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<h1>Source code for networkx.algorithms.chordal.chordal_alg</h1><div class="highlight"><pre>
<span class="c"># -*- coding: utf-8 -*-</span>
<span class="sd">"""</span>
<span class="sd">Algorithms for chordal graphs.</span>
<span class="sd">A graph is chordal if every cycle of length at least 4 has a chord</span>
<span class="sd">(an edge joining two nodes not adjacent in the cycle).</span>
<span class="sd">http://en.wikipedia.org/wiki/Chordal_graph</span>
<span class="sd">"""</span>
<span class="kn">import</span> <span class="nn">networkx</span> <span class="kn">as</span> <span class="nn">nx</span>
<span class="kn">import</span> <span class="nn">random</span>
<span class="kn">import</span> <span class="nn">sys</span>
<span class="n">__authors__</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">'Jesus Cerquides <cerquide@iiia.csic.es>'</span><span class="p">])</span>
<span class="c"># Copyright (C) 2010 by </span>
<span class="c"># Jesus Cerquides <cerquide@iiia.csic.es></span>
<span class="c"># All rights reserved.</span>
<span class="c"># BSD license.</span>
<span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span><span class="s">'is_chordal'</span><span class="p">,</span>
<span class="s">'find_induced_nodes'</span><span class="p">,</span>
<span class="s">'chordal_graph_cliques'</span><span class="p">,</span>
<span class="s">'chordal_graph_treewidth'</span><span class="p">,</span>
<span class="s">'NetworkXTreewidthBoundExceeded'</span><span class="p">]</span>
<span class="k">class</span> <span class="nc">NetworkXTreewidthBoundExceeded</span><span class="p">(</span><span class="n">nx</span><span class="o">.</span><span class="n">NetworkXException</span><span class="p">):</span>
<span class="sd">"""Exception raised when a treewidth bound has been provided and it has </span>
<span class="sd"> been exceeded"""</span>
<div class="viewcode-block" id="is_chordal"><a class="viewcode-back" href="../../../../reference/generated/networkx.algorithms.chordal.chordal_alg.is_chordal.html#networkx.algorithms.chordal.chordal_alg.is_chordal">[docs]</a><span class="k">def</span> <span class="nf">is_chordal</span><span class="p">(</span><span class="n">G</span><span class="p">):</span>
<span class="sd">"""Checks whether G is a chordal graph.</span>
<span class="sd"> A graph is chordal if every cycle of length at least 4 has a chord</span>
<span class="sd"> (an edge joining two nodes not adjacent in the cycle).</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : graph </span>
<span class="sd"> A NetworkX graph. </span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> chordal : bool</span>
<span class="sd"> True if G is a chordal graph and False otherwise.</span>
<span class="sd"> </span>
<span class="sd"> Raises</span>
<span class="sd"> ------</span>
<span class="sd"> NetworkXError</span>
<span class="sd"> The algorithm does not support DiGraph, MultiGraph and MultiDiGraph. </span>
<span class="sd"> If the input graph is an instance of one of these classes, a</span>
<span class="sd"> NetworkXError is raised.</span>
<span class="sd"> </span>
<span class="sd"> Examples</span>
<span class="sd"> --------</span>
<span class="sd"> >>> import networkx as nx</span>
<span class="sd"> >>> e=[(1,2),(1,3),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)]</span>
<span class="sd"> >>> G=nx.Graph(e)</span>
<span class="sd"> >>> nx.is_chordal(G)</span>
<span class="sd"> True</span>
<span class="sd"> </span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> The routine tries to go through every node following maximum cardinality </span>
<span class="sd"> search. It returns False when it finds that the separator for any node </span>
<span class="sd"> is not a clique. Based on the algorithms in [1]_.</span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> .. [1] R. E. Tarjan and M. Yannakakis, Simple linear-time algorithms </span>
<span class="sd"> to test chordality of graphs, test acyclicity of hypergraphs, and </span>
<span class="sd"> selectively reduce acyclic hypergraphs, SIAM J. Comput., 13 (1984), </span>
<span class="sd"> pp. 566–579.</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">G</span><span class="o">.</span><span class="n">is_directed</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">'Directed graphs not supported'</span><span class="p">)</span>
<span class="k">if</span> <span class="n">G</span><span class="o">.</span><span class="n">is_multigraph</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">'Multiply connected graphs not supported.'</span><span class="p">)</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">_find_chordality_breaker</span><span class="p">(</span><span class="n">G</span><span class="p">))</span><span class="o">==</span><span class="mi">0</span><span class="p">:</span>
