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<h1>Source code for networkx.algorithms.dag</h1><div class="highlight"><pre>
<span class="c"># -*- coding: utf-8 -*-</span>
<span class="kn">from</span> <span class="nn">fractions</span> <span class="kn">import</span> <span class="n">gcd</span>
<span class="kn">import</span> <span class="nn">networkx</span> <span class="kn">as</span> <span class="nn">nx</span>
<span class="sd">"""Algorithms for directed acyclic graphs (DAGs)."""</span>
<span class="c"># Copyright (C) 2006-2011 by </span>
<span class="c"># Aric Hagberg <hagberg@lanl.gov></span>
<span class="c"># Dan Schult <dschult@colgate.edu></span>
<span class="c"># Pieter Swart <swart@lanl.gov></span>
<span class="c"># All rights reserved.</span>
<span class="c"># BSD license.</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">'Aric Hagberg <aric.hagberg@gmail.com>'</span><span class="p">,</span>
<span class="s">'Dan Schult (dschult@colgate.edu)'</span><span class="p">,</span>
<span class="s">'Ben Edwards (bedwards@cs.unm.edu)'</span><span class="p">])</span>
<span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span><span class="s">'descendants'</span><span class="p">,</span>
<span class="s">'ancestors'</span><span class="p">,</span>
<span class="s">'topological_sort'</span><span class="p">,</span>
<span class="s">'topological_sort_recursive'</span><span class="p">,</span>
<span class="s">'is_directed_acyclic_graph'</span><span class="p">,</span>
<span class="s">'is_aperiodic'</span><span class="p">]</span>
<div class="viewcode-block" id="descendants"><a class="viewcode-back" href="../../../reference/generated/networkx.algorithms.dag.descendants.html#networkx.algorithms.dag.descendants">[docs]</a><span class="k">def</span> <span class="nf">descendants</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">source</span><span class="p">):</span>
<span class="sd">"""Return all nodes reachable from `source` in G.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : NetworkX DiGraph</span>
<span class="sd"> source : node in G</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> des : set()</span>
<span class="sd"> The descendants of source in G</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">G</span><span class="o">.</span><span class="n">has_node</span><span class="p">(</span><span class="n">source</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">"The node </span><span class="si">%s</span><span class="s"> is not in the graph."</span> <span class="o">%</span> <span class="n">source</span><span class="p">)</span>
<span class="n">des</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">nx</span><span class="o">.</span><span class="n">shortest_path_length</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">source</span><span class="o">=</span><span class="n">source</span><span class="p">)</span><span class="o">.</span><span class="n">keys</span><span class="p">())</span> <span class="o">-</span> <span class="nb">set</span><span class="p">([</span><span class="n">source</span><span class="p">])</span>
<span class="k">return</span> <span class="n">des</span>
</div>
<div class="viewcode-block" id="ancestors"><a class="viewcode-back" href="../../../reference/generated/networkx.algorithms.dag.ancestors.html#networkx.algorithms.dag.ancestors">[docs]</a><span class="k">def</span> <span class="nf">ancestors</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">source</span><span class="p">):</span>
<span class="sd">"""Return all nodes having a path to `source` in G.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : NetworkX DiGraph</span>
<span class="sd"> source : node in G</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> ancestors : set()</span>
<span class="sd"> The ancestors of source in G</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">G</span><span class="o">.</span><span class="n">has_node</span><span class="p">(</span><span class="n">source</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">"The node </span><span class="si">%s</span><span class="s"> is not in the graph."</span> <span class="o">%</span> <span class="n">source</span><span class="p">)</span>
<span class="n">anc</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">nx</span><span class="o">.</span><span class="n">shortest_path_length</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">target</span><span class="o">=</span><span class="n">source</span><span class="p">)</span><span class="o">.</span><span class="n">keys</span><span class="p">())</span> <span class="o">-</span> <span class="nb">set</span><span class="p">([</span><span class="n">source</span><span class="p">])</span>
<span class="k">return</span> <span class="n">anc</span>
</div>
<div class="viewcode-block" id="is_directed_acyclic_graph"><a class="viewcode-back" href="../../../reference/generated/networkx.algorithms.dag.is_directed_acyclic_graph.html#networkx.algorithms.dag.is_directed_acyclic_graph">[docs]</a><span class="k">def</span> <span class="nf">is_directed_acyclic_graph</span><span class="p">(</span><span class="n">G</span><span class="p">):</span>
