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<h1>Source code for networkx.algorithms.isomorphism.isomorphvf2</h1><div class="highlight"><pre>
<span></span><span class="sd">"""</span>
<span class="sd">*************</span>
<span class="sd">VF2 Algorithm</span>
<span class="sd">*************</span>
<span class="sd">An implementation of VF2 algorithm for graph isomorphism testing.</span>
<span class="sd">The simplest interface to use this module is to call networkx.is_isomorphic().</span>
<span class="sd">Introduction</span>
<span class="sd">------------</span>
<span class="sd">The GraphMatcher and DiGraphMatcher are responsible for matching</span>
<span class="sd">graphs or directed graphs in a predetermined manner. This</span>
<span class="sd">usually means a check for an isomorphism, though other checks</span>
<span class="sd">are also possible. For example, a subgraph of one graph</span>
<span class="sd">can be checked for isomorphism to a second graph.</span>
<span class="sd">Matching is done via syntactic feasibility. It is also possible</span>
<span class="sd">to check for semantic feasibility. Feasibility, then, is defined</span>
<span class="sd">as the logical AND of the two functions.</span>
<span class="sd">To include a semantic check, the (Di)GraphMatcher class should be</span>
<span class="sd">subclassed, and the semantic_feasibility() function should be</span>
<span class="sd">redefined. By default, the semantic feasibility function always</span>
<span class="sd">returns True. The effect of this is that semantics are not</span>
<span class="sd">considered in the matching of G1 and G2.</span>
<span class="sd">Examples</span>
<span class="sd">--------</span>
<span class="sd">Suppose G1 and G2 are isomorphic graphs. Verification is as follows:</span>
<span class="sd">>>> from networkx.algorithms import isomorphism</span>
<span class="sd">>>> G1 = nx.path_graph(4)</span>
<span class="sd">>>> G2 = nx.path_graph(4)</span>
<span class="sd">>>> GM = isomorphism.GraphMatcher(G1, G2)</span>
<span class="sd">>>> GM.is_isomorphic()</span>
<span class="sd">True</span>
<span class="sd">GM.mapping stores the isomorphism mapping from G1 to G2.</span>
<span class="sd">>>> GM.mapping</span>
<span class="sd">{0: 0, 1: 1, 2: 2, 3: 3}</span>
<span class="sd">Suppose G1 and G2 are isomorphic directed graphs.</span>
<span class="sd">Verification is as follows:</span>
<span class="sd">>>> G1 = nx.path_graph(4, create_using=nx.DiGraph())</span>
<span class="sd">>>> G2 = nx.path_graph(4, create_using=nx.DiGraph())</span>
<span class="sd">>>> DiGM = isomorphism.DiGraphMatcher(G1, G2)</span>
<span class="sd">>>> DiGM.is_isomorphic()</span>
<span class="sd">True</span>
<span class="sd">DiGM.mapping stores the isomorphism mapping from G1 to G2.</span>
<span class="sd">>>> DiGM.mapping</span>
<span class="sd">{0: 0, 1: 1, 2: 2, 3: 3}</span>
<span class="sd">Subgraph Isomorphism</span>
<span class="sd">--------------------</span>
<span class="sd">Graph theory literature can be ambiguous about the meaning of the</span>
<span class="sd">above statement, and we seek to clarify it now.</span>
<span class="sd">In the VF2 literature, a mapping M is said to be a graph-subgraph</span>
<span class="sd">isomorphism iff M is an isomorphism between G2 and a subgraph of G1.</span>
<span class="sd">Thus, to say that G1 and G2 are graph-subgraph isomorphic is to say</span>
<span class="sd">that a subgraph of G1 is isomorphic to G2.</span>
<span class="sd">Other literature uses the phrase 'subgraph isomorphic' as in 'G1 does</span>
<span class="sd">not have a subgraph isomorphic to G2'. Another use is as an in adverb</span>
<span class="sd">for isomorphic. Thus, to say that G1 and G2 are subgraph isomorphic</span>
<span class="sd">is to say that a subgraph of G1 is isomorphic to G2.</span>
<span class="sd">Finally, the term 'subgraph' can have multiple meanings. In this</span>
<span class="sd">context, 'subgraph' always means a 'node-induced subgraph'. Edge-induced</span>
<span class="sd">subgraph isomorphisms are not directly supported, but one should be</span>
<span class="sd">able to perform the check by making use of nx.line_graph(). For</span>
<span class="sd">subgraphs which are not induced, the term 'monomorphism' is preferred</span>
<span class="sd">over 'isomorphism'.</span>
<span class="sd">Let G=(N,E) be a graph with a set of nodes N and set of edges E.</span>
<span class="sd">If G'=(N',E') is a subgraph, then:</span>
<span class="sd"> N' is a subset of N</span>
<span class="sd"> E' is a subset of E</span>
<span class="sd">If G'=(N',E') is a node-induced subgraph, then:</span>
<span class="sd"> N' is a subset of N</span>
<span class="sd"> E' is the subset of edges in E relating nodes in N'</span>
<span class="sd">If G'=(N',E') is an edge-induced subgraph, then:</span>
<span class="sd"> N' is the subset of nodes in N related by edges in E'</span>
<span class="sd"> E' is a subset of E</span>
<span class="sd">If G'=(N',E') is a monomorphism, then:</span>
<span class="sd"> N' is a subset of N</span>
<span class="sd"> E' is a subset of the set of edges in E relating nodes in N'</span>
<span class="sd">Note that if G' is a node-induced subgraph of G, then it is always a</span>
<span class="sd">subgraph monomorphism of G, but the opposite is not always true, as a</span>
<span class="sd">monomorphism can have fewer edges.</span>
<span class="sd">References</span>
<span class="sd">----------</span>
<span class="sd">[1] Luigi P. Cordella, Pasquale Foggia, Carlo Sansone, Mario Vento,</span>
<span class="sd"> "A (Sub)Graph Isomorphism Algorithm for Matching Large Graphs",</span>
<span class="sd"> IEEE Transactions on Pattern Analysis and Machine Intelligence,</span>
<span class="sd"> vol. 26, no. 10, pp. 1367-1372, Oct., 2004.</span>
<span class="sd"> http://ieeexplore.ieee.org/iel5/34/29305/01323804.pdf</span>
<span class="sd">[2] L. P. Cordella, P. Foggia, C. Sansone, M. Vento, "An Improved</span>
<span class="sd"> Algorithm for Matching Large Graphs", 3rd IAPR-TC15 Workshop</span>