<span class="k">return</span> <span class="bp">True</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="bp">False</span>
</div>
<div class="viewcode-block" id="find_induced_nodes"><a class="viewcode-back" href="../../../../reference/generated/networkx.algorithms.chordal.chordal_alg.find_induced_nodes.html#networkx.algorithms.chordal.chordal_alg.find_induced_nodes">[docs]</a><span class="k">def</span> <span class="nf">find_induced_nodes</span><span class="p">(</span><span class="n">G</span><span class="p">,</span><span class="n">s</span><span class="p">,</span><span class="n">t</span><span class="p">,</span><span class="n">treewidth_bound</span><span class="o">=</span><span class="n">sys</span><span class="o">.</span><span class="n">maxsize</span><span class="p">):</span>
<span class="sd">"""Returns the set of induced nodes in the path from s to t. </span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : graph</span>
<span class="sd"> A chordal NetworkX graph </span>
<span class="sd"> s : node</span>
<span class="sd"> Source node to look for induced nodes</span>
<span class="sd"> t : node</span>
<span class="sd"> Destination node to look for induced nodes</span>
<span class="sd"> treewith_bound: float</span>
<span class="sd"> Maximum treewidth acceptable for the graph H. The search </span>
<span class="sd"> for induced nodes will end as soon as the treewidth_bound is exceeded.</span>
<span class="sd"> </span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> I : Set of nodes</span>
<span class="sd"> The set of induced nodes in the path from s to t in G</span>
<span class="sd"> </span>
<span class="sd"> Raises</span>
<span class="sd"> ------</span>
<span class="sd"> NetworkXError</span>
<span class="sd"> The algorithm does not support DiGraph, MultiGraph and MultiDiGraph. </span>
<span class="sd"> If the input graph is an instance of one of these classes, a</span>
<span class="sd"> NetworkXError is raised.</span>
<span class="sd"> The algorithm can only be applied to chordal graphs. If</span>
<span class="sd"> the input graph is found to be non-chordal, a NetworkXError is raised.</span>
<span class="sd"> </span>
<span class="sd"> Examples</span>
<span class="sd"> --------</span>
<span class="sd"> >>> import networkx as nx</span>
<span class="sd"> >>> G=nx.Graph() </span>
<span class="sd"> >>> G = nx.generators.classic.path_graph(10)</span>
<span class="sd"> >>> I = nx.find_induced_nodes(G,1,9,2)</span>
<span class="sd"> >>> list(I)</span>
<span class="sd"> [1, 2, 3, 4, 5, 6, 7, 8, 9]</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> G must be a chordal graph and (s,t) an edge that is not in G. </span>
<span class="sd"> If a treewidth_bound is provided, the search for induced nodes will end </span>
<span class="sd"> as soon as the treewidth_bound is exceeded.</span>
<span class="sd"> </span>
<span class="sd"> The algorithm is inspired by Algorithm 4 in [1]_.</span>
<span class="sd"> A formal definition of induced node can also be found on that reference.</span>
<span class="sd"> </span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> .. [1] Learning Bounded Treewidth Bayesian Networks. </span>
<span class="sd"> Gal Elidan, Stephen Gould; JMLR, 9(Dec):2699--2731, 2008. </span>
<span class="sd"> http://jmlr.csail.mit.edu/papers/volume9/elidan08a/elidan08a.pdf</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">is_chordal</span><span class="p">(</span><span class="n">G</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">"Input graph is not chordal."</span><span class="p">)</span>
<span class="n">H</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">G</span><span class="p">)</span>
<span class="n">H</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="n">s</span><span class="p">,</span><span class="n">t</span><span class="p">)</span>
<span class="n">I</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
<span class="n">triplet</span> <span class="o">=</span> <span class="n">_find_chordality_breaker</span><span class="p">(</span><span class="n">H</span><span class="p">,</span><span class="n">s</span><span class="p">,</span><span class="n">treewidth_bound</span><span class="p">)</span>
<span class="k">while</span> <span class="n">triplet</span><span class="p">:</span>
<span class="p">(</span><span class="n">u</span><span class="p">,</span><span class="n">v</span><span class="p">,</span><span class="n">w</span><span class="p">)</span> <span class="o">=</span> <span class="n">triplet</span>
<span class="n">I</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">triplet</span><span class="p">)</span>
<span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">triplet</span><span class="p">:</span>