<span class="sd">"""Return True if the graph G is a directed acyclic graph (DAG) or </span>
<span class="sd"> False if not.</span>
<span class="sd"> </span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : NetworkX graph</span>
<span class="sd"> A graph</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> is_dag : bool</span>
<span class="sd"> True if G is a DAG, false otherwise</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">G</span><span class="o">.</span><span class="n">is_directed</span><span class="p">():</span>
<span class="k">return</span> <span class="bp">False</span>
<span class="k">try</span><span class="p">:</span>
<span class="n">topological_sort</span><span class="p">(</span><span class="n">G</span><span class="p">)</span>
<span class="k">return</span> <span class="bp">True</span>
<span class="k">except</span> <span class="n">nx</span><span class="o">.</span><span class="n">NetworkXUnfeasible</span><span class="p">:</span>
<span class="k">return</span> <span class="bp">False</span>
</div>
<div class="viewcode-block" id="topological_sort"><a class="viewcode-back" href="../../../reference/generated/networkx.algorithms.dag.topological_sort.html#networkx.algorithms.dag.topological_sort">[docs]</a><span class="k">def</span> <span class="nf">topological_sort</span><span class="p">(</span><span class="n">G</span><span class="p">,</span><span class="n">nbunch</span><span class="o">=</span><span class="bp">None</span><span class="p">):</span>
<span class="sd">"""Return a list of nodes in topological sort order.</span>
<span class="sd"> A topological sort is a nonunique permutation of the nodes</span>
<span class="sd"> such that an edge from u to v implies that u appears before v in the</span>
<span class="sd"> topological sort order.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : NetworkX digraph</span>
<span class="sd"> A directed graph</span>
<span class="sd"> nbunch : container of nodes (optional)</span>
<span class="sd"> Explore graph in specified order given in nbunch</span>
<span class="sd"> Raises</span>
<span class="sd"> ------</span>
<span class="sd"> NetworkXError</span>
<span class="sd"> Topological sort is defined for directed graphs only. If the</span>
<span class="sd"> graph G is undirected, a NetworkXError is raised.</span>
<span class="sd"> NetworkXUnfeasible</span>
<span class="sd"> If G is not a directed acyclic graph (DAG) no topological sort</span>
<span class="sd"> exists and a NetworkXUnfeasible exception is raised.</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> This algorithm is based on a description and proof in</span>
<span class="sd"> The Algorithm Design Manual [1]_ .</span>
<span class="sd"> See also</span>
<span class="sd"> --------</span>
<span class="sd"> is_directed_acyclic_graph</span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> .. [1] Skiena, S. S. The Algorithm Design Manual (Springer-Verlag, 1998). </span>
<span class="sd"> http://www.amazon.com/exec/obidos/ASIN/0387948600/ref=ase_thealgorithmrepo/</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="ow">not</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">"Topological sort not defined on undirected graphs."</span><span class="p">)</span>
<span class="c"># nonrecursive version</span>
<span class="n">seen</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
<span class="n">order</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">explored</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
<span class="k">if</span> <span class="n">nbunch</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">nbunch</span> <span class="o">=</span> <span class="n">G</span><span class="o">.</span><span class="n">nodes_iter</span><span class="p">()</span>
<span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">nbunch</span><span class="p">:</span> <span class="c"># process all vertices in G</span>
<span class="k">if</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">explored</span><span class="p">:</span>
<span class="k">continue</span>
<span class="n">fringe</span> <span class="o">=</span> <span class="p">[</span><span class="n">v</span><span class="p">]</span> <span class="c"># nodes yet to look at</span>
<span class="k">while</span> <span class="n">fringe</span><span class="p">:</span>
<span class="n">w</span> <span class="o">=</span> <span class="n">fringe</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="c"># depth first search</span>
<span class="k">if</span> <span class="n">w</span> <span class="ow">in</span> <span class="n">explored</span><span class="p">:</span> <span class="c"># already looked down this branch</span>
<span class="n">fringe</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
<span class="k">continue</span>
<span class="n">seen</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">w</span><span class="p">)</span> <span class="c"># mark as seen</span>
<span class="c"># Check successors for cycles and for new nodes</span>
<span class="n">new_nodes</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">G</span><span class="p">[</span><span class="n">w</span><span class="p">]:</span>