<span class="sd"> on Graph-based Representations in Pattern Recognition, Cuen,</span>
<span class="sd"> pp. 149-159, 2001.</span>
<span class="sd"> https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.101.5342</span>
<span class="sd">See Also</span>
<span class="sd">--------</span>
<span class="sd">syntactic_feasibility(), semantic_feasibility()</span>
<span class="sd">Notes</span>
<span class="sd">-----</span>
<span class="sd">The implementation handles both directed and undirected graphs as well</span>
<span class="sd">as multigraphs.</span>
<span class="sd">In general, the subgraph isomorphism problem is NP-complete whereas the</span>
<span class="sd">graph isomorphism problem is most likely not NP-complete (although no</span>
<span class="sd">polynomial-time algorithm is known to exist).</span>
<span class="sd">"""</span>
<span class="c1"># This work was originally coded by Christopher Ellison</span>
<span class="c1"># as part of the Computational Mechanics Python (CMPy) project.</span>
<span class="c1"># James P. Crutchfield, principal investigator.</span>
<span class="c1"># Complexity Sciences Center and Physics Department, UC Davis.</span>
<span class="kn">import</span> <span class="nn">sys</span>
<span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"GraphMatcher"</span><span class="p">,</span> <span class="s2">"DiGraphMatcher"</span><span class="p">]</span>
<span class="k">class</span> <span class="nc">GraphMatcher</span><span class="p">:</span>
<span class="sd">"""Implementation of VF2 algorithm for matching undirected graphs.</span>
<span class="sd"> Suitable for Graph and MultiGraph instances.</span>
<span class="sd"> """</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">G1</span><span class="p">,</span> <span class="n">G2</span><span class="p">):</span>
<span class="sd">"""Initialize GraphMatcher.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G1,G2: NetworkX Graph or MultiGraph instances.</span>
<span class="sd"> The two graphs to check for isomorphism or monomorphism.</span>
<span class="sd"> Examples</span>
<span class="sd"> --------</span>
<span class="sd"> To create a GraphMatcher which checks for syntactic feasibility:</span>
<span class="sd"> >>> from networkx.algorithms import isomorphism</span>
<span class="sd"> >>> G1 = nx.path_graph(4)</span>
<span class="sd"> >>> G2 = nx.path_graph(4)</span>
<span class="sd"> >>> GM = isomorphism.GraphMatcher(G1, G2)</span>
<span class="sd"> """</span>
<span class="bp">self</span><span class="o">.</span><span class="n">G1</span> <span class="o">=</span> <span class="n">G1</span>
<span class="bp">self</span><span class="o">.</span><span class="n">G2</span> <span class="o">=</span> <span class="n">G2</span>
<span class="bp">self</span><span class="o">.</span><span class="n">G1_nodes</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">G1</span><span class="o">.</span><span class="n">nodes</span><span class="p">())</span>
<span class="bp">self</span><span class="o">.</span><span class="n">G2_nodes</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">G2</span><span class="o">.</span><span class="n">nodes</span><span class="p">())</span>
<span class="bp">self</span><span class="o">.</span><span class="n">G2_node_order</span> <span class="o">=</span> <span class="p">{</span><span class="n">n</span><span class="p">:</span> <span class="n">i</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">G2</span><span class="p">)}</span>
<span class="c1"># Set recursion limit.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">old_recursion_limit</span> <span class="o">=</span> <span class="n">sys</span><span class="o">.</span><span class="n">getrecursionlimit</span><span class="p">()</span>
<span class="n">expected_max_recursion_level</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="p">)</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">old_recursion_limit</span> <span class="o"><</span> <span class="mf">1.5</span> <span class="o">*</span> <span class="n">expected_max_recursion_level</span><span class="p">:</span>
<span class="c1"># Give some breathing room.</span>
<span class="n">sys</span><span class="o">.</span><span class="n">setrecursionlimit</span><span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="mf">1.5</span> <span class="o">*</span> <span class="n">expected_max_recursion_level</span><span class="p">))</span>
<span class="c1"># Declare that we will be searching for a graph-graph isomorphism.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">test</span> <span class="o">=</span> <span class="s2">"graph"</span>
<span class="c1"># Initialize state</span>
<span class="bp">self</span><span class="o">.</span><span class="n">initialize</span><span class="p">()</span>
<span class="k">def</span> <span class="nf">reset_recursion_limit</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">"""Restores the recursion limit."""</span>
<span class="c1"># TODO:</span>
<span class="c1"># Currently, we use recursion and set the recursion level higher.</span>
<span class="c1"># It would be nice to restore the level, but because the</span>
<span class="c1"># (Di)GraphMatcher classes make use of cyclic references, garbage</span>
<span class="c1"># collection will never happen when we define __del__() to</span>
<span class="c1"># restore the recursion level. The result is a memory leak.</span>
<span class="c1"># So for now, we do not automatically restore the recursion level,</span>
<span class="c1"># and instead provide a method to do this manually. Eventually,</span>
<span class="c1"># we should turn this into a non-recursive implementation.</span>
<span class="n">sys</span><span class="o">.</span><span class="n">setrecursionlimit</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">old_recursion_limit</span><span class="p">)</span>
<div class="viewcode-block" id="GraphMatcher.candidate_pairs_iter"><a class="viewcode-back" href="../../../../reference/algorithms/generated/networkx.algorithms.isomorphism.GraphMatcher.candidate_pairs_iter.html#networkx.algorithms.isomorphism.GraphMatcher.candidate_pairs_iter">[docs]</a> <span class="k">def</span> <span class="nf">candidate_pairs_iter</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">"""Iterator over candidate pairs of nodes in G1 and G2."""</span>
