic.html#IGRAPH_UNLIMITED" title='6.3. IGRAPH_UNLIMITED — Constant for "do not limit results".'><code class="function">IGRAPH_UNLIMITED</code></a>, no limit is applied.
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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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</p>
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<p><b>See also: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<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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<a class="link" href="igraph-Cliques.html#igraph_largest_cliques" title="1.7. igraph_largest_cliques — Finds the largest clique(s) in a graph."><code class="function">igraph_largest_cliques()</code></a> and <a class="link" href="igraph-Cliques.html#igraph_clique_number" title="1.14. igraph_clique_number — Finds the clique number of the graph."><code class="function">igraph_clique_number()</code></a>.
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</p></td>
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||
</tr></tbody>
|
||
</table></div>
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<p>
|
||
|
||
Time complexity: Exponential
|
||
|
||
</p>
|
||
<div class="hideshow" onClick="toggle(this, event)">
|
||
<div class="example">
|
||
<a name="id-1.20.3.4.13.1"></a><p class="title"><b>Example 19.1. File <code class="code">examples/simple/igraph_cliques.c</code></b></p>
|
||
<div class="example-contents">
|
||
<pre class="programlisting"><span class="strong"><strong>#include</strong></span> <igraph.h>
|
||
<span class="strong"><strong>#include</strong></span> <stdlib.h>
|
||
|
||
int <span class="strong"><strong>compare_vectors</strong></span>(<span class="strong"><strong>const</strong></span> igraph_vector_int_t *v1, <span class="strong"><strong>const</strong></span> igraph_vector_int_t *v2) {
|
||
igraph_int_t s1, s2, i;
|
||
|
||
s1 = <span class="strong"><strong>igraph_vector_int_size</strong></span>(v1);
|
||
s2 = <span class="strong"><strong>igraph_vector_int_size</strong></span>(v2);
|
||
<span class="strong"><strong>if</strong></span> (s1 < s2) {
|
||
<span class="strong"><strong>return</strong></span> -1;
|
||
}
|
||
<span class="strong"><strong>if</strong></span> (s1 > s2) {
|
||
<span class="strong"><strong>return</strong></span> 1;
|
||
}
|
||
<span class="strong"><strong>for</strong></span> (i = 0; i < s1; ++i) {
|
||
<span class="strong"><strong>if</strong></span> (<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>(*v1)[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>(*v2)[i]) {
|
||
<span class="strong"><strong>return</strong></span> -1;
|
||
}
|
||
<span class="strong"><strong>if</strong></span> (<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>(*v1)[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>(*v2)[i]) {
|
||
<span class="strong"><strong>return</strong></span> 1;
|
||
}
|
||
}
|
||
<span class="strong"><strong>return</strong></span> 0;
|
||
}
|
||
|
||
<span class="emphasis"><em>/* Takes a pointer vector of vectors. Sorts each vector, then sorts the pointer vector */</em></span>
|
||
void <span class="strong"><strong>canonicalize_list</strong></span>(igraph_vector_int_list_t *list) {
|
||
igraph_int_t len = <span class="strong"><strong>igraph_vector_int_list_size</strong></span>(list);
|
||
<span class="strong"><strong>for</strong></span> (igraph_int_t i = 0; i < len; ++i) {
|
||
<span class="strong"><strong>igraph_vector_int_sort</strong></span>(<span class="strong"><strong>igraph_vector_int_list_get_ptr</strong></span>(list, i));
|
||
}
|
||
<span class="strong"><strong>igraph_vector_int_list_sort</strong></span>(list, &compare_vectors);
|
||
}
|
||
|
||
<span class="strong"><strong>struct</strong></span> userdata {
|
||
igraph_int_t i;
|
||
igraph_vector_int_list_t *list;
|
||
};
|
||
|
||
<a class="link" href="igraph-Error.html#igraph_error_t" title="3.1. igraph_error_t — Return type for functions returning an error code.">igraph_error_t</a> <span class="strong"><strong>handler</strong></span>(<span class="strong"><strong>const</strong></span> igraph_vector_int_t *clique, void *arg) {
|
||
<span class="strong"><strong>struct</strong></span> userdata *ud;
|
||
igraph_bool_t cont;
|
||
|
||
ud = (<span class="strong"><strong>struct</strong></span> userdata *) arg;
|
||
cont = 1; <span class="emphasis"><em>/* true */</em></span>
|
||
|
||
<span class="strong"><strong>if</strong></span> (<span class="strong"><strong>compare_vectors</strong></span>(clique, <span class="strong"><strong>igraph_vector_int_list_get_ptr</strong></span>(ud->list, ud->i)) != 0) {
|
||
<span class="strong"><strong>printf</strong></span>("igraph_cliques() and igraph_cliques_callback() give different results.\n");
|
||
cont = 0; <span class="emphasis"><em>/* false */</em></span>
|
||
}
|
||
|
||
ud->i += 1;
|
||
|
||
<span class="strong"><strong>return</strong></span> cont ? IGRAPH_SUCCESS : IGRAPH_STOP;
|
||
}
|
||
|
||
void <span class="strong"><strong>test_callback</strong></span>(<span class="strong"><strong>const</strong></span> igraph_t *graph) {
|
||
igraph_vector_int_list_t list;
|
||
<span class="strong"><strong>struct</strong></span> userdata ud;
|
||
|
||
<span class="strong"><strong>igraph_vector_int_list_init</strong></span>(&list, 0);
|
||
<span class="strong"><strong><a class="link" href="igraph-Cliques.html#igraph_cliques" title="1.3. igraph_cliques — Finds all or some cliques in a graph.">igraph_cliques</a></strong></span>(graph, &list, 0, 0, <a class="link" href="igraph-Basic.html#IGRAPH_UNLIMITED" title='6.3. IGRAPH_UNLIMITED — Constant for "do not limit results".'>IGRAPH_UNLIMITED</a>);
|
||
|
||
ud.i = 0;
|
||
ud.list = &list;
|
||
|
||
<span class="strong"><strong><a class="link" href="igraph-Cliques.html#igraph_cliques_callback" title="1.5. igraph_cliques_callback — Calls a function for each clique in the graph.">igraph_cliques_callback</a></strong></span>(graph, 0, 0, &handler, (void *) &ud);
|
||
|
||
<span class="strong"><strong>igraph_vector_int_list_destroy</strong></span>(&list);
|
||
}
|
||
|
||
|
||
int <span class="strong"><strong>main</strong></span>(void) {
|
||
|
||
igraph_t g;
|
||
igraph_vector_int_list_t result;
|
||
igraph_es_t es;
|
||
igraph_int_t omega;
|
||
igraph_int_t i, j, n;
|
||
<span class="strong"><strong>const</strong></span> int params[] = {4, -1, 2, 2, 0, 0, -1, -1};
|
||
|
||
<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-Error.html#igraph_set_warning_handler" title="4.2. igraph_set_warning_handler — Installs a warning handler.">igraph_set_warning_handler</a></strong></span>(<a class="link" href="igraph-Error.html#igraph_warning_handler_ignore" title="4.7. igraph_warning_handler_ignore — Ignores all warnings.">igraph_warning_handler_ignore</a>);
|
||
|
||
<span class="strong"><strong>igraph_vector_int_list_init</strong></span>(&result, 0);
|
||
<span class="strong"><strong><a class="link" href="igraph-Generators.html#igraph_full" title="7.1. igraph_full — Creates a full graph (complete graph).">igraph_full</a></strong></span>(&g, 6, 0, 0);
|
||
<span class="strong"><strong><a class="link" href="igraph-Iterators.html#igraph_es_pairs_small" title="6.9. igraph_es_pairs_small — Edge selector, multiple edges defined by their endpoints as arguments.">igraph_es_pairs_small</a></strong></span>(&es, 0, 0, 1, 0, 2, 3, 5, -1);
|
||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_delete_edges" title="5.3.4. igraph_delete_edges — Removes edges from a graph.">igraph_delete_edges</a></strong></span>(&g, es);
|
||
<span class="strong"><strong><a class="link" href="igraph-Iterators.html#igraph_es_destroy" title="8.3. igraph_es_destroy — Destroys an edge selector object.">igraph_es_destroy</a></strong></span>(&es);
|
||
|
||
<span class="strong"><strong>for</strong></span> (j = 0; j < <span class="strong"><strong>sizeof</strong></span>(params) / (2 * <span class="strong"><strong>sizeof</strong></span>(params[0])); j++) {
|
||
<span class="strong"><strong>if</strong></span> (params[2 * j + 1] != 0) {
|
||
<span class="strong"><strong><a class="link" href="igraph-Cliques.html#igraph_cliques" title="1.3. igraph_cliques — Finds all or some cliques in a graph.">igraph_cliques</a></strong></span>(&g, &result, params[2 * j], params[2 * j + 1], <a class="link" href="igraph-Basic.html#IGRAPH_UNLIMITED" title='6.3. IGRAPH_UNLIMITED — Constant for "do not limit results".'>IGRAPH_UNLIMITED</a>);
|
||
} <span class="strong"><strong>else</strong></span> {
|
||