<span class="k">if</span> <span class="n">n</span><span class="o">!=</span><span class="n">s</span><span class="p">:</span>
<span class="n">H</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="n">s</span><span class="p">,</span><span class="n">n</span><span class="p">)</span>
<span class="n">triplet</span> <span class="o">=</span> <span class="n">_find_chordality_breaker</span><span class="p">(</span><span class="n">H</span><span class="p">,</span><span class="n">s</span><span class="p">,</span><span class="n">treewidth_bound</span><span class="p">)</span>
<span class="k">if</span> <span class="n">I</span><span class="p">:</span>
<span class="c"># Add t and the second node in the induced path from s to t.</span>
<span class="n">I</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
<span class="k">for</span> <span class="n">u</span> <span class="ow">in</span> <span class="n">G</span><span class="p">[</span><span class="n">s</span><span class="p">]:</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">I</span> <span class="o">&</span> <span class="nb">set</span><span class="p">(</span><span class="n">G</span><span class="p">[</span><span class="n">u</span><span class="p">]))</span><span class="o">==</span><span class="mi">2</span><span class="p">:</span>
<span class="n">I</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">u</span><span class="p">)</span>
<span class="k">break</span>
<span class="k">return</span> <span class="n">I</span>
</div>
<div class="viewcode-block" id="chordal_graph_cliques"><a class="viewcode-back" href="../../../../reference/generated/networkx.algorithms.chordal.chordal_alg.chordal_graph_cliques.html#networkx.algorithms.chordal.chordal_alg.chordal_graph_cliques">[docs]</a><span class="k">def</span> <span class="nf">chordal_graph_cliques</span><span class="p">(</span><span class="n">G</span><span class="p">):</span>
<span class="sd">"""Returns the set of maximal cliques of a chordal graph.</span>
<span class="sd"> </span>
<span class="sd"> The algorithm breaks the graph in connected components and performs a </span>
<span class="sd"> maximum cardinality search in each component to get the cliques.</span>
<span class="sd"> </span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : graph</span>
<span class="sd"> A NetworkX graph </span>
<span class="sd"> </span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> cliques : A set containing the maximal cliques in G.</span>
<span class="sd"> </span>
<span class="sd"> Raises</span>
<span class="sd"> ------</span>
<span class="sd"> NetworkXError</span>
<span class="sd"> The algorithm does not support DiGraph, MultiGraph and MultiDiGraph. </span>
<span class="sd"> If the input graph is an instance of one of these classes, a</span>
<span class="sd"> NetworkXError is raised.</span>
<span class="sd"> The algorithm can only be applied to chordal graphs. If the</span>
<span class="sd"> input graph is found to be non-chordal, a NetworkXError is raised.</span>
<span class="sd"> </span>
<span class="sd"> Examples</span>
<span class="sd"> --------</span>
<span class="sd"> >>> import networkx as nx</span>
<span class="sd"> >>> e= [(1,2),(1,3),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6),(7,8)]</span>
<span class="sd"> >>> G = nx.Graph(e)</span>
<span class="sd"> >>> G.add_node(9) </span>
<span class="sd"> >>> setlist = nx.chordal_graph_cliques(G)</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">is_chordal</span><span class="p">(</span><span class="n">G</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">"Input graph is not chordal."</span><span class="p">)</span>
<span class="n">cliques</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
<span class="k">for</span> <span class="n">C</span> <span class="ow">in</span> <span class="n">nx</span><span class="o">.</span><span class="n">connected</span><span class="o">.</span><span class="n">connected_component_subgraphs</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="n">_connected_chordal_graph_cliques</span><span class="p">(</span><span class="n">C</span><span class="p">)</span>
<span class="k">return</span> <span class="n">cliques</span>
</div>
<div class="viewcode-block" id="chordal_graph_treewidth"><a class="viewcode-back" href="../../../../reference/generated/networkx.algorithms.chordal.chordal_alg.chordal_graph_treewidth.html#networkx.algorithms.chordal.chordal_alg.chordal_graph_treewidth">[docs]</a><span class="k">def</span> <span class="nf">chordal_graph_treewidth</span><span class="p">(</span><span class="n">G</span><span class="p">):</span>
<span class="sd">"""Returns the treewidth of the chordal graph G.</span>
<span class="sd"> </span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : graph</span>