<span class="c1"># All computations are done using the current state!</span>
<span class="n">G1_nodes</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1_nodes</span>
<span class="n">G2_nodes</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2_nodes</span>
<span class="n">min_key</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2_node_order</span><span class="o">.</span><span class="fm">__getitem__</span>
<span class="c1"># First we compute the inout-terminal sets.</span>
<span class="n">T1_inout</span> <span class="o">=</span> <span class="p">[</span><span class="n">node</span> <span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">inout_1</span> <span class="k">if</span> <span class="n">node</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_1</span><span class="p">]</span>
<span class="n">T2_inout</span> <span class="o">=</span> <span class="p">[</span><span class="n">node</span> <span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">inout_2</span> <span class="k">if</span> <span class="n">node</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_2</span><span class="p">]</span>
<span class="c1"># If T1_inout and T2_inout are both nonempty.</span>
<span class="c1"># P(s) = T1_inout x {min T2_inout}</span>
<span class="k">if</span> <span class="n">T1_inout</span> <span class="ow">and</span> <span class="n">T2_inout</span><span class="p">:</span>
<span class="n">node_2</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">T2_inout</span><span class="p">,</span> <span class="n">key</span><span class="o">=</span><span class="n">min_key</span><span class="p">)</span>
<span class="k">for</span> <span class="n">node_1</span> <span class="ow">in</span> <span class="n">T1_inout</span><span class="p">:</span>
<span class="k">yield</span> <span class="n">node_1</span><span class="p">,</span> <span class="n">node_2</span>
<span class="k">else</span><span class="p">:</span>
<span class="c1"># If T1_inout and T2_inout were both empty....</span>
<span class="c1"># P(s) = (N_1 - M_1) x {min (N_2 - M_2)}</span>
<span class="c1"># if not (T1_inout or T2_inout): # as suggested by [2], incorrect</span>
<span class="k">if</span> <span class="mi">1</span><span class="p">:</span> <span class="c1"># as inferred from [1], correct</span>
<span class="c1"># First we determine the candidate node for G2</span>
<span class="n">other_node</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">G2_nodes</span> <span class="o">-</span> <span class="nb">set</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">core_2</span><span class="p">),</span> <span class="n">key</span><span class="o">=</span><span class="n">min_key</span><span class="p">)</span>
<span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="p">:</span>
<span class="k">if</span> <span class="n">node</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_1</span><span class="p">:</span>
<span class="k">yield</span> <span class="n">node</span><span class="p">,</span> <span class="n">other_node</span></div>
<span class="c1"># For all other cases, we don't have any candidate pairs.</span>
<div class="viewcode-block" id="GraphMatcher.initialize"><a class="viewcode-back" href="../../../../reference/algorithms/generated/networkx.algorithms.isomorphism.GraphMatcher.initialize.html#networkx.algorithms.isomorphism.GraphMatcher.initialize">[docs]</a> <span class="k">def</span> <span class="nf">initialize</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">"""Reinitializes the state of the algorithm.</span>
<span class="sd"> This method should be redefined if using something other than GMState.</span>
<span class="sd"> If only subclassing GraphMatcher, a redefinition is not necessary.</span>
<span class="sd"> """</span>
<span class="c1"># core_1[n] contains the index of the node paired with n, which is m,</span>
<span class="c1"># provided n is in the mapping.</span>
<span class="c1"># core_2[m] contains the index of the node paired with m, which is n,</span>
<span class="c1"># provided m is in the mapping.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">core_1</span> <span class="o">=</span> <span class="p">{}</span>
<span class="bp">self</span><span class="o">.</span><span class="n">core_2</span> <span class="o">=</span> <span class="p">{}</span>
<span class="c1"># See the paper for definitions of M_x and T_x^{y}</span>
<span class="c1"># inout_1[n] is non-zero if n is in M_1 or in T_1^{inout}</span>
<span class="c1"># inout_2[m] is non-zero if m is in M_2 or in T_2^{inout}</span>
<span class="c1">#</span>
<span class="c1"># The value stored is the depth of the SSR tree when the node became</span>
<span class="c1"># part of the corresponding set.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">inout_1</span> <span class="o">=</span> <span class="p">{}</span>
<span class="bp">self</span><span class="o">.</span><span class="n">inout_2</span> <span class="o">=</span> <span class="p">{}</span>
<span class="c1"># Practically, these sets simply store the nodes in the subgraph.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">state</span> <span class="o">=</span> <span class="n">GMState</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span>
<span class="c1"># Provide a convenient way to access the isomorphism mapping.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">mapping</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_1</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span></div>
<div class="viewcode-block" id="GraphMatcher.is_isomorphic"><a class="viewcode-back" href="../../../../reference/algorithms/generated/networkx.algorithms.isomorphism.GraphMatcher.is_isomorphic.html#networkx.algorithms.isomorphism.GraphMatcher.is_isomorphic">[docs]</a> <span class="k">def</span> <span class="nf">is_isomorphic</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">"""Returns True if G1 and G2 are isomorphic graphs."""</span>