<span class="k">if</span> <span class="n">n</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">explored</span><span class="p">:</span>
<span class="k">if</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">seen</span><span class="p">:</span> <span class="c">#CYCLE !!</span>
<span class="k">raise</span> <span class="n">nx</span><span class="o">.</span><span class="n">NetworkXUnfeasible</span><span class="p">(</span><span class="s">"Graph contains a cycle."</span><span class="p">)</span>
<span class="n">new_nodes</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<span class="k">if</span> <span class="n">new_nodes</span><span class="p">:</span> <span class="c"># Add new_nodes to fringe</span>
<span class="n">fringe</span><span class="o">.</span><span class="n">extend</span><span class="p">(</span><span class="n">new_nodes</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span> <span class="c"># No new nodes so w is fully explored</span>
<span class="n">explored</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">w</span><span class="p">)</span>
<span class="n">order</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">w</span><span class="p">)</span>
<span class="n">fringe</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span> <span class="c"># done considering this node</span>
<span class="k">return</span> <span class="nb">list</span><span class="p">(</span><span class="nb">reversed</span><span class="p">(</span><span class="n">order</span><span class="p">))</span>
</div>
<div class="viewcode-block" id="topological_sort_recursive"><a class="viewcode-back" href="../../../reference/generated/networkx.algorithms.dag.topological_sort_recursive.html#networkx.algorithms.dag.topological_sort_recursive">[docs]</a><span class="k">def</span> <span class="nf">topological_sort_recursive</span><span class="p">(</span><span class="n">G</span><span class="p">,</span><span class="n">nbunch</span><span class="o">=</span><span class="bp">None</span><span class="p">):</span>
<span class="sd">"""Return a list of nodes in topological sort order.</span>
<span class="sd"> A topological sort is a nonunique permutation of the nodes such</span>
<span class="sd"> that an edge from u to v implies that u appears before v in the</span>
<span class="sd"> topological sort order.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : NetworkX digraph</span>
<span class="sd"> nbunch : container of nodes (optional)</span>
<span class="sd"> Explore graph in specified order given in nbunch</span>
<span class="sd"> Raises</span>
<span class="sd"> ------</span>
<span class="sd"> NetworkXError</span>
<span class="sd"> Topological sort is defined for directed graphs only. If the</span>
<span class="sd"> graph G is undirected, a NetworkXError is raised.</span>
<span class="sd"> NetworkXUnfeasible</span>
<span class="sd"> If G is not a directed acyclic graph (DAG) no topological sort</span>
<span class="sd"> exists and a NetworkXUnfeasible exception is raised.</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> This is a recursive version of topological sort.</span>
<span class="sd"> See also</span>
<span class="sd"> --------</span>
<span class="sd"> topological_sort</span>
<span class="sd"> is_directed_acyclic_graph</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="ow">not</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">"Topological sort not defined on undirected graphs."</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">_dfs</span><span class="p">(</span><span class="n">v</span><span class="p">):</span>
<span class="n">ancestors</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">for</span> <span class="n">w</span> <span class="ow">in</span> <span class="n">G</span><span class="p">[</span><span class="n">v</span><span class="p">]:</span>
<span class="k">if</span> <span class="n">w</span> <span class="ow">in</span> <span class="n">ancestors</span><span class="p">:</span>
<span class="k">raise</span> <span class="n">nx</span><span class="o">.</span><span class="n">NetworkXUnfeasible</span><span class="p">(</span><span class="s">"Graph contains a cycle."</span><span class="p">)</span>
<span class="k">if</span> <span class="n">w</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">explored</span><span class="p">:</span>
<span class="n">_dfs</span><span class="p">(</span><span class="n">w</span><span class="p">)</span>
<span class="n">ancestors</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">explored</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">order</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="n">ancestors</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
<span class="n">explored</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
<span class="n">order</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">if</span> <span class="n">nbunch</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">nbunch</span> <span class="o">=</span> <span class="n">G</span><span class="o">.</span><span class="n">nodes_iter</span><span class="p">()</span>
<span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">nbunch</span><span class="p">:</span>