<span class="strong"><strong><a class="link" href="igraph-Cliques.html#igraph_largest_cliques" title="1.7. igraph_largest_cliques — Finds the largest clique(s) in a graph.">igraph_largest_cliques</a></strong></span>(&g, &result);
|
||
}
|
||
n = <span class="strong"><strong>igraph_vector_int_list_size</strong></span>(&result);
|
||
<span class="strong"><strong>printf</strong></span>("%" IGRAPH_PRId " <a class="link" href="igraph-Cliques.html#cliques" title="1. Cliques">cliques</a> found\n", n);
|
||
<span class="strong"><strong>canonicalize_list</strong></span>(&result);
|
||
<span class="strong"><strong>for</strong></span> (i = 0; i < n; i++) {
|
||
igraph_vector_int_t* v = <span class="strong"><strong>igraph_vector_int_list_get_ptr</strong></span>(&result, i);
|
||
<span class="strong"><strong>igraph_vector_int_print</strong></span>(v);
|
||
}
|
||
}
|
||
|
||
<span class="strong"><strong><a class="link" href="igraph-Cliques.html#igraph_clique_number" title="1.14. igraph_clique_number — Finds the clique number of the graph.">igraph_clique_number</a></strong></span>(&g, &omega);
|
||
<span class="strong"><strong>printf</strong></span>("omega=%" IGRAPH_PRId "\n", omega);
|
||
|
||
<span class="strong"><strong>test_callback</strong></span>(&g);
|
||
|
||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_destroy" title="5.1.4. igraph_destroy — Frees the memory allocated for a graph object.">igraph_destroy</a></strong></span>(&g);
|
||
|
||
<span class="strong"><strong><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.">igraph_kary_tree</a></strong></span>(&g, 5, 2, IGRAPH_TREE_OUT);
|
||
<span class="strong"><strong><a class="link" href="igraph-Cliques.html#igraph_cliques" title="1.3. igraph_cliques — Finds all or some cliques in a graph.">igraph_cliques</a></strong></span>(&g, &result, 5, 5, <a class="link" href="igraph-Basic.html#IGRAPH_UNLIMITED" title='6.3. IGRAPH_UNLIMITED — Constant for "do not limit results".'>IGRAPH_UNLIMITED</a>);
|
||
<span class="strong"><strong>if</strong></span> (<span class="strong"><strong>igraph_vector_int_list_size</strong></span>(&result) != 0) {
|
||
<span class="strong"><strong>return</strong></span> 1;
|
||
}
|
||
|
||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_destroy" title="5.1.4. igraph_destroy — Frees the memory allocated for a graph object.">igraph_destroy</a></strong></span>(&g);
|
||
<span class="strong"><strong>igraph_vector_int_list_destroy</strong></span>(&result);
|
||
|
||
<span class="strong"><strong>return</strong></span> 0;
|
||
}
|
||
</pre>
|
||
<p></p>
|
||
</div>
|
||
</div>
|
||
<br class="example-break">
|
||
</div>
|
||
<p>
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_clique_size_hist"></a>1.4. <code class="function">igraph_clique_size_hist</code> — Counts cliques of each size in the graph.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.20.3.5.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_clique_size_hist(const igraph_t *graph, igraph_vector_t *hist,
|
||
igraph_int_t min_size, igraph_int_t max_size);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
</p>
|
||
<p>
|
||
Cliques are fully connected subgraphs of a graph.
|
||
|
||
</p>
|
||
<p>The current implementation of this function
|
||
uses version 1.21 of the Cliquer library by Sampo Niskanen and
|
||
Patric R. J. Östergård, <a class="ulink" href="http://users.aalto.fi/~pat/cliquer.html" target="_top">http://users.aalto.fi/~pat/cliquer.html</a>
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
The input graph.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>hist</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized vector. The result will be stored
|
||
here. The first element will store the number of size-1 cliques, the second
|
||
element the number of size-2 cliques, etc. For cliques smaller than <em class="parameter"><code>min_size</code></em>,
|
||
zero counts will be returned.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>min_size</code></em>:</span></p></td>
|
||
<td><p>
|
||
Integer specifying the minimum size of the cliques to be
|
||
returned. If negative or zero, no lower bound will be used.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>max_size</code></em>:</span></p></td>
|
||
<td><p>
|
||
Integer specifying the maximum size of the cliques to be
|
||
returned. If negative or zero, no upper bound will be used.
|
||
</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-Cliques.html#igraph_cliques" title="1.3. igraph_cliques — Finds all or some cliques in a graph."><code class="function">igraph_cliques()</code></a> and <a class="link" href="igraph-Cliques.html#igraph_cliques_callback" title="1.5. igraph_cliques_callback — Calls a function for each clique in the graph."><code class="function">igraph_cliques_callback()</code></a>
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: Exponential
|
||
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_cliques_callback"></a>1.5. <code class="function">igraph_cliques_callback</code> — Calls a function for each clique in the graph.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.20.3.6.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_cliques_callback(const igraph_t *graph,
|
||
igraph_int_t min_size, igraph_int_t max_size,
|
||
igraph_clique_handler_t *cliquehandler_fn, void *arg);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
</p>
|
||
<p>
|
||
Cliques are fully connected subgraphs of a graph. This function
|
||
enumerates all cliques within the given size range and calls
|
||
<em class="parameter"><code>cliquehandler_fn</code></em> for each of them. The cliques are passed to the
|
||
callback function as a pointer to an <a class="link" href="igraph-Data-structures.html#igraph_vector_t" title="2.1. About igraph_vector_t objects"><code class="function">igraph_vector_int_t</code></a>. Destroying and
|
||
freeing this vector is left up to the user. Use <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_int_destroy()</code></a>
|
||
to destroy it first, then free it using <a class="link" href="igraph-Memory.html#igraph_free" title="2.4. igraph_free — Deallocates memory that was allocated by igraph functions."><code class="function">igraph_free()</code></a>.
|
||
|
||
</p>
|
||
<p>The current implementation of this function
|
||
uses version 1.21 of the Cliquer library by Sampo Niskanen and
|
||
Patric R. J. Östergård, <a class="ulink" href="http://users.aalto.fi/~pat/cliquer.html" target="_top">http://users.aalto.fi/~pat/cliquer.html</a>
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
The input graph.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>min_size</code></em>:</span></p></td>
|
||
<td><p>
|
||
Integer specifying the minimum size of the cliques to be
|
||
returned. If negative or zero, no lower bound will be used.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>max_size</code></em>:</span></p></td>
|
||
<td><p>
|
||
Integer specifying the maximum size of the cliques to be
|
||
returned. If negative or zero, no upper bound will be used.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>cliquehandler_fn</code></em>:</span></p></td>
|
||
<td><p>
|
||
Callback function to be called for each clique.
|
||
See also <a class="link" href="igraph-Cliques.html#igraph_clique_handler_t" title="1.6. igraph_clique_handler_t — Type of clique handler functions."><code class="function">igraph_clique_handler_t</code></a>.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>arg</code></em>:</span></p></td>
|
||
<td><p>
|
||
Extra argument to supply to <em class="parameter"><code>cliquehandler_fn</code></em>.
|
||
</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-Cliques.html#igraph_cliques" title="1.3. igraph_cliques — Finds all or some cliques in a graph."><code class="function">igraph_cliques()</code></a>
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: Exponential
|
||
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_clique_handler_t"></a>1.6. <code class="function">igraph_clique_handler_t</code> — Type of clique handler functions.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.20.3.7.2"></a><pre class="programlisting">
|
||
typedef igraph_error_t igraph_clique_handler_t(const igraph_vector_int_t *clique, void *arg);
|
||
</pre>
|
||
<p>
|
||
|
||
|
||
Callback type, called when a clique was found.
|
||
|
||
See the details at the documentation of <a class="link" href="igraph-Cliques.html#igraph_cliques_callback" title="1.5. igraph_cliques_callback — Calls a function for each clique in the graph."><code class="function">igraph_cliques_callback()</code></a>.