<span class="sd"> A NetworkX graph </span>
<span class="sd"> </span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> treewidth : int</span>
<span class="sd"> The size of the largest clique in the graph minus one.</span>
<span class="sd"> </span>
<span class="sd"> Raises</span>
<span class="sd"> ------</span>
<span class="sd"> NetworkXError</span>
<span class="sd"> The algorithm does not support DiGraph, MultiGraph and MultiDiGraph. </span>
<span class="sd"> If the input graph is an instance of one of these classes, a</span>
<span class="sd"> NetworkXError is raised.</span>
<span class="sd"> The algorithm can only be applied to chordal graphs. If</span>
<span class="sd"> the input graph is found to be non-chordal, a NetworkXError is raised.</span>
<span class="sd"> </span>
<span class="sd"> Examples</span>
<span class="sd"> --------</span>
<span class="sd"> >>> import networkx as nx</span>
<span class="sd"> >>> e = [(1,2),(1,3),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6),(7,8)]</span>
<span class="sd"> >>> G = nx.Graph(e)</span>
<span class="sd"> >>> G.add_node(9) </span>
<span class="sd"> >>> nx.chordal_graph_treewidth(G)</span>
<span class="sd"> 3</span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> .. [1] http://en.wikipedia.org/wiki/Tree_decomposition#Treewidth</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">is_chordal</span><span class="p">(</span><span class="n">G</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">"Input graph is not chordal."</span><span class="p">)</span>
<span class="n">max_clique</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span>
<span class="k">for</span> <span class="n">clique</span> <span class="ow">in</span> <span class="n">nx</span><span class="o">.</span><span class="n">chordal_graph_cliques</span><span class="p">(</span><span class="n">G</span><span class="p">):</span>
<span class="n">max_clique</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">max_clique</span><span class="p">,</span><span class="nb">len</span><span class="p">(</span><span class="n">clique</span><span class="p">))</span>
<span class="k">return</span> <span class="n">max_clique</span> <span class="o">-</span> <span class="mi">1</span>
</div>
<span class="k">def</span> <span class="nf">_is_complete_graph</span><span class="p">(</span><span class="n">G</span><span class="p">):</span>
<span class="sd">"""Returns True if G is a complete graph."""</span>
<span class="k">if</span> <span class="n">G</span><span class="o">.</span><span class="n">number_of_selfloops</span><span class="p">()</span><span class="o">></span><span class="mi">0</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">"Self loop found in _is_complete_graph()"</span><span class="p">)</span>
<span class="n">n</span> <span class="o">=</span> <span class="n">G</span><span class="o">.</span><span class="n">number_of_nodes</span><span class="p">()</span>
<span class="k">if</span> <span class="n">n</span> <span class="o"><</span> <span class="mi">2</span><span class="p">:</span>
<span class="k">return</span> <span class="bp">True</span>
<span class="n">e</span> <span class="o">=</span> <span class="n">G</span><span class="o">.</span><span class="n">number_of_edges</span><span class="p">()</span>
<span class="n">max_edges</span> <span class="o">=</span> <span class="p">((</span><span class="n">n</span> <span class="o">*</span> <span class="p">(</span><span class="n">n</span><span class="o">-</span><span class="mi">1</span><span class="p">))</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span>
<span class="k">return</span> <span class="n">e</span> <span class="o">==</span> <span class="n">max_edges</span>
<span class="k">def</span> <span class="nf">_find_missing_edge</span><span class="p">(</span><span class="n">G</span><span class="p">):</span>
<span class="sd">""" Given a non-complete graph G, returns a missing edge."""</span>
<span class="n">nodes</span><span class="o">=</span><span class="nb">set</span><span class="p">(</span><span class="n">G</span><span class="p">)</span>
<span class="k">for</span> <span class="n">u</span> <span class="ow">in</span> <span class="n">G</span><span class="p">:</span>
<span class="n">missing</span><span class="o">=</span><span class="n">nodes</span><span class="o">-</span><span class="nb">set</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">G</span><span class="p">[</span><span class="n">u</span><span class="p">]</span><span class="o">.</span><span class="n">keys</span><span class="p">())</span><span class="o">+</span><span class="p">[</span><span class="n">u</span><span class="p">])</span>
<span class="k">if</span> <span class="n">missing</span><span class="p">:</span>