<span class="c1"># Let's do two very quick checks!</span>
<span class="c1"># QUESTION: Should we call faster_graph_could_be_isomorphic(G1,G2)?</span>
<span class="c1"># For now, I just copy the code.</span>
<span class="c1"># Check global properties</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="o">.</span><span class="n">order</span><span class="p">()</span> <span class="o">!=</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="o">.</span><span class="n">order</span><span class="p">():</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="c1"># Check local properties</span>
<span class="n">d1</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">d</span> <span class="k">for</span> <span class="n">n</span><span class="p">,</span> <span class="n">d</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="o">.</span><span class="n">degree</span><span class="p">())</span>
<span class="n">d2</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">d</span> <span class="k">for</span> <span class="n">n</span><span class="p">,</span> <span class="n">d</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="o">.</span><span class="n">degree</span><span class="p">())</span>
<span class="k">if</span> <span class="n">d1</span> <span class="o">!=</span> <span class="n">d2</span><span class="p">:</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">try</span><span class="p">:</span>
<span class="n">x</span> <span class="o">=</span> <span class="nb">next</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">isomorphisms_iter</span><span class="p">())</span>
<span class="k">return</span> <span class="kc">True</span>
<span class="k">except</span> <span class="ne">StopIteration</span><span class="p">:</span>
<span class="k">return</span> <span class="kc">False</span></div>
<div class="viewcode-block" id="GraphMatcher.isomorphisms_iter"><a class="viewcode-back" href="../../../../reference/algorithms/generated/networkx.algorithms.isomorphism.GraphMatcher.isomorphisms_iter.html#networkx.algorithms.isomorphism.GraphMatcher.isomorphisms_iter">[docs]</a> <span class="k">def</span> <span class="nf">isomorphisms_iter</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">"""Generator over isomorphisms between G1 and G2."""</span>
<span class="c1"># Declare that we are looking for a graph-graph isomorphism.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">test</span> <span class="o">=</span> <span class="s2">"graph"</span>
<span class="bp">self</span><span class="o">.</span><span class="n">initialize</span><span class="p">()</span>
<span class="k">yield from</span> <span class="bp">self</span><span class="o">.</span><span class="n">match</span><span class="p">()</span></div>
<div class="viewcode-block" id="GraphMatcher.match"><a class="viewcode-back" href="../../../../reference/algorithms/generated/networkx.algorithms.isomorphism.GraphMatcher.match.html#networkx.algorithms.isomorphism.GraphMatcher.match">[docs]</a> <span class="k">def</span> <span class="nf">match</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">"""Extends the isomorphism mapping.</span>
<span class="sd"> This function is called recursively to determine if a complete</span>
<span class="sd"> isomorphism can be found between G1 and G2. It cleans up the class</span>
<span class="sd"> variables after each recursive call. If an isomorphism is found,</span>
<span class="sd"> we yield the mapping.</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">core_1</span><span class="p">)</span> <span class="o">==</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="p">):</span>
<span class="c1"># Save the final mapping, otherwise garbage collection deletes it.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">mapping</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_1</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
<span class="c1"># The mapping is complete.</span>
<span class="k">yield</span> <span class="bp">self</span><span class="o">.</span><span class="n">mapping</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">for</span> <span class="n">G1_node</span><span class="p">,</span> <span class="n">G2_node</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">candidate_pairs_iter</span><span class="p">():</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">syntactic_feasibility</span><span class="p">(</span><span class="n">G1_node</span><span class="p">,</span> <span class="n">G2_node</span><span class="p">):</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">semantic_feasibility</span><span class="p">(</span><span class="n">G1_node</span><span class="p">,</span> <span class="n">G2_node</span><span class="p">):</span>
<span class="c1"># Recursive call, adding the feasible state.</span>
<span class="n">newstate</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">state</span><span class="o">.</span><span class="vm">__class__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">G1_node</span><span class="p">,</span> <span class="n">G2_node</span><span class="p">)</span>
<span class="k">yield from</span> <span class="bp">self</span><span class="o">.</span><span class="n">match</span><span class="p">()</span>
<span class="c1"># restore data structures</span>
<span class="n">newstate</span><span class="o">.</span><span class="n">restore</span><span class="p">()</span></div>
<span class="k">def</span> <span class="nf">semantic_feasibility</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">G1_node</span><span class="p">,</span> <span class="n">G2_node</span><span class="p">):</span>
<span class="sd">"""Returns True if adding (G1_node, G2_node) is symantically feasible.</span>
<span class="sd"> The semantic feasibility function should return True if it is</span>
<span class="sd"> acceptable to add the candidate pair (G1_node, G2_node) to the current</span>
<span class="sd"> partial isomorphism mapping. The logic should focus on semantic</span>
<span class="sd"> information contained in the edge data or a formalized node class.</span>
<span class="sd"> By acceptable, we mean that the subsequent mapping can still become a</span>