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>clique</code></em>:</span></p></td>
|
||
<td><p>
|
||
The current clique. The clique is owned by the clique search
|
||
routine. You do not need to destroy or free it if you do not want to store
|
||
it; however, if you want to hold on to it for a longer period of time, you
|
||
need to make a copy of it on your own and store the copy itself.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>arg</code></em>:</span></p></td>
|
||
<td><p>
|
||
This extra argument was passed to <a class="link" href="igraph-Cliques.html#igraph_cliques_callback" title="1.5. igraph_cliques_callback — Calls a function for each clique in the graph."><code class="function">igraph_cliques_callback()</code></a> when it was called.
|
||
</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; <code class="constant">IGRAPH_SUCCESS</code> to continue the search or
|
||
<code class="constant">IGRAPH_STOP</code> to stop the search without signaling an error.
|
||
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_largest_cliques"></a>1.7. <code class="function">igraph_largest_cliques</code> — Finds the largest clique(s) in a graph.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.20.3.8.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_largest_cliques(const igraph_t *graph, igraph_vector_int_list_t *res);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
</p>
|
||
<p>
|
||
A clique is largest (quite intuitively) if there is no other clique
|
||
in the graph which contains more vertices.
|
||
|
||
</p>
|
||
<p>
|
||
Note that this is not necessarily the same as a maximal clique,
|
||
i.e. the largest cliques are always maximal but a maximal clique is
|
||
not always largest.
|
||
|
||
</p>
|
||
<p>The current implementation of this function searches
|
||
for maximal cliques using <a class="link" href="igraph-Cliques.html#igraph_maximal_cliques_callback" title="1.13. igraph_maximal_cliques_callback — Finds maximal cliques in a graph and calls a function for each one."><code class="function">igraph_maximal_cliques_callback()</code></a> and drops
|
||
those that are not the largest.
|
||
|
||
</p>
|
||
<p>The implementation of this function changed between
|
||
igraph 0.5 and 0.6, so the order of the cliques and the order of
|
||
vertices within the cliques will almost surely be different between
|
||
these two versions.
|
||
|
||
</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 an initialized list of integer vectors. The cliques
|
||
will be stored here as vectors of vertex IDs.
|
||
</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-Cliques.html#igraph_cliques" title="1.3. igraph_cliques — Finds all or some cliques in a graph."><code class="function">igraph_cliques()</code></a>, <a class="link" href="igraph-Cliques.html#igraph_maximal_cliques" title="1.8. igraph_maximal_cliques — Finds all maximal cliques in a graph."><code class="function">igraph_maximal_cliques()</code></a>
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: O(3^(|V|/3)) worst case.
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_maximal_cliques"></a>1.8. <code class="function">igraph_maximal_cliques</code> — Finds all maximal cliques in a graph.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.20.3.9.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_maximal_cliques(
|
||
const igraph_t *graph,
|
||
igraph_vector_int_list_t *res,
|
||
igraph_int_t min_size, igraph_int_t max_size,
|
||
igraph_int_t max_results);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
This function lists maximal cliques within a size range, ignoring edge
|
||
directions. A clique is a subset of vertices in which all vertex pairs are
|
||
connected. A <span class="emphasis"><em>maximal</em></span> clique is a clique which is not a strict subset
|
||
of any larger clique.
|
||
|
||
</p>
|
||
<p>
|
||
No guarantees are given about the order in which cliques are returned.
|
||
|
||
</p>
|
||
<p>
|
||
The current implementation uses a modified Bron-Kerbosch algorithm due to
|
||
Eppstein, Löffler and Strash.
|
||
|
||
</p>
|
||
<p>
|
||
Reference:
|
||
|
||
</p>
|
||
<p>
|
||
David Eppstein, Maarten Löffler, Darren Strash:
|
||
Listing All Maximal Cliques in Sparse Graphs in Near-Optimal Time.
|
||
Algorithms and Computation, Lecture Notes in Computer Science,
|
||
volume 6506, pp 403-414 (2010).
|
||
<a class="ulink" href="https://doi.org/10.1007/978-3-642-17517-6_36" target="_top">https://doi.org/10.1007/978-3-642-17517-6_36</a>
|
||
<a class="ulink" href="https://arxiv.org/abs/1006.5440" target="_top">https://arxiv.org/abs/1006.5440</a>
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
The input graph. Edge directions are ignored.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to list of integer vectors. The maximal cliques
|
||
will be returned here as vectors of vertex IDs. Note that vertices
|
||
of a clique may be returned in arbitrary order.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>min_size</code></em>:</span></p></td>
|
||
<td><p>
|
||
Integer giving the minimum size of the cliques to be
|
||
returned. If negative or zero, no lower bound will be used.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>max_size</code></em>:</span></p></td>
|
||
<td><p>
|
||
Integer giving the maximum size of the cliques to be
|
||
returned. If negative or zero, no upper bound will be used.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>max_results</code></em>:</span></p></td>
|
||
<td><p>
|
||
At most this many cliques will be recorded. If
|
||
negative, or <a class="link" href="igraph-Basic.html#IGRAPH_UNLIMITED" title='6.3. IGRAPH_UNLIMITED — Constant for "do not limit results".'><code class="function">IGRAPH_UNLIMITED</code></a>, no limit is applied.
|
||
</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-Cliques.html#igraph_maximal_independent_vertex_sets" title="3.4. igraph_maximal_independent_vertex_sets — Finds all maximal independent vertex sets of a graph."><code class="function">igraph_maximal_independent_vertex_sets()</code></a> to find maximal
|
||
independent sets, which are cliques of the complement graph;
|
||
<a class="link" href="igraph-Cliques.html#igraph_clique_number" title="1.14. igraph_clique_number — Finds the clique number of the graph."><code class="function">igraph_clique_number()</code></a> to find the size of the largest clique;
|
||
<a class="link" href="igraph-Cliques.html#igraph_cliques" title="1.3. igraph_cliques — Finds all or some cliques in a graph."><code class="function">igraph_cliques()</code></a> to find all cliques.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: O(d(n-d)3^(d/3)) worst case, d is the degeneracy
|
||
of the graph, this is typically small for sparse graphs.
|
||
|
||
</p>
|
||
<div class="hideshow" onClick="toggle(this, event)">
|
||
<div class="example">
|
||
<a name="id-1.20.3.9.14.1"></a><p class="title"><b>Example 19.2. File <code class="code">examples/simple/igraph_maximal_cliques.c</code></b></p>
|
||
<div class="example-contents">
|
||
<pre class="programlisting"><span class="strong"><strong>#include</strong></span> <igraph.h>
|
||
|
||
int <span class="strong"><strong>main</strong></span>(void) {
|
||
igraph_t g;
|
||
igraph_vector_int_list_t <a class="link" href="igraph-Cliques.html#cliques" title="1. Cliques">cliques</a>;
|
||
igraph_int_t no;
|
||
|
||
<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_small" title="2.2. igraph_small — Shorthand to create a small graph, giving the edges as arguments.">igraph_small</a></strong></span>(&g, 9, IGRAPH_UNDIRECTED,
|
||
0,1, 0,2, 1,2, 2,3, 3,4, 3, 5, 4,5, 5,6, 6,7, -1);
|
||
<span class="strong"><strong>igraph_vector_int_list_init</strong></span>(&<a class="link" href="igraph-Cliques.html#cliques" title="1. Cliques">cliques</a>, 0);
|
||
<span class="strong"><strong><a class="link" href="igraph-Cliques.html#igraph_maximal_cliques" title="1.8. igraph_maximal_cliques — Finds all maximal cliques in a graph.">igraph_maximal_cliques</a></strong></span>(&g, &<a class="link" href="igraph-Cliques.html#cliques" title="1. Cliques">cliques</a>, <span class="emphasis"><em>/*min_size=*/</em></span> <a class="link" href="igraph-Basic.html#IGRAPH_UNLIMITED" title='6.3. IGRAPH_UNLIMITED — Constant for "do not limit results".'>IGRAPH_UNLIMITED</a>,
|
||
<span class="emphasis"><em>/*max_size=*/</em></span> <a class="link" href="igraph-Basic.html#IGRAPH_UNLIMITED" title='6.3. IGRAPH_UNLIMITED — Constant for "do not limit results".'>IGRAPH_UNLIMITED</a>,
|
||
<span class="emphasis"><em>/*max_results=*/</em></span> <a class="link" href="igraph-Basic.html#IGRAPH_UNLIMITED" title='6.3. IGRAPH_UNLIMITED — Constant for "do not limit results".'>IGRAPH_UNLIMITED</a>);
|
||
<span class="strong"><strong><a class="link" href="igraph-Cliques.html#igraph_maximal_cliques_count" title="1.9. igraph_maximal_cliques_count — Count the number of maximal cliques in a graph.">igraph_maximal_cliques_count</a></strong></span>(&g, &no, <span class="emphasis"><em>/*min_size=*/</em></span> <a class="link" href="igraph-Basic.html#IGRAPH_UNLIMITED" title='6.3. IGRAPH_UNLIMITED — Constant for "do not limit results".'>IGRAPH_UNLIMITED</a>,
|
||
<span class="emphasis"><em>/*max_size=*/</em></span> <a class="link" href="igraph-Basic.html#IGRAPH_UNLIMITED" title='6.3. IGRAPH_UNLIMITED — Constant for "do not limit results".'>IGRAPH_UNLIMITED</a>);
|
||
|
||
<span class="strong"><strong>if</strong></span> (no != <span class="strong"><strong>igraph_vector_int_list_size</strong></span>(&<a class="link" href="igraph-Cliques.html#cliques" title="1. Cliques">cliques</a>)) {
|
||
<span class="strong"><strong>return</strong></span> 1;
|
||
}
|
||
|
||
<span class="strong"><strong>for</strong></span> (igraph_int_t i = 0; i < <span class="strong"><strong>igraph_vector_int_list_size</strong></span>(&<a class="link" href="igraph-Cliques.html#cliques" title="1. Cliques">cliques</a>); i++) {
|
||
igraph_vector_int_t *v = <span class="strong"><strong>igraph_vector_int_list_get_ptr</strong></span>(&<a class="link" href="igraph-Cliques.html#cliques" title="1. Cliques">cliques</a>, i);
|
||
<span class="strong"><strong>igraph_vector_int_print</strong></span>(v);
|
||
}
|
||
|
||
<span class="strong"><strong>igraph_vector_int_list_destroy</strong></span>(&<a class="link" href="igraph-Cliques.html#cliques" title="1. Cliques">cliques</a>);
|
||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_destroy" title="5.1.4. igraph_destroy — Frees the memory allocated for a graph object.">igraph_destroy</a></strong></span>(&g);
|
||
|
||
<span class="strong"><strong>return</strong></span> 0;
|
||
}
|
||
</pre>
|
||
<p></p>
|
||
</div>
|
||
</div>
|
||
<br class="example-break">
|
||
</div>
|
||
<p>
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_maximal_cliques_count"></a>1.9. <code class="function">igraph_maximal_cliques_count</code> — Count the number of maximal cliques in a graph.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.20.3.10.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_maximal_cliques_count(
|
||
const igraph_t *graph,
|
||
igraph_int_t *res,
|
||
igraph_int_t min_size, igraph_int_t max_size);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
See <a class="link" href="igraph-Cliques.html#igraph_maximal_cliques" title="1.8. igraph_maximal_cliques — Finds all maximal cliques in a graph."><code class="function">igraph_maximal_cliques()</code></a> for 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>
|
||
The input graph. Edge directions are ignored.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an <code class="constant">igraph_int_t</code>; the number of maximal
|
||
cliques will be stored here.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>min_size</code></em>:</span></p></td>
|
||
<td><p>
|
||
Integer giving the minimum size of the cliques to be
|
||
returned. If negative or zero, no lower bound will be used.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>max_size</code></em>:</span></p></td>
|
||
<td><p>
|
||
Integer giving the maximum size of the cliques to be
|
||
returned. If negative or zero, no upper bound will be used.