<span class="k">return</span> <span class="p">(</span><span class="n">u</span><span class="p">,</span><span class="n">missing</span><span class="o">.</span><span class="n">pop</span><span class="p">())</span>
<span class="k">def</span> <span class="nf">_max_cardinality_node</span><span class="p">(</span><span class="n">G</span><span class="p">,</span><span class="n">choices</span><span class="p">,</span><span class="n">wanna_connect</span><span class="p">):</span>
<span class="sd">"""Returns a the node in choices that has more connections in G </span>
<span class="sd"> to nodes in wanna_connect.</span>
<span class="sd"> """</span>
<span class="c"># max_number = None </span>
<span class="n">max_number</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span>
<span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">choices</span><span class="p">:</span>
<span class="n">number</span><span class="o">=</span><span class="nb">len</span><span class="p">([</span><span class="n">y</span> <span class="k">for</span> <span class="n">y</span> <span class="ow">in</span> <span class="n">G</span><span class="p">[</span><span class="n">x</span><span class="p">]</span> <span class="k">if</span> <span class="n">y</span> <span class="ow">in</span> <span class="n">wanna_connect</span><span class="p">])</span>
<span class="k">if</span> <span class="n">number</span> <span class="o">></span> <span class="n">max_number</span><span class="p">:</span>
<span class="n">max_number</span> <span class="o">=</span> <span class="n">number</span>
<span class="n">max_cardinality_node</span> <span class="o">=</span> <span class="n">x</span>
<span class="k">return</span> <span class="n">max_cardinality_node</span>
<span class="k">def</span> <span class="nf">_find_chordality_breaker</span><span class="p">(</span><span class="n">G</span><span class="p">,</span><span class="n">s</span><span class="o">=</span><span class="bp">None</span><span class="p">,</span><span class="n">treewidth_bound</span><span class="o">=</span><span class="n">sys</span><span class="o">.</span><span class="n">maxsize</span><span class="p">):</span>
<span class="sd">""" Given a graph G, starts a max cardinality search </span>
<span class="sd"> (starting from s if s is given and from a random node otherwise)</span>
<span class="sd"> trying to find a non-chordal cycle. </span>
<span class="sd"> If it does find one, it returns (u,v,w) where u,v,w are the three</span>
<span class="sd"> nodes that together with s are involved in the cycle.</span>
<span class="sd"> """</span>
<span class="n">unnumbered</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">G</span><span class="p">)</span>
<span class="k">if</span> <span class="n">s</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">s</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">choice</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">unnumbered</span><span class="p">))</span>
<span class="n">unnumbered</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
<span class="n">numbered</span> <span class="o">=</span> <span class="nb">set</span><span class="p">([</span><span class="n">s</span><span class="p">])</span>
<span class="c"># current_treewidth = None</span>
<span class="n">current_treewidth</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span>
<span class="k">while</span> <span class="n">unnumbered</span><span class="p">:</span><span class="c"># and current_treewidth <= treewidth_bound:</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">_max_cardinality_node</span><span class="p">(</span><span class="n">G</span><span class="p">,</span><span class="n">unnumbered</span><span class="p">,</span><span class="n">numbered</span><span class="p">)</span>
<span class="n">unnumbered</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="n">numbered</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="n">clique_wanna_be</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">G</span><span class="p">[</span><span class="n">v</span><span class="p">])</span> <span class="o">&</span> <span class="n">numbered</span>
<span class="n">sg</span> <span class="o">=</span> <span class="n">G</span><span class="o">.</span><span class="n">subgraph</span><span class="p">(</span><span class="n">clique_wanna_be</span><span class="p">)</span>
<span class="k">if</span> <span class="n">_is_complete_graph</span><span class="p">(</span><span class="n">sg</span><span class="p">):</span>
<span class="c"># The graph seems to be chordal by now. We update the treewidth</span>
<span class="n">current_treewidth</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">current_treewidth</span><span class="p">,</span><span class="nb">len</span><span class="p">(</span><span class="n">clique_wanna_be</span><span class="p">))</span>