<span class="k">if</span> <span class="n">v</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">explored</span><span class="p">:</span>
<span class="n">_dfs</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="k">return</span> <span class="nb">list</span><span class="p">(</span><span class="nb">reversed</span><span class="p">(</span><span class="n">order</span><span class="p">))</span>
</div>
<div class="viewcode-block" id="is_aperiodic"><a class="viewcode-back" href="../../../reference/generated/networkx.algorithms.dag.is_aperiodic.html#networkx.algorithms.dag.is_aperiodic">[docs]</a><span class="k">def</span> <span class="nf">is_aperiodic</span><span class="p">(</span><span class="n">G</span><span class="p">):</span>
<span class="sd">"""Return True if G is aperiodic.</span>
<span class="sd"> A directed graph is aperiodic if there is no integer k > 1 that </span>
<span class="sd"> divides the length of every cycle in the graph.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G : NetworkX DiGraph</span>
<span class="sd"> Graph</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> aperiodic : boolean</span>
<span class="sd"> True if the graph is aperiodic False otherwise</span>
<span class="sd"> Raises</span>
<span class="sd"> ------</span>
<span class="sd"> NetworkXError</span>
<span class="sd"> If G is not directed</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> This uses the method outlined in [1]_, which runs in O(m) time</span>
<span class="sd"> given m edges in G. Note that a graph is not aperiodic if it is</span>
<span class="sd"> acyclic as every integer trivial divides length 0 cycles.</span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> .. [1] Jarvis, J. P.; Shier, D. R. (1996),</span>
<span class="sd"> Graph-theoretic analysis of finite Markov chains,</span>
<span class="sd"> in Shier, D. R.; Wallenius, K. T., Applied Mathematical Modeling:</span>
<span class="sd"> A Multidisciplinary Approach, CRC Press.</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="ow">not</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">"is_aperiodic not defined for undirected graphs"</span><span class="p">)</span>
<span class="n">s</span> <span class="o">=</span> <span class="nb">next</span><span class="p">(</span><span class="n">G</span><span class="o">.</span><span class="n">nodes_iter</span><span class="p">())</span>
<span class="n">levels</span> <span class="o">=</span> <span class="p">{</span><span class="n">s</span><span class="p">:</span><span class="mi">0</span><span class="p">}</span>
<span class="n">this_level</span> <span class="o">=</span> <span class="p">[</span><span class="n">s</span><span class="p">]</span>
<span class="n">g</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">l</span> <span class="o">=</span> <span class="mi">1</span>
<span class="k">while</span> <span class="n">this_level</span><span class="p">:</span>
<span class="n">next_level</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">u</span> <span class="ow">in</span> <span class="n">this_level</span><span class="p">:</span>
<span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">G</span><span class="p">[</span><span class="n">u</span><span class="p">]:</span>
<span class="k">if</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">levels</span><span class="p">:</span> <span class="c"># Non-Tree Edge</span>
<span class="n">g</span> <span class="o">=</span> <span class="n">gcd</span><span class="p">(</span><span class="n">g</span><span class="p">,</span> <span class="n">levels</span><span class="p">[</span><span class="n">u</span><span class="p">]</span><span class="o">-</span><span class="n">levels</span><span class="p">[</span><span class="n">v</span><span class="p">]</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span> <span class="c"># Tree Edge</span>
<span class="n">next_level</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="n">levels</span><span class="p">[</span><span class="n">v</span><span class="p">]</span> <span class="o">=</span> <span class="n">l</span>
<span class="n">this_level</span> <span class="o">=</span> <span class="n">next_level</span>
<span class="n">l</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">levels</span><span class="p">)</span><span class="o">==</span><span class="nb">len</span><span class="p">(</span><span class="n">G</span><span class="p">):</span> <span class="c">#All nodes in tree</span>
<span class="k">return</span> <span class="n">g</span><span class="o">==</span><span class="mi">1</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="n">g</span><span class="o">==</span><span class="mi">1</span> <span class="ow">and</span> <span class="n">nx</span><span class="o">.</span><span class="n">is_aperiodic</span><span class="p">(</span><span class="n">G</span><span class="o">.</span><span class="n">subgraph</span><span class="p">(</span><span class="nb">set</span><span class="p">(</span><span class="n">G</span><span class="p">)</span><span class="o">-</span><span class="nb">set</span><span class="p">(</span><span class="n">levels</span><span class="p">)))</span></div>
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