<span class="sd"> complete isomorphism mapping. Thus, if adding the candidate pair</span>
<span class="sd"> definitely makes it so that the subsequent mapping cannot become a</span>
<span class="sd"> complete isomorphism mapping, then this function must return False.</span>
<span class="sd"> The default semantic feasibility function always returns True. The</span>
<span class="sd"> effect is that semantics are not considered in the matching of G1</span>
<span class="sd"> and G2.</span>
<span class="sd"> The semantic checks might differ based on the what type of test is</span>
<span class="sd"> being performed. A keyword description of the test is stored in</span>
<span class="sd"> self.test. Here is a quick description of the currently implemented</span>
<span class="sd"> tests::</span>
<span class="sd"> test='graph'</span>
<span class="sd"> Indicates that the graph matcher is looking for a graph-graph</span>
<span class="sd"> isomorphism.</span>
<span class="sd"> test='subgraph'</span>
<span class="sd"> Indicates that the graph matcher is looking for a subgraph-graph</span>
<span class="sd"> isomorphism such that a subgraph of G1 is isomorphic to G2.</span>
<span class="sd"> test='mono'</span>
<span class="sd"> Indicates that the graph matcher is looking for a subgraph-graph</span>
<span class="sd"> monomorphism such that a subgraph of G1 is monomorphic to G2.</span>
<span class="sd"> Any subclass which redefines semantic_feasibility() must maintain</span>
<span class="sd"> the above form to keep the match() method functional. Implementations</span>
<span class="sd"> should consider multigraphs.</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="kc">True</span>
<div class="viewcode-block" id="GraphMatcher.subgraph_is_isomorphic"><a class="viewcode-back" href="../../../../reference/algorithms/generated/networkx.algorithms.isomorphism.GraphMatcher.subgraph_is_isomorphic.html#networkx.algorithms.isomorphism.GraphMatcher.subgraph_is_isomorphic">[docs]</a> <span class="k">def</span> <span class="nf">subgraph_is_isomorphic</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">"""Returns True if a subgraph of G1 is isomorphic to G2."""</span>
<span class="k">try</span><span class="p">:</span>
<span class="n">x</span> <span class="o">=</span> <span class="nb">next</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">subgraph_isomorphisms_iter</span><span class="p">())</span>
<span class="k">return</span> <span class="kc">True</span>
<span class="k">except</span> <span class="ne">StopIteration</span><span class="p">:</span>
<span class="k">return</span> <span class="kc">False</span></div>
<span class="k">def</span> <span class="nf">subgraph_is_monomorphic</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">"""Returns True if a subgraph of G1 is monomorphic to G2."""</span>
<span class="k">try</span><span class="p">:</span>
<span class="n">x</span> <span class="o">=</span> <span class="nb">next</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">subgraph_monomorphisms_iter</span><span class="p">())</span>
<span class="k">return</span> <span class="kc">True</span>
<span class="k">except</span> <span class="ne">StopIteration</span><span class="p">:</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="c1"># subgraph_is_isomorphic.__doc__ += "\n" + subgraph.replace('\n','\n'+indent)</span>
<div class="viewcode-block" id="GraphMatcher.subgraph_isomorphisms_iter"><a class="viewcode-back" href="../../../../reference/algorithms/generated/networkx.algorithms.isomorphism.GraphMatcher.subgraph_isomorphisms_iter.html#networkx.algorithms.isomorphism.GraphMatcher.subgraph_isomorphisms_iter">[docs]</a> <span class="k">def</span> <span class="nf">subgraph_isomorphisms_iter</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">"""Generator over isomorphisms between a subgraph of G1 and G2."""</span>
<span class="c1"># Declare that we are looking for graph-subgraph isomorphism.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">test</span> <span class="o">=</span> <span class="s2">"subgraph"</span>
<span class="bp">self</span><span class="o">.</span><span class="n">initialize</span><span class="p">()</span>
<span class="k">yield from</span> <span class="bp">self</span><span class="o">.</span><span class="n">match</span><span class="p">()</span></div>
<span class="k">def</span> <span class="nf">subgraph_monomorphisms_iter</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">"""Generator over monomorphisms between a subgraph of G1 and G2."""</span>
<span class="c1"># Declare that we are looking for graph-subgraph monomorphism.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">test</span> <span class="o">=</span> <span class="s2">"mono"</span>
<span class="bp">self</span><span class="o">.</span><span class="n">initialize</span><span class="p">()</span>
<span class="k">yield from</span> <span class="bp">self</span><span class="o">.</span><span class="n">match</span><span class="p">()</span>
<span class="c1"># subgraph_isomorphisms_iter.__doc__ += "\n" + subgraph.replace('\n','\n'+indent)</span>
<div class="viewcode-block" id="GraphMatcher.syntactic_feasibility"><a class="viewcode-back" href="../../../../reference/algorithms/generated/networkx.algorithms.isomorphism.GraphMatcher.syntactic_feasibility.html#networkx.algorithms.isomorphism.GraphMatcher.syntactic_feasibility">[docs]</a> <span class="k">def</span> <span class="nf">syntactic_feasibility</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">G1_node</span><span class="p">,</span> <span class="n">G2_node</span><span class="p">):</span>
<span class="sd">"""Returns True if adding (G1_node, G2_node) is syntactically feasible.</span>
<span class="sd"> This function returns True if it is adding the candidate pair</span>
<span class="sd"> to the current partial isomorphism/monomorphism mapping is allowable.</span>
<span class="sd"> The addition is allowable if the inclusion of the candidate pair does</span>
<span class="sd"> not make it impossible for an isomorphism/monomorphism to be found.</span>
