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<h1>Source code for networkx.algorithms.community.kclique</h1><div class="highlight"><pre>
<span class="c">#-*- coding: utf-8 -*-</span>
<span class="c"># Copyright (C) 2011 by </span>
<span class="c"># Conrad Lee <conradlee@gmail.com></span>
<span class="c"># Aric Hagberg <hagberg@lanl.gov></span>
<span class="c"># All rights reserved.</span>
<span class="c"># BSD license.</span>
<span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">defaultdict</span>
<span class="kn">import</span> <span class="nn">networkx</span> <span class="kn">as</span> <span class="nn">nx</span>
<span class="n">__author__</span> <span class="o">=</span> <span class="s">"""</span><span class="se">\n</span><span class="s">"""</span><span class="o">.</span><span class="n">join</span><span class="p">([</span><span class="s">'Conrad Lee <conradlee@gmail.com>'</span><span class="p">,</span>
<span class="s">'Aric Hagberg <aric.hagberg@gmail.com>'</span><span class="p">])</span>
<span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span><span class="s">'k_clique_communities'</span><span class="p">]</span>
<div class="viewcode-block" id="k_clique_communities"><a class="viewcode-back" href="../../../../reference/generated/networkx.algorithms.community.kclique.k_clique_communities.html#networkx.algorithms.community.kclique.k_clique_communities">[docs]</a><span class="k">def</span> <span class="nf">k_clique_communities</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">cliques</span><span class="o">=</span><span class="bp">None</span><span class="p">):</span>
<span class="sd">"""Find k-clique communities in graph using the percolation method.</span>
<span class="sd"> A k-clique community is the union of all cliques of size k that</span>
<span class="sd"> can be reached through adjacent (sharing k-1 nodes) k-cliques.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : NetworkX graph</span>
<span class="sd"> k : int</span>
<span class="sd"> Size of smallest clique</span>
<span class="sd"> cliques: list or generator </span>
<span class="sd"> Precomputed cliques (use networkx.find_cliques(G))</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> Yields sets of nodes, one for each k-clique community.</span>
<span class="sd"> Examples</span>
<span class="sd"> --------</span>
<span class="sd"> >>> G = nx.complete_graph(5)</span>
<span class="sd"> >>> K5 = nx.convert_node_labels_to_integers(G,first_label=2)</span>
<span class="sd"> >>> G.add_edges_from(K5.edges())</span>
<span class="sd"> >>> c = list(nx.k_clique_communities(G, 4))</span>
<span class="sd"> >>> list(c[0])</span>
<span class="sd"> [0, 1, 2, 3, 4, 5, 6]</span>
<span class="sd"> >>> list(nx.k_clique_communities(G, 6))</span>
<span class="sd"> []</span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> .. [1] Gergely Palla, Imre Derényi, Illés Farkas1, and Tamás Vicsek,</span>
<span class="sd"> Uncovering the overlapping community structure of complex networks </span>
<span class="sd"> in nature and society Nature 435, 814-818, 2005,</span>
<span class="sd"> doi:10.1038/nature03607</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">k</span> <span class="o"><</span> <span class="mi">2</span><span class="p">:</span>
<span class="k">raise</span> <span class="n">nx</span><span class="o">.</span><span class="n">NetworkXError</span><span class="p">(</span><span class="s">"k=</span><span class="si">%d</span><span class="s">, k must be greater than 1."</span><span class="o">%</span><span class="n">k</span><span class="p">)</span>
<span class="k">if</span> <span class="n">cliques</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">cliques</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">find_cliques</span><span class="p">(</span><span class="n">G</span><span class="p">)</span>
<span class="n">cliques</span> <span class="o">=</span> <span class="p">[</span><span class="nb">frozenset</span><span class="p">(</span><span class="n">c</span><span class="p">)</span> <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">cliques</span> <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">c</span><span class="p">)</span> <span class="o">>=</span> <span class="n">k</span><span class="p">]</span>
<span class="c"># First index which nodes are in which cliques</span>
<span class="n">membership_dict</span> <span class="o">=</span> <span class="n">defaultdict</span><span class="p">(</span><span class="nb">list</span><span class="p">)</span>
<span class="k">for</span> <span class="n">clique</span> <span class="ow">in</span> <span class="n">cliques</span><span class="p">:</span>
<span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="n">clique</span><span class="p">:</span>
<span class="n">membership_dict</span><span class="p">[</span><span class="n">node</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">clique</span><span class="p">)</span>
<span class="c"># For each clique, see which adjacent cliques percolate</span>
<span class="n">perc_graph</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">Graph</span><span class="p">()</span>
<span class="n">perc_graph</span><span class="o">.</span><span class="n">add_nodes_from</span><span class="p">(</span><span class="n">cliques</span><span class="p">)</span>
<span class="k">for</span> <span class="n">clique</span> <span class="ow">in</span> <span class="n">cliques</span><span class="p">:</span>
<span class="k">for</span> <span class="n">adj_clique</span> <span class="ow">in</span> <span class="n">_get_adjacent_cliques</span><span class="p">(</span><span class="n">clique</span><span class="p">,</span> <span class="n">membership_dict</span><span class="p">):</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">clique</span><span class="o">.</span><span class="n">intersection</span><span class="p">(</span><span class="n">adj_clique</span><span class="p">))</span> <span class="o">>=</span> <span class="p">(</span><span class="n">k</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
<span class="n">perc_graph</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="n">clique</span><span class="p">,</span> <span class="n">adj_clique</span><span class="p">)</span>
<span class="c"># Connected components of clique graph with perc edges</span>
<span class="c"># are the percolated cliques</span>
<span class="k">for</span> <span class="n">component</span> <span class="ow">in</span> <span class="n">nx</span><span class="o">.</span><span class="n">connected_components</span><span class="p">(</span><span class="n">perc_graph</span><span class="p">):</span>
<span class="k">yield</span><span class="p">(</span><span class="nb">frozenset</span><span class="o">.</span><span class="n">union</span><span class="p">(</span><span class="o">*</span><span class="n">component</span><span class="p">))</span>
</div>
<span class="k">def</span> <span class="nf">_get_adjacent_cliques</span><span class="p">(</span><span class="n">clique</span><span class="p">,</span> <span class="n">membership_dict</span><span class="p">):</span>
<span class="n">adjacent_cliques</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
<span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">clique</span><span class="p">:</span>
<span class="k">for</span> <span class="n">adj_clique</span> <span class="ow">in</span> <span class="n">membership_dict</span><span class="p">[</span><span class="n">n</span><span class="p">]:</span>
<span class="k">if</span> <span class="n">clique</span> <span class="o">!=</span> <span class="n">adj_clique</span><span class="p">:</span>
<span class="n">adjacent_cliques</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">adj_clique</span><span class="p">)</span>
<span class="k">return</span> <span class="n">adjacent_cliques</span>
</pre></div>
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