|
||
</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-Cliques.html#igraph_maximal_cliques" title="1.8. igraph_maximal_cliques — Finds all maximal cliques in a graph."><code class="function">igraph_maximal_cliques()</code></a>.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: O(d(n-d)3^(d/3)) worst case, d is the degeneracy
|
||
of the graph, this is typically small for sparse graphs.
|
||
|
||
</p>
|
||
<div class="hideshow" onClick="toggle(this, event)">
|
||
<div class="example">
|
||
<a name="id-1.20.3.10.10.1"></a><p class="title"><b>Example 19.3. File <code class="code">examples/simple/igraph_maximal_cliques.c</code></b></p>
|
||
<div class="example-contents">
|
||
<pre class="programlisting"><span class="strong"><strong>#include</strong></span> <igraph.h>
|
||
|
||
int <span class="strong"><strong>main</strong></span>(void) {
|
||
igraph_t g;
|
||
igraph_vector_int_list_t <a class="link" href="igraph-Cliques.html#cliques" title="1. Cliques">cliques</a>;
|
||
igraph_int_t no;
|
||
|
||
<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_small" title="2.2. igraph_small — Shorthand to create a small graph, giving the edges as arguments.">igraph_small</a></strong></span>(&g, 9, IGRAPH_UNDIRECTED,
|
||
0,1, 0,2, 1,2, 2,3, 3,4, 3, 5, 4,5, 5,6, 6,7, -1);
|
||
<span class="strong"><strong>igraph_vector_int_list_init</strong></span>(&<a class="link" href="igraph-Cliques.html#cliques" title="1. Cliques">cliques</a>, 0);
|
||
<span class="strong"><strong><a class="link" href="igraph-Cliques.html#igraph_maximal_cliques" title="1.8. igraph_maximal_cliques — Finds all maximal cliques in a graph.">igraph_maximal_cliques</a></strong></span>(&g, &<a class="link" href="igraph-Cliques.html#cliques" title="1. Cliques">cliques</a>, <span class="emphasis"><em>/*min_size=*/</em></span> <a class="link" href="igraph-Basic.html#IGRAPH_UNLIMITED" title='6.3. IGRAPH_UNLIMITED — Constant for "do not limit results".'>IGRAPH_UNLIMITED</a>,
|
||
<span class="emphasis"><em>/*max_size=*/</em></span> <a class="link" href="igraph-Basic.html#IGRAPH_UNLIMITED" title='6.3. IGRAPH_UNLIMITED — Constant for "do not limit results".'>IGRAPH_UNLIMITED</a>,
|
||
<span class="emphasis"><em>/*max_results=*/</em></span> <a class="link" href="igraph-Basic.html#IGRAPH_UNLIMITED" title='6.3. IGRAPH_UNLIMITED — Constant for "do not limit results".'>IGRAPH_UNLIMITED</a>);
|
||
<span class="strong"><strong><a class="link" href="igraph-Cliques.html#igraph_maximal_cliques_count" title="1.9. igraph_maximal_cliques_count — Count the number of maximal cliques in a graph.">igraph_maximal_cliques_count</a></strong></span>(&g, &no, <span class="emphasis"><em>/*min_size=*/</em></span> <a class="link" href="igraph-Basic.html#IGRAPH_UNLIMITED" title='6.3. IGRAPH_UNLIMITED — Constant for "do not limit results".'>IGRAPH_UNLIMITED</a>,
|
||
<span class="emphasis"><em>/*max_size=*/</em></span> <a class="link" href="igraph-Basic.html#IGRAPH_UNLIMITED" title='6.3. IGRAPH_UNLIMITED — Constant for "do not limit results".'>IGRAPH_UNLIMITED</a>);
|
||
|
||
<span class="strong"><strong>if</strong></span> (no != <span class="strong"><strong>igraph_vector_int_list_size</strong></span>(&<a class="link" href="igraph-Cliques.html#cliques" title="1. Cliques">cliques</a>)) {
|
||
<span class="strong"><strong>return</strong></span> 1;
|
||
}
|
||
|
||
<span class="strong"><strong>for</strong></span> (igraph_int_t i = 0; i < <span class="strong"><strong>igraph_vector_int_list_size</strong></span>(&<a class="link" href="igraph-Cliques.html#cliques" title="1. Cliques">cliques</a>); i++) {
|
||
igraph_vector_int_t *v = <span class="strong"><strong>igraph_vector_int_list_get_ptr</strong></span>(&<a class="link" href="igraph-Cliques.html#cliques" title="1. Cliques">cliques</a>, i);
|
||
<span class="strong"><strong>igraph_vector_int_print</strong></span>(v);
|
||
}
|
||
|
||
<span class="strong"><strong>igraph_vector_int_list_destroy</strong></span>(&<a class="link" href="igraph-Cliques.html#cliques" title="1. Cliques">cliques</a>);
|
||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_destroy" title="5.1.4. igraph_destroy — Frees the memory allocated for a graph object.">igraph_destroy</a></strong></span>(&g);
|
||
|
||
<span class="strong"><strong>return</strong></span> 0;
|
||
}
|
||
</pre>
|
||
<p></p>
|
||
</div>
|
||
</div>
|
||
<br class="example-break">
|
||
</div>
|
||
<p>
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_maximal_cliques_file"></a>1.10. <code class="function">igraph_maximal_cliques_file</code> — Find maximal cliques and write them to a file.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.20.3.11.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_maximal_cliques_file(
|
||
const igraph_t *graph,
|
||
FILE *outfile,
|
||
igraph_int_t min_size, igraph_int_t max_size,
|
||
igraph_int_t max_results);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
This function enumerates all maximal cliques within a size range
|
||
and writes them to file. See <a class="link" href="igraph-Cliques.html#igraph_maximal_cliques" title="1.8. igraph_maximal_cliques — Finds all maximal cliques in a graph."><code class="function">igraph_maximal_cliques()</code></a> for
|
||
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>
|
||
The input graph. Edge directions are ignored.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>outfile</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to the output file, it should be writable.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>min_size</code></em>:</span></p></td>
|
||
<td><p>
|
||
Integer giving the minimum size of the cliques to be
|
||
returned. If negative or zero, no lower bound will be used.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>max_size</code></em>:</span></p></td>
|
||
<td><p>
|
||
Integer giving the maximum size of the cliques to be
|
||
returned. If negative or zero, no upper bound will be used.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>max_results</code></em>:</span></p></td>
|
||
<td><p>
|
||
At most this many cliques will be output. If
|
||
negative, or <a class="link" href="igraph-Basic.html#IGRAPH_UNLIMITED" title='6.3. IGRAPH_UNLIMITED — Constant for "do not limit results".'><code class="function">IGRAPH_UNLIMITED</code></a>, no limit is applied.