<span class="sd"> """</span>
<span class="c1"># The VF2 algorithm was designed to work with graphs having, at most,</span>
<span class="c1"># one edge connecting any two nodes. This is not the case when</span>
<span class="c1"># dealing with an MultiGraphs.</span>
<span class="c1">#</span>
<span class="c1"># Basically, when we test the look-ahead rules R_neighbor, we will</span>
<span class="c1"># make sure that the number of edges are checked. We also add</span>
<span class="c1"># a R_self check to verify that the number of selfloops is acceptable.</span>
<span class="c1">#</span>
<span class="c1"># Users might be comparing Graph instances with MultiGraph instances.</span>
<span class="c1"># So the generic GraphMatcher class must work with MultiGraphs.</span>
<span class="c1"># Care must be taken since the value in the innermost dictionary is a</span>
<span class="c1"># singlet for Graph instances. For MultiGraphs, the value in the</span>
<span class="c1"># innermost dictionary is a list.</span>
<span class="c1">###</span>
<span class="c1"># Test at each step to get a return value as soon as possible.</span>
<span class="c1">###</span>
<span class="c1"># Look ahead 0</span>
<span class="c1"># R_self</span>
<span class="c1"># The number of selfloops for G1_node must equal the number of</span>
<span class="c1"># self-loops for G2_node. Without this check, we would fail on</span>
<span class="c1"># R_neighbor at the next recursion level. But it is good to prune the</span>
<span class="c1"># search tree now.</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">test</span> <span class="o">==</span> <span class="s2">"mono"</span><span class="p">:</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="o">.</span><span class="n">number_of_edges</span><span class="p">(</span><span class="n">G1_node</span><span class="p">,</span> <span class="n">G1_node</span><span class="p">)</span> <span class="o"><</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="o">.</span><span class="n">number_of_edges</span><span class="p">(</span>
<span class="n">G2_node</span><span class="p">,</span> <span class="n">G2_node</span>
<span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="o">.</span><span class="n">number_of_edges</span><span class="p">(</span><span class="n">G1_node</span><span class="p">,</span> <span class="n">G1_node</span><span class="p">)</span> <span class="o">!=</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="o">.</span><span class="n">number_of_edges</span><span class="p">(</span>
<span class="n">G2_node</span><span class="p">,</span> <span class="n">G2_node</span>
<span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="c1"># R_neighbor</span>
<span class="c1"># For each neighbor n' of n in the partial mapping, the corresponding</span>
<span class="c1"># node m' is a neighbor of m, and vice versa. Also, the number of</span>
<span class="c1"># edges must be equal.</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">test</span> <span class="o">!=</span> <span class="s2">"mono"</span><span class="p">:</span>
<span class="k">for</span> <span class="n">neighbor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="p">[</span><span class="n">G1_node</span><span class="p">]:</span>
<span class="k">if</span> <span class="n">neighbor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_1</span><span class="p">:</span>
<span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">core_1</span><span class="p">[</span><span class="n">neighbor</span><span class="p">]</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="p">[</span><span class="n">G2_node</span><span class="p">]):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="o">.</span><span class="n">number_of_edges</span><span class="p">(</span>
<span class="n">neighbor</span><span class="p">,</span> <span class="n">G1_node</span>
<span class="p">)</span> <span class="o">!=</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="o">.</span><span class="n">number_of_edges</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">core_1</span><span class="p">[</span><span class="n">neighbor</span><span class="p">],</span> <span class="n">G2_node</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">for</span> <span class="n">neighbor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="p">[</span><span class="n">G2_node</span><span class="p">]:</span>
<span class="k">if</span> <span class="n">neighbor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_2</span><span class="p">:</span>
<span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">core_2</span><span class="p">[</span><span class="n">neighbor</span><span class="p">]</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="p">[</span><span class="n">G1_node</span><span class="p">]):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">test</span> <span class="o">==</span> <span class="s2">"mono"</span><span class="p">:</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="o">.</span><span class="n">number_of_edges</span><span class="p">(</span>
<span class="bp">self</span><span class="o">.</span><span class="n">core_2</span><span class="p">[</span><span class="n">neighbor</span><span class="p">],</span> <span class="n">G1_node</span>
<span class="p">)</span> <span class="o"><</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="o">.</span><span class="n">number_of_edges</span><span class="p">(</span><span class="n">neighbor</span><span class="p">,</span> <span class="n">G2_node</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="o">.</span><span class="n">number_of_edges</span><span class="p">(</span>
<span class="bp">self</span><span class="o">.</span><span class="n">core_2</span><span class="p">[</span><span class="n">neighbor</span><span class="p">],</span> <span class="n">G1_node</span>
<span class="p">)</span> <span class="o">!=</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="o">.</span><span class="n">number_of_edges</span><span class="p">(</span><span class="n">neighbor</span><span class="p">,</span> <span class="n">G2_node</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">test</span> <span class="o">!=</span> <span class="s2">"mono"</span><span class="p">:</span>