<span class="k">if</span> <span class="n">current_treewidth</span> <span class="o">></span> <span class="n">treewidth_bound</span><span class="p">:</span>
<span class="k">raise</span> <span class="n">nx</span><span class="o">.</span><span class="n">NetworkXTreewidthBoundExceeded</span><span class="p">(</span>\
<span class="s">"treewidth_bound exceeded: </span><span class="si">%s</span><span class="s">"</span><span class="o">%</span><span class="n">current_treewidth</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="c"># sg is not a clique,</span>
<span class="c"># look for an edge that is not included in sg</span>
<span class="p">(</span><span class="n">u</span><span class="p">,</span><span class="n">w</span><span class="p">)</span> <span class="o">=</span> <span class="n">_find_missing_edge</span><span class="p">(</span><span class="n">sg</span><span class="p">)</span>
<span class="k">return</span> <span class="p">(</span><span class="n">u</span><span class="p">,</span><span class="n">v</span><span class="p">,</span><span class="n">w</span><span class="p">)</span>
<span class="k">return</span> <span class="p">()</span>
<span class="k">def</span> <span class="nf">_connected_chordal_graph_cliques</span><span class="p">(</span><span class="n">G</span><span class="p">):</span>
<span class="sd">"""Return the set of maximal cliques of a connected chordal graph."""</span>
<span class="k">if</span> <span class="n">G</span><span class="o">.</span><span class="n">number_of_nodes</span><span class="p">()</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="n">x</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">(</span><span class="n">G</span><span class="o">.</span><span class="n">nodes</span><span class="p">())</span>
<span class="k">return</span> <span class="nb">set</span><span class="p">([</span><span class="n">x</span><span class="p">])</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">cliques</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
<span class="n">unnumbered</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">G</span><span class="o">.</span><span class="n">nodes</span><span class="p">())</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">choice</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">unnumbered</span><span class="p">))</span>
<span class="n">unnumbered</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="n">numbered</span> <span class="o">=</span> <span class="nb">set</span><span class="p">([</span><span class="n">v</span><span class="p">])</span>
<span class="n">clique_wanna_be</span> <span class="o">=</span> <span class="nb">set</span><span class="p">([</span><span class="n">v</span><span class="p">])</span>
<span class="k">while</span> <span class="n">unnumbered</span><span class="p">:</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">_max_cardinality_node</span><span class="p">(</span><span class="n">G</span><span class="p">,</span><span class="n">unnumbered</span><span class="p">,</span><span class="n">numbered</span><span class="p">)</span>
<span class="n">unnumbered</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="n">numbered</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="n">new_clique_wanna_be</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">G</span><span class="o">.</span><span class="n">neighbors</span><span class="p">(</span><span class="n">v</span><span class="p">))</span> <span class="o">&</span> <span class="n">numbered</span>
<span class="n">sg</span> <span class="o">=</span> <span class="n">G</span><span class="o">.</span><span class="n">subgraph</span><span class="p">(</span><span class="n">clique_wanna_be</span><span class="p">)</span>
<span class="k">if</span> <span class="n">_is_complete_graph</span><span class="p">(</span><span class="n">sg</span><span class="p">):</span>
<span class="n">new_clique_wanna_be</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">new_clique_wanna_be</span> <span class="o">>=</span> <span class="n">clique_wanna_be</span><span class="p">:</span>
<span class="n">cliques</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="nb">frozenset</span><span class="p">(</span><span class="n">clique_wanna_be</span><span class="p">))</span>
<span class="n">clique_wanna_be</span> <span class="o">=</span> <span class="n">new_clique_wanna_be</span>
<span class="k">else</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">"Input graph is not chordal."</span><span class="p">)</span>
<span class="n">cliques</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="nb">frozenset</span><span class="p">(</span><span class="n">clique_wanna_be</span><span class="p">))</span>
<span class="k">return</span> <span class="n">cliques</span>
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