|
||
</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-Cliques.html#igraph_maximal_cliques" title="1.8. igraph_maximal_cliques — Finds all maximal cliques in a graph."><code class="function">igraph_maximal_cliques()</code></a>.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: O(d(n-d)3^(d/3)) worst case, d is the degeneracy
|
||
of the graph, this is typically small for sparse graphs.*
|
||
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_maximal_cliques_subset"></a>1.11. <code class="function">igraph_maximal_cliques_subset</code> — Maximal cliques for a subset of initial vertices.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.20.3.12.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_maximal_cliques_subset(
|
||
const igraph_t *graph, const igraph_vector_int_t *subset,
|
||
igraph_vector_int_list_t *res, igraph_int_t *no, FILE *outfile,
|
||
igraph_int_t min_size, igraph_int_t max_size,
|
||
igraph_int_t max_results);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
This function enumerates all maximal cliques for a subset of initial
|
||
vertices and writes them to file. See <a class="link" href="igraph-Cliques.html#igraph_maximal_cliques" title="1.8. igraph_maximal_cliques — Finds all maximal cliques in a graph."><code class="function">igraph_maximal_cliques()</code></a>
|
||
for 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>
|
||
The input graph. Edge directions are ignored.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>subset</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an <code class="constant">igraph_vector_int_t</code> containing the
|
||
subset of initial vertices.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to a list of integer vectors; the cliques will be
|
||
stored here.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>no</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an <code class="constant">igraph_int_t</code>; the number of maximal
|
||
cliques will be stored here.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>outfile</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an output file or <code class="constant">NULL</code>.
|
||
When not <code class="constant">NULL</code>, the file should be writable.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>min_size</code></em>:</span></p></td>
|
||
<td><p>
|
||
Integer giving the minimum size of the cliques to be
|
||
returned. If negative or zero, no lower bound will be used.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>max_size</code></em>:</span></p></td>
|
||
<td><p>
|
||
Integer giving the maximum size of the cliques to be
|
||
returned. If negative or zero, no upper bound will be used.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>max_results</code></em>:</span></p></td>
|
||
<td><p>
|
||
At most this many cliques will be recorded. If
|
||
negative, or <a class="link" href="igraph-Basic.html#IGRAPH_UNLIMITED" title='6.3. IGRAPH_UNLIMITED — Constant for "do not limit results".'><code class="function">IGRAPH_UNLIMITED</code></a>, no limit is applied.
|
||
</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-Cliques.html#igraph_maximal_cliques" title="1.8. igraph_maximal_cliques — Finds all maximal cliques in a graph."><code class="function">igraph_maximal_cliques()</code></a>.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: O(d(n-d)3^(d/3)) worst case, d is the degeneracy
|
||
of the graph, this is typically small for sparse graphs.
|
||
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_maximal_cliques_hist"></a>1.12. <code class="function">igraph_maximal_cliques_hist</code> — Counts the number of maximal cliques of each size in a graph.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.20.3.13.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_maximal_cliques_hist(
|
||
const igraph_t *graph,
|
||
igraph_vector_t *hist,
|
||
igraph_int_t min_size, igraph_int_t max_size);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
This function counts how many maximal cliques of each size are present in
|
||
the graph. Maximal cliques of size one are simply isolated 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>
|
||
The input graph. Edge directions are ignored.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>hist</code></em>:</span></p></td>
|
||
<td><p>
|
||
Pointer to an initialized vector. The result will be stored
|
||
here. The first element will store the number of size-1 maximal cliques,
|
||
the second element the number of size-2 maximal cliques, etc.
|
||
For cliques smaller than <em class="parameter"><code>min_size</code></em>, zero counts will be returned.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>min_size</code></em>:</span></p></td>
|
||
<td><p>
|
||
Integer giving the minimum size of the cliques to be
|
||
returned. If negative or zero, no lower bound will be used.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>max_size</code></em>:</span></p></td>
|
||
<td><p>
|
||
Integer giving the maximum size of the cliques to be
|
||
returned. If negative or zero, no upper bound will be used.
|
||
</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-Cliques.html#igraph_maximal_cliques" title="1.8. igraph_maximal_cliques — Finds all maximal cliques in a graph."><code class="function">igraph_maximal_cliques()</code></a>, <a class="link" href="igraph-Cliques.html#igraph_clique_size_hist" title="1.4. igraph_clique_size_hist — Counts cliques of each size in the graph."><code class="function">igraph_clique_size_hist()</code></a>.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: O(d(n-d)3^(d/3)) worst case, d is the degeneracy
|
||
of the graph, this is typically small for sparse graphs.
|
||
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_maximal_cliques_callback"></a>1.13. <code class="function">igraph_maximal_cliques_callback</code> — Finds maximal cliques in a graph and calls a function for each one.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.20.3.14.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_maximal_cliques_callback(
|
||
const igraph_t *graph,
|
||
igraph_int_t min_size, igraph_int_t max_size,
|
||
igraph_clique_handler_t *cliquehandler_fn, void *arg);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
This function enumerates all maximal cliques within the given size range
|
||
and calls <em class="parameter"><code>cliquehandler_fn</code></em> for each of them. The cliques are passed to the
|
||
callback function as a pointer to an <a class="link" href="igraph-Data-structures.html#igraph_vector_t" title="2.1. About igraph_vector_t objects"><code class="function">igraph_vector_int_t</code></a>. The vector is
|
||
owned by the maximal clique search routine so users are expected to make a
|
||
copy of the vector using <a class="link" href="igraph-Data-structures.html#igraph_vector_init_copy" title="2.2.3. igraph_vector_init_copy — Initializes a vector from another vector object (constructor)."><code class="function">igraph_vector_int_init_copy()</code></a> if they want to
|
||
hold on to it.
|
||
|
||
</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>cliquehandler_fn</code></em>:</span></p></td>
|
||
<td><p>
|
||
Callback function to be called for each clique.
|
||
See also <a class="link" href="igraph-Cliques.html#igraph_clique_handler_t" title="1.6. igraph_clique_handler_t — Type of clique handler functions."><code class="function">igraph_clique_handler_t</code></a>.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>arg</code></em>:</span></p></td>
|
||
<td><p>
|
||
Extra argument to supply to <em class="parameter"><code>cliquehandler_fn</code></em>.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>min_size</code></em>:</span></p></td>
|
||
<td><p>
|
||
Integer giving the minimum size of the cliques to be
|
||
returned. If negative or zero, no lower bound will be used.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>max_size</code></em>:</span></p></td>
|
||
<td><p>
|
||
Integer giving the maximum size of the cliques to be
|
||
returned. If negative or zero, no upper bound will be used.
|
||
</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-Cliques.html#igraph_maximal_cliques" title="1.8. igraph_maximal_cliques — Finds all maximal cliques in a graph."><code class="function">igraph_maximal_cliques()</code></a>, <a class="link" href="igraph-Cliques.html#igraph_cliques_callback" title="1.5. igraph_cliques_callback — Calls a function for each clique in the graph."><code class="function">igraph_cliques_callback()</code></a>.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: O(d(n-d)3^(d/3)) worst case, d is the degeneracy
|
||
of the graph, this is typically small for sparse graphs.
|
||
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_clique_number"></a>1.14. <code class="function">igraph_clique_number</code> — Finds the clique number of the graph.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.20.3.15.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_clique_number(const igraph_t *graph, igraph_int_t *no);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
</p>
|
||
<p>
|
||
The clique number of a graph is the size of the largest clique.
|
||
|
||
</p>
|
||
<p>The current implementation of this function searches
|
||
for maximal cliques using <a class="link" href="igraph-Cliques.html#igraph_maximal_cliques_callback" title="1.13. igraph_maximal_cliques_callback — Finds maximal cliques in a graph and calls a function for each one."><code class="function">igraph_maximal_cliques_callback()</code></a> and keeps
|
||
track of the size of the largest clique that was found.
|
||
|
||
</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>no</code></em>:</span></p></td>
|
||
<td><p>
|
||
The clique number will be returned to the <code class="constant">igraph_int_t</code>
|
||
pointed by this variable.
|
||
</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-Cliques.html#igraph_cliques" title="1.3. igraph_cliques — Finds all or some cliques in a graph."><code class="function">igraph_cliques()</code></a>, <a class="link" href="igraph-Cliques.html#igraph_largest_cliques" title="1.7. igraph_largest_cliques — Finds the largest clique(s) in a graph."><code class="function">igraph_largest_cliques()</code></a>.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: O(3^(|V|/3)) worst case.