<span class="c1"># Look ahead 1</span>
<span class="c1"># R_terminout</span>
<span class="c1"># The number of neighbors of n in T_1^{inout} is equal to the</span>
<span class="c1"># number of neighbors of m that are in T_2^{inout}, and vice versa.</span>
<span class="n">num1</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">neighbor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="p">[</span><span class="n">G1_node</span><span class="p">]:</span>
<span class="k">if</span> <span class="p">(</span><span class="n">neighbor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">inout_1</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">neighbor</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_1</span><span class="p">):</span>
<span class="n">num1</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">num2</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">neighbor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="p">[</span><span class="n">G2_node</span><span class="p">]:</span>
<span class="k">if</span> <span class="p">(</span><span class="n">neighbor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">inout_2</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">neighbor</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_2</span><span class="p">):</span>
<span class="n">num2</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">test</span> <span class="o">==</span> <span class="s2">"graph"</span><span class="p">:</span>
<span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">num1</span> <span class="o">==</span> <span class="n">num2</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">else</span><span class="p">:</span> <span class="c1"># self.test == 'subgraph'</span>
<span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">num1</span> <span class="o">>=</span> <span class="n">num2</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="c1"># Look ahead 2</span>
<span class="c1"># R_new</span>
<span class="c1"># The number of neighbors of n that are neither in the core_1 nor</span>
<span class="c1"># T_1^{inout} is equal to the number of neighbors of m</span>
<span class="c1"># that are neither in core_2 nor T_2^{inout}.</span>
<span class="n">num1</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">neighbor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="p">[</span><span class="n">G1_node</span><span class="p">]:</span>
<span class="k">if</span> <span class="n">neighbor</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">inout_1</span><span class="p">:</span>
<span class="n">num1</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">num2</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">neighbor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="p">[</span><span class="n">G2_node</span><span class="p">]:</span>
<span class="k">if</span> <span class="n">neighbor</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">inout_2</span><span class="p">:</span>
<span class="n">num2</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">test</span> <span class="o">==</span> <span class="s2">"graph"</span><span class="p">:</span>
<span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">num1</span> <span class="o">==</span> <span class="n">num2</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">else</span><span class="p">:</span> <span class="c1"># self.test == 'subgraph'</span>
<span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">num1</span> <span class="o">>=</span> <span class="n">num2</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="c1"># Otherwise, this node pair is syntactically feasible!</span>
<span class="k">return</span> <span class="kc">True</span></div>
<span class="k">class</span> <span class="nc">DiGraphMatcher</span><span class="p">(</span><span class="n">GraphMatcher</span><span class="p">):</span>
<span class="sd">"""Implementation of VF2 algorithm for matching directed graphs.</span>
<span class="sd"> Suitable for DiGraph and MultiDiGraph instances.</span>
<span class="sd"> """</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">G1</span><span class="p">,</span> <span class="n">G2</span><span class="p">):</span>
<span class="sd">"""Initialize DiGraphMatcher.</span>
<span class="sd"> G1 and G2 should be nx.Graph or nx.MultiGraph instances.</span>
<span class="sd"> Examples</span>
<span class="sd"> --------</span>
<span class="sd"> To create a GraphMatcher which checks for syntactic feasibility:</span>
<span class="sd"> >>> from networkx.algorithms import isomorphism</span>
<span class="sd"> >>> G1 = nx.DiGraph(nx.path_graph(4, create_using=nx.DiGraph()))</span>
<span class="sd"> >>> G2 = nx.DiGraph(nx.path_graph(4, create_using=nx.DiGraph()))</span>
<span class="sd"> >>> DiGM = isomorphism.DiGraphMatcher(G1, G2)</span>
<span class="sd"> """</span>
<span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">G1</span><span class="p">,</span> <span class="n">G2</span><span class="p">)</span>
<div class="viewcode-block" id="DiGraphMatcher.candidate_pairs_iter"><a class="viewcode-back" href="../../../../reference/algorithms/generated/networkx.algorithms.isomorphism.DiGraphMatcher.candidate_pairs_iter.html#networkx.algorithms.isomorphism.DiGraphMatcher.candidate_pairs_iter">[docs]</a> <span class="k">def</span> <span class="nf">candidate_pairs_iter</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">"""Iterator over candidate pairs of nodes in G1 and G2."""</span>
<span class="c1"># All computations are done using the current state!</span>
<span class="n">G1_nodes</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1_nodes</span>
<span class="n">G2_nodes</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2_nodes</span>
<span class="n">min_key</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2_node_order</span><span class="o">.</span><span class="fm">__getitem__</span>
<span class="c1"># First we compute the out-terminal sets.</span>