|
||
|
||
</p>
|
||
</div>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||
<a name="weighted-cliques"></a>2. Weighted cliques</h2></div></div></div>
|
||
<div class="toc"><dl class="toc">
|
||
<dt><span class="section"><a href="igraph-Cliques.html#igraph_weighted_cliques">2.1. <code class="function">igraph_weighted_cliques</code> — Finds all cliques in a given weight range in a vertex weighted graph.</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-Cliques.html#igraph_largest_weighted_cliques">2.2. <code class="function">igraph_largest_weighted_cliques</code> — Finds the largest weight clique(s) in a graph.</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-Cliques.html#igraph_weighted_clique_number">2.3. <code class="function">igraph_weighted_clique_number</code> — Finds the weight of the largest weight clique in the graph.</a></span></dt>
|
||
</dl></div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_weighted_cliques"></a>2.1. <code class="function">igraph_weighted_cliques</code> — Finds all cliques in a given weight range in a vertex weighted graph.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.20.4.2.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_weighted_cliques(
|
||
const igraph_t *graph, const igraph_vector_t *vertex_weights,
|
||
igraph_vector_int_list_t *res,
|
||
igraph_bool_t maximal,
|
||
igraph_real_t min_weight, igraph_real_t max_weight,
|
||
igraph_int_t max_results);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
</p>
|
||
<p>
|
||
Cliques are fully connected subgraphs of a graph.
|
||
The weight of a clique is the sum of the weights
|
||
of individual vertices within the clique.
|
||
|
||
</p>
|
||
<p>
|
||
Only positive integer vertex weights are supported.
|
||
|
||
</p>
|
||
<p>
|
||
The current implementation of this function
|
||
uses version 1.21 of the Cliquer library by Sampo Niskanen and
|
||
Patric R. J. Östergård, <a class="ulink" href="http://users.aalto.fi/~pat/cliquer.html" target="_top">http://users.aalto.fi/~pat/cliquer.html</a>
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
The input graph.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>vertex_weights</code></em>:</span></p></td>
|
||
<td><p>
|
||
A vector of vertex weights. The current implementation
|
||
will truncate all weights to their integer parts. You may pass <code class="constant">NULL</code>
|
||
here to make each vertex have a weight of 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 list of integer vectors. The cliques
|
||
will be stored here as vectors of vertex IDs.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>maximal</code></em>:</span></p></td>
|
||
<td><p>
|
||
If true, only maximal cliques will be returned
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>min_weight</code></em>:</span></p></td>
|
||
<td><p>
|
||
Integer specifying the minimum weight of the cliques to be
|
||
returned. If negative or zero, no lower bound will be used.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>max_weight</code></em>:</span></p></td>
|
||
<td><p>
|
||
Integer specifying the maximum weight of the cliques to be
|
||
returned. If negative or zero, no upper bound will be used.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>max_results</code></em>:</span></p></td>
|
||
<td><p>
|
||
At most this many cliques will be recorded. If
|
||
negative, or <a class="link" href="igraph-Basic.html#IGRAPH_UNLIMITED" title='6.3. IGRAPH_UNLIMITED — Constant for "do not limit results".'><code class="function">IGRAPH_UNLIMITED</code></a>, no limit is applied.
|
||
</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-Cliques.html#igraph_cliques" title="1.3. igraph_cliques — Finds all or some cliques in a graph."><code class="function">igraph_cliques()</code></a>, <a class="link" href="igraph-Cliques.html#igraph_maximal_cliques" title="1.8. igraph_maximal_cliques — Finds all maximal cliques in a graph."><code class="function">igraph_maximal_cliques()</code></a>
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: Exponential
|
||
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_largest_weighted_cliques"></a>2.2. <code class="function">igraph_largest_weighted_cliques</code> — Finds the largest weight clique(s) in a graph.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.20.4.3.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_largest_weighted_cliques(const igraph_t *graph,
|
||
const igraph_vector_t *vertex_weights, igraph_vector_int_list_t *res);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
The weight of a clique is the sum of the weights of its vertices.
|
||
This function finds the clique(s) having the largest weight in the graph.
|
||
|
||
</p>
|
||
<p>
|
||
Only positive integer vertex weights are supported.
|
||
|
||
</p>
|
||
<p>
|
||
The current implementation of this function
|
||
uses version 1.21 of the Cliquer library by Sampo Niskanen and
|
||
Patric R. J. Östergård, <a class="ulink" href="http://users.aalto.fi/~pat/cliquer.html" target="_top">http://users.aalto.fi/~pat/cliquer.html</a>
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
The input graph.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>vertex_weights</code></em>:</span></p></td>
|
||
<td><p>
|
||
A vector of vertex weights. The current implementation
|
||
will truncate all weights to their integer parts. You may pass <code class="constant">NULL</code>
|
||
here to make each vertex have a weight of 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 list of integer vectors. The cliques
|
||
will be stored here as vectors of vertex IDs.
|
||
</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-Cliques.html#igraph_weighted_cliques" title="2.1. igraph_weighted_cliques — Finds all cliques in a given weight range in a vertex weighted graph."><code class="function">igraph_weighted_cliques()</code></a>, <a class="link" href="igraph-Cliques.html#igraph_weighted_clique_number" title="2.3. igraph_weighted_clique_number — Finds the weight of the largest weight clique in the graph."><code class="function">igraph_weighted_clique_number()</code></a>, <a class="link" href="igraph-Cliques.html#igraph_largest_cliques" title="1.7. igraph_largest_cliques — Finds the largest clique(s) in a graph."><code class="function">igraph_largest_cliques()</code></a>
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: TODO
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_weighted_clique_number"></a>2.3. <code class="function">igraph_weighted_clique_number</code> — Finds the weight of the largest weight clique in the graph.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.20.4.4.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_weighted_clique_number(const igraph_t *graph,
|
||
const igraph_vector_t *vertex_weights, igraph_real_t *res);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
The weight of a clique is the sum of the weights of its vertices.
|
||
This function finds the weight of the largest weight clique.
|
||
|
||
</p>
|
||
<p>
|
||
Only positive integer vertex weights are supported.
|
||
|
||
</p>
|
||
<p>
|
||
The current implementation of this function
|
||
uses version 1.21 of the Cliquer library by Sampo Niskanen and
|
||
Patric R. J. Östergård, <a class="ulink" href="http://users.aalto.fi/~pat/cliquer.html" target="_top">http://users.aalto.fi/~pat/cliquer.html</a>
|
||
|
||
</p>
|
||
<p><b>Arguments: </b>
|
||
</p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>graph</code></em>:</span></p></td>
|
||
<td><p>
|
||
The input graph.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>vertex_weights</code></em>:</span></p></td>
|
||
<td><p>
|
||
A vector of vertex weights. The current implementation
|
||
will truncate all weights to their integer parts. You may pass <code class="constant">NULL</code>
|
||
here to make each vertex have a weight of 1.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||
<td><p>
|
||
The largest weight will be returned to the <code class="constant">igraph_real_t</code>
|
||
pointed to by this variable.
|
||
</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-Cliques.html#igraph_weighted_cliques" title="2.1. igraph_weighted_cliques — Finds all cliques in a given weight range in a vertex weighted graph."><code class="function">igraph_weighted_cliques()</code></a>, <a class="link" href="igraph-Cliques.html#igraph_largest_weighted_cliques" title="2.2. igraph_largest_weighted_cliques — Finds the largest weight clique(s) in a graph."><code class="function">igraph_largest_weighted_cliques()</code></a>, <a class="link" href="igraph-Cliques.html#igraph_clique_number" title="1.14. igraph_clique_number — Finds the clique number of the graph."><code class="function">igraph_clique_number()</code></a>
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: TODO
|
||
|
||
|
||
</p>
|
||
</div>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||
<a name="independent-vertex-sets"></a>3. Independent vertex sets</h2></div></div></div>
|
||
<div class="toc"><dl class="toc">
|
||
<dt><span class="section"><a href="igraph-Cliques.html#igraph_is_independent_vertex_set">3.1. <code class="function">igraph_is_independent_vertex_set</code> — Does a set of vertices form an independent set?</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-Cliques.html#igraph_independent_vertex_sets">3.2. <code class="function">igraph_independent_vertex_sets</code> — Finds all independent vertex sets in a graph.</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-Cliques.html#igraph_largest_independent_vertex_sets">3.3. <code class="function">igraph_largest_independent_vertex_sets</code> — Finds the largest independent vertex set(s) in a graph.</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-Cliques.html#igraph_maximal_independent_vertex_sets">3.4. <code class="function">igraph_maximal_independent_vertex_sets</code> — Finds all maximal independent vertex sets of a graph.</a></span></dt>
|
||
<dt><span class="section"><a href="igraph-Cliques.html#igraph_independence_number">3.5. <code class="function">igraph_independence_number</code> — Finds the independence number of the graph.</a></span></dt>
|
||
</dl></div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_is_independent_vertex_set"></a>3.1. <code class="function">igraph_is_independent_vertex_set</code> — Does a set of vertices form an independent set?</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.20.5.2.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_is_independent_vertex_set(const igraph_t *graph, igraph_vs_t candidate,
|
||
igraph_bool_t *res);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
|
||
Tests if no pairs within a set of vertices are adjacenct, i.e. whether they
|
||
form an independent set. An empty set and singleton set are both considered
|
||
to be an independent set.
|
||
|
||
</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>candidate</code></em>:</span></p></td>
|
||
<td><p>
|
||
The vertex set to test for being an independent set.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>res</code></em>:</span></p></td>
|
||
<td><p>
|
||
The result will be stored here.
|
||
</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<p>
|
||
</p>
|
||
<p><b>Returns: </b></p>
|
||
<div class="variablelist"><table border="0" class="variablelist">
|
||
<colgroup>
|
||
<col align="left" valign="top">
|
||
<col>
|
||
</colgroup>
|
||
<tbody><tr>
|
||
<td><p><span class="term"><em class="parameter"><code></code></em></span></p></td>
|
||
<td><p>
|
||
Error code.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
</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-Cliques.html#igraph_is_clique" title="1.2. igraph_is_clique — Does a set of vertices form a clique?"><code class="function">igraph_is_clique()</code></a> to test for cliques; <a class="link" href="igraph-Cliques.html#igraph_independent_vertex_sets" title="3.2. igraph_independent_vertex_sets — Finds all independent vertex sets in a graph."><code class="function">igraph_independent_vertex_sets()</code></a>,
|
||
<a class="link" href="igraph-Cliques.html#igraph_maximal_independent_vertex_sets" title="3.4. igraph_maximal_independent_vertex_sets — Finds all maximal independent vertex sets of a graph."><code class="function">igraph_maximal_independent_vertex_sets()</code></a> and
|
||
<a class="link" href="igraph-Cliques.html#igraph_largest_independent_vertex_sets" title="3.3. igraph_largest_independent_vertex_sets — Finds the largest independent vertex set(s) in a graph."><code class="function">igraph_largest_independent_vertex_sets()</code></a> to find independent vertex sets.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: O(n^2 log(d)) where n is the number of vertices in the
|
||
candidate set and d is the typical vertex degree.
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_independent_vertex_sets"></a>3.2. <code class="function">igraph_independent_vertex_sets</code> — Finds all independent vertex sets in a graph.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.20.5.3.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_independent_vertex_sets(
|
||
const igraph_t *graph,
|
||
igraph_vector_int_list_t *res,
|
||
igraph_int_t min_size, igraph_int_t max_size,
|
||
igraph_int_t max_results);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
</p>
|
||
<p>
|
||
A vertex set is considered independent if there are no edges between
|
||
them.
|
||
|
||
</p>
|
||
<p>
|
||
If you are interested in the size of the largest independent vertex set,
|
||
use <a class="link" href="igraph-Cliques.html#igraph_independence_number" title="3.5. igraph_independence_number — Finds the independence number of the graph."><code class="function">igraph_independence_number()</code></a> instead.
|
||
|
||
</p>
|
||
<p>
|
||
The current implementation was ported to igraph from the Very Nauty Graph
|
||
Library by Keith Briggs and uses the algorithm from the paper
|
||
S. Tsukiyama, M. Ide, H. Ariyoshi and I. Shirawaka. A new algorithm
|
||
for generating all the maximal independent sets. SIAM J Computing,
|
||
6:505--517, 1977.
|
||
|
||
</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 an initialized list of integer vectors. The cliques
|
||
will be stored here as vectors of vertex IDs.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>min_size</code></em>:</span></p></td>
|
||
<td><p>
|
||
Integer specifying the minimum size of the sets to be
|
||
returned. If negative or zero, no lower bound will be used.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>max_size</code></em>:</span></p></td>
|
||
<td><p>
|
||
Integer specifying the maximum size of the sets to be
|
||
returned. If negative or zero, no upper bound will be used.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>max_results</code></em>:</span></p></td>
|
||
<td><p>
|
||
At most this many independent vertex sets will be recorded.
|
||
If negative, or <a class="link" href="igraph-Basic.html#IGRAPH_UNLIMITED" title='6.3. IGRAPH_UNLIMITED — Constant for "do not limit results".'><code class="function">IGRAPH_UNLIMITED</code></a>, no limit is applied.
|
||
</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-Cliques.html#igraph_largest_independent_vertex_sets" title="3.3. igraph_largest_independent_vertex_sets — Finds the largest independent vertex set(s) in a graph."><code class="function">igraph_largest_independent_vertex_sets()</code></a>,
|
||
<a class="link" href="igraph-Cliques.html#igraph_independence_number" title="3.5. igraph_independence_number — Finds the independence number of the graph."><code class="function">igraph_independence_number()</code></a>.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: TODO
|
||
|
||
</p>
|
||
<div class="hideshow" onClick="toggle(this, event)">
|
||
<div class="example">
|
||
<a name="id-1.20.5.3.13.1"></a><p class="title"><b>Example 19.4. File <code class="code">examples/simple/igraph_independent_sets.c</code></b></p>
|
||
<div class="example-contents">
|
||
<pre class="programlisting"><span class="strong"><strong>#include</strong></span> <igraph.h>
|
||
<span class="strong"><strong>#include</strong></span> <stdlib.h>
|
||
|
||
int <span class="strong"><strong>main</strong></span>(void) {
|
||
|
||
igraph_t g;
|
||
igraph_vector_int_list_t result;
|
||
igraph_int_t n;
|
||
igraph_int_t alpha;
|
||
<span class="strong"><strong>const</strong></span> int params[] = {4, -1, 2, 2, 0, 0, -1, -1};
|
||
|
||
<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_list_init</strong></span>(&result, 0);
|
||
|
||
<span class="strong"><strong><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.">igraph_kary_tree</a></strong></span>(&g, 5, 2, IGRAPH_TREE_OUT);
|
||
<span class="strong"><strong>for</strong></span> (size_t j = 0; j < <span class="strong"><strong>sizeof</strong></span>(params) / (2 * <span class="strong"><strong>sizeof</strong></span>(params[0])); j++) {
|
||
<span class="strong"><strong>if</strong></span> (params[2 * j + 1] != 0) {
|
||
<span class="strong"><strong><a class="link" href="igraph-Cliques.html#igraph_independent_vertex_sets" title="3.2. igraph_independent_vertex_sets — Finds all independent vertex sets in a graph.">igraph_independent_vertex_sets</a></strong></span>(&g, &result, params[2 * j], params[2 * j + 1], <a class="link" href="igraph-Basic.html#IGRAPH_UNLIMITED" title='6.3. IGRAPH_UNLIMITED — Constant for "do not limit results".'>IGRAPH_UNLIMITED</a>);
|
||
} <span class="strong"><strong>else</strong></span> {
|
||
<span class="strong"><strong><a class="link" href="igraph-Cliques.html#igraph_largest_independent_vertex_sets" title="3.3. igraph_largest_independent_vertex_sets — Finds the largest independent vertex set(s) in a graph.">igraph_largest_independent_vertex_sets</a></strong></span>(&g, &result);
|
||
}
|
||
n = <span class="strong"><strong>igraph_vector_int_list_size</strong></span>(&result);
|
||
<span class="strong"><strong>printf</strong></span>("%" IGRAPH_PRId " independent sets found\n", n);
|
||
<span class="strong"><strong>for</strong></span> (igraph_int_t i = 0; i < n; i++) {
|
||
<span class="strong"><strong>igraph_vector_int_print</strong></span>(<span class="strong"><strong>igraph_vector_int_list_get_ptr</strong></span>(&result, i));
|
||
}
|
||
}
|
||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_destroy" title="5.1.4. igraph_destroy — Frees the memory allocated for a graph object.">igraph_destroy</a></strong></span>(&g);
|
||
|
||
<span class="strong"><strong><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.">igraph_kary_tree</a></strong></span>(&g, 10, 2, IGRAPH_TREE_OUT);
|
||
<span class="strong"><strong><a class="link" href="igraph-Cliques.html#igraph_maximal_independent_vertex_sets" title="3.4. igraph_maximal_independent_vertex_sets — Finds all maximal independent vertex sets of a graph.">igraph_maximal_independent_vertex_sets</a></strong></span>(&g, &result, <a class="link" href="igraph-Basic.html#IGRAPH_UNLIMITED" title='6.3. IGRAPH_UNLIMITED — Constant for "do not limit results".'>IGRAPH_UNLIMITED</a>, <a class="link" href="igraph-Basic.html#IGRAPH_UNLIMITED" title='6.3. IGRAPH_UNLIMITED — Constant for "do not limit results".'>IGRAPH_UNLIMITED</a>, <a class="link" href="igraph-Basic.html#IGRAPH_UNLIMITED" title='6.3. IGRAPH_UNLIMITED — Constant for "do not limit results".'>IGRAPH_UNLIMITED</a>);
|
||
n = <span class="strong"><strong>igraph_vector_int_list_size</strong></span>(&result);
|
||
<span class="strong"><strong>printf</strong></span>("%" IGRAPH_PRId " maximal independent sets found\n", n);
|
||
<span class="strong"><strong>for</strong></span> (igraph_int_t i = 0; i < n; i++) {
|
||
<span class="strong"><strong>igraph_vector_int_print</strong></span>(<span class="strong"><strong>igraph_vector_int_list_get_ptr</strong></span>(&result, i));
|
||
}
|
||
|
||
<span class="strong"><strong><a class="link" href="igraph-Cliques.html#igraph_maximal_independent_vertex_sets" title="3.4. igraph_maximal_independent_vertex_sets — Finds all maximal independent vertex sets of a graph.">igraph_maximal_independent_vertex_sets</a></strong></span>(&g, &result, 4, 5, <a class="link" href="igraph-Basic.html#IGRAPH_UNLIMITED" title='6.3. IGRAPH_UNLIMITED — Constant for "do not limit results".'>IGRAPH_UNLIMITED</a>);
|
||
n = <span class="strong"><strong>igraph_vector_int_list_size</strong></span>(&result);
|
||
<span class="strong"><strong>printf</strong></span>("%" IGRAPH_PRId " maximal independent sets between sizes 4 and 5 found\n", n);
|
||
<span class="strong"><strong>for</strong></span> (igraph_int_t i = 0; i < n; i++) {
|
||
<span class="strong"><strong>igraph_vector_int_print</strong></span>(<span class="strong"><strong>igraph_vector_int_list_get_ptr</strong></span>(&result, i));
|
||
}
|
||
|
||
<span class="strong"><strong><a class="link" href="igraph-Cliques.html#igraph_independence_number" title="3.5. igraph_independence_number — Finds the independence number of the graph.">igraph_independence_number</a></strong></span>(&g, &alpha);
|
||
<span class="strong"><strong>printf</strong></span>("alpha=%" IGRAPH_PRId "\n", alpha);
|
||
|
||
<span class="strong"><strong><a class="link" href="igraph-Basic.html#igraph_destroy" title="5.1.4. igraph_destroy — Frees the memory allocated for a graph object.">igraph_destroy</a></strong></span>(&g);
|
||
|
||
<span class="strong"><strong>igraph_vector_int_list_destroy</strong></span>(&result);
|
||
|
||
<span class="strong"><strong>return</strong></span> 0;
|
||
}
|
||
</pre>
|
||
<p></p>
|
||
</div>
|
||
</div>
|
||
<br class="example-break">
|
||
</div>
|
||
<p>
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_largest_independent_vertex_sets"></a>3.3. <code class="function">igraph_largest_independent_vertex_sets</code> — Finds the largest independent vertex set(s) in a graph.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.20.5.4.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_largest_independent_vertex_sets(const igraph_t *graph,
|
||
igraph_vector_int_list_t *res);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
</p>
|
||
<p>
|
||
An independent vertex set is largest if there is no other
|
||
independent vertex set with more vertices in the graph.
|
||
|
||
</p>
|
||
<p>
|
||
The current implementation was ported to igraph from the Very Nauty Graph
|
||
Library by Keith Briggs and uses the algorithm from the paper
|
||
S. Tsukiyama, M. Ide, H. Ariyoshi and I. Shirawaka. A new algorithm
|
||
for generating all the maximal independent sets. SIAM J Computing,
|
||
6:505--517, 1977.
|
||
|
||
</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 an initialized list of integer vectors. The cliques
|
||
will be stored here as vectors of vertex IDs.
|
||
</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-Cliques.html#igraph_independent_vertex_sets" title="3.2. igraph_independent_vertex_sets — Finds all independent vertex sets in a graph."><code class="function">igraph_independent_vertex_sets()</code></a>, <a class="link" href="igraph-Cliques.html#igraph_maximal_independent_vertex_sets" title="3.4. igraph_maximal_independent_vertex_sets — Finds all maximal independent vertex sets of a graph."><code class="function">igraph_maximal_independent_vertex_sets()</code></a>.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: TODO
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_maximal_independent_vertex_sets"></a>3.4. <code class="function">igraph_maximal_independent_vertex_sets</code> — Finds all maximal independent vertex sets of a graph.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.20.5.5.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_maximal_independent_vertex_sets(
|
||
const igraph_t *graph,
|
||
igraph_vector_int_list_t *res,
|
||
igraph_int_t min_size, igraph_int_t max_size,
|
||
igraph_int_t max_results);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
</p>
|
||
<p>
|
||
A maximal independent vertex set is an independent vertex set which
|
||
can't be extended any more by adding a new vertex to it.
|
||
|
||
</p>
|
||
<p>
|
||
The algorithm used here is based on the following paper:
|
||
S. Tsukiyama, M. Ide, H. Ariyoshi and I. Shirawaka. A new algorithm for
|
||
generating all the maximal independent sets. SIAM J Computing,
|
||
6:505--517, 1977.
|
||
|
||
</p>
|
||
<p>
|
||
The implementation was originally written by Kevin O'Neill and modified
|
||
by K M Briggs in the Very Nauty Graph Library. I simply re-wrote it to
|
||
use igraph's data structures.
|
||
|
||
</p>
|
||
<p>
|
||
If you are interested in the size of the largest independent vertex set,
|
||
use <a class="link" href="igraph-Cliques.html#igraph_independence_number" title="3.5. igraph_independence_number — Finds the independence number of the graph."><code class="function">igraph_independence_number()</code></a> instead.
|
||
|
||
</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 an initialized list of integer vectors. The cliques
|
||
will be stored here as vectors of vertex IDs.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>min_size</code></em>:</span></p></td>
|
||
<td><p>
|
||
Integer specifying the minimum size of the sets to be
|
||
returned. If negative or zero, no lower bound will be used.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>max_size</code></em>:</span></p></td>
|
||
<td><p>
|
||
Integer specifying the maximum size of the sets to be
|
||
returned. If negative or zero, no upper bound will be used.
|
||
</p></td>
|
||
</tr>
|
||
<tr>
|
||
<td><p><span class="term"><em class="parameter"><code>max_results</code></em>:</span></p></td>
|
||
<td><p>
|
||
At most this many independent vertex sets will be recorded.
|
||
If negative, or <a class="link" href="igraph-Basic.html#IGRAPH_UNLIMITED" title='6.3. IGRAPH_UNLIMITED — Constant for "do not limit results".'><code class="function">IGRAPH_UNLIMITED</code></a>, no limit is applied.
|
||
</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-Cliques.html#igraph_maximal_cliques" title="1.8. igraph_maximal_cliques — Finds all maximal cliques in a graph."><code class="function">igraph_maximal_cliques()</code></a>, <a class="link" href="igraph-Cliques.html#igraph_independence_number" title="3.5. igraph_independence_number — Finds the independence number of the graph."><code class="function">igraph_independence_number()</code></a>
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: TODO.
|
||
|
||
</p>
|
||
</div>
|
||
<div class="section">
|
||
<div class="titlepage"><div><div><h3 class="title">
|
||
<a name="igraph_independence_number"></a>3.5. <code class="function">igraph_independence_number</code> — Finds the independence number of the graph.</h3></div></div></div>
|
||
<a class="indexterm" name="id-1.20.5.6.2"></a><p>
|
||
</p>
|
||
<div class="informalexample"><pre class="programlisting">
|
||
igraph_error_t igraph_independence_number(const igraph_t *graph, igraph_int_t *no);
|
||
</pre></div>
|
||
<p>
|
||
</p>
|
||
<p>
|
||
|
||
|
||
|
||
</p>
|
||
<p>
|
||
The independence number of a graph is the cardinality of the largest
|
||
independent vertex set.
|
||
|
||
</p>
|
||
<p>
|
||
The current implementation was ported to igraph from the Very Nauty Graph
|
||
Library by Keith Briggs and uses the algorithm from the paper
|
||
S. Tsukiyama, M. Ide, H. Ariyoshi and I. Shirawaka. A new algorithm
|
||
for generating all the maximal independent sets. SIAM J Computing,
|
||
6:505--517, 1977.
|
||
|
||
</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>no</code></em>:</span></p></td>
|
||
<td><p>
|
||
The independence number will be returned to the <code class="constant">igraph_int_t</code> pointed by this variable.
|
||
</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-Cliques.html#igraph_independent_vertex_sets" title="3.2. igraph_independent_vertex_sets — Finds all independent vertex sets in a graph."><code class="function">igraph_independent_vertex_sets()</code></a>.
|
||
</p></td>
|
||
</tr></tbody>
|
||
</table></div>
|
||
<p>
|
||
|
||
Time complexity: TODO.
|
||
|
||
</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-Cycles.html"><b>← Chapter 18. Graph cycles</b></a></td>
|
||
<td align="right"><a accesskey="n" href="igraph-Motifs.html"><b>Chapter 20. Graph motifs, dyad census and triad census →</b></a></td>
|
||
</tr></table>
|
||
</body>
|
||
</html>
|