<span class="n">T1_out</span> <span class="o">=</span> <span class="p">[</span><span class="n">node</span> <span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">out_1</span> <span class="k">if</span> <span class="n">node</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_1</span><span class="p">]</span>
<span class="n">T2_out</span> <span class="o">=</span> <span class="p">[</span><span class="n">node</span> <span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">out_2</span> <span class="k">if</span> <span class="n">node</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_2</span><span class="p">]</span>
<span class="c1"># If T1_out and T2_out are both nonempty.</span>
<span class="c1"># P(s) = T1_out x {min T2_out}</span>
<span class="k">if</span> <span class="n">T1_out</span> <span class="ow">and</span> <span class="n">T2_out</span><span class="p">:</span>
<span class="n">node_2</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">T2_out</span><span class="p">,</span> <span class="n">key</span><span class="o">=</span><span class="n">min_key</span><span class="p">)</span>
<span class="k">for</span> <span class="n">node_1</span> <span class="ow">in</span> <span class="n">T1_out</span><span class="p">:</span>
<span class="k">yield</span> <span class="n">node_1</span><span class="p">,</span> <span class="n">node_2</span>
<span class="c1"># If T1_out and T2_out were both empty....</span>
<span class="c1"># We compute the in-terminal sets.</span>
<span class="c1"># elif not (T1_out or T2_out): # as suggested by [2], incorrect</span>
<span class="k">else</span><span class="p">:</span> <span class="c1"># as suggested by [1], correct</span>
<span class="n">T1_in</span> <span class="o">=</span> <span class="p">[</span><span class="n">node</span> <span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">in_1</span> <span class="k">if</span> <span class="n">node</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_1</span><span class="p">]</span>
<span class="n">T2_in</span> <span class="o">=</span> <span class="p">[</span><span class="n">node</span> <span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">in_2</span> <span class="k">if</span> <span class="n">node</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_2</span><span class="p">]</span>
<span class="c1"># If T1_in and T2_in are both nonempty.</span>
<span class="c1"># P(s) = T1_out x {min T2_out}</span>
<span class="k">if</span> <span class="n">T1_in</span> <span class="ow">and</span> <span class="n">T2_in</span><span class="p">:</span>
<span class="n">node_2</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">T2_in</span><span class="p">,</span> <span class="n">key</span><span class="o">=</span><span class="n">min_key</span><span class="p">)</span>
<span class="k">for</span> <span class="n">node_1</span> <span class="ow">in</span> <span class="n">T1_in</span><span class="p">:</span>
<span class="k">yield</span> <span class="n">node_1</span><span class="p">,</span> <span class="n">node_2</span>
<span class="c1"># If all terminal sets are empty...</span>
<span class="c1"># P(s) = (N_1 - M_1) x {min (N_2 - M_2)}</span>
<span class="c1"># elif not (T1_in or T2_in): # as suggested by [2], incorrect</span>
<span class="k">else</span><span class="p">:</span> <span class="c1"># as inferred from [1], correct</span>
<span class="n">node_2</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">G2_nodes</span> <span class="o">-</span> <span class="nb">set</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">core_2</span><span class="p">),</span> <span class="n">key</span><span class="o">=</span><span class="n">min_key</span><span class="p">)</span>
<span class="k">for</span> <span class="n">node_1</span> <span class="ow">in</span> <span class="n">G1_nodes</span><span class="p">:</span>
<span class="k">if</span> <span class="n">node_1</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_1</span><span class="p">:</span>
<span class="k">yield</span> <span class="n">node_1</span><span class="p">,</span> <span class="n">node_2</span></div>
<span class="c1"># For all other cases, we don't have any candidate pairs.</span>
<div class="viewcode-block" id="DiGraphMatcher.initialize"><a class="viewcode-back" href="../../../../reference/algorithms/generated/networkx.algorithms.isomorphism.DiGraphMatcher.initialize.html#networkx.algorithms.isomorphism.DiGraphMatcher.initialize">[docs]</a> <span class="k">def</span> <span class="nf">initialize</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">"""Reinitializes the state of the algorithm.</span>
<span class="sd"> This method should be redefined if using something other than DiGMState.</span>
<span class="sd"> If only subclassing GraphMatcher, a redefinition is not necessary.</span>
<span class="sd"> """</span>
<span class="c1"># core_1[n] contains the index of the node paired with n, which is m,</span>
<span class="c1"># provided n is in the mapping.</span>
<span class="c1"># core_2[m] contains the index of the node paired with m, which is n,</span>
<span class="c1"># provided m is in the mapping.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">core_1</span> <span class="o">=</span> <span class="p">{}</span>
<span class="bp">self</span><span class="o">.</span><span class="n">core_2</span> <span class="o">=</span> <span class="p">{}</span>
<span class="c1"># See the paper for definitions of M_x and T_x^{y}</span>
<span class="c1"># in_1[n] is non-zero if n is in M_1 or in T_1^{in}</span>
<span class="c1"># out_1[n] is non-zero if n is in M_1 or in T_1^{out}</span>
<span class="c1">#</span>
<span class="c1"># in_2[m] is non-zero if m is in M_2 or in T_2^{in}</span>
<span class="c1"># out_2[m] is non-zero if m is in M_2 or in T_2^{out}</span>
<span class="c1">#</span>
<span class="c1"># The value stored is the depth of the search tree when the node became</span>
<span class="c1"># part of the corresponding set.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">in_1</span> <span class="o">=</span> <span class="p">{}</span>
<span class="bp">self</span><span class="o">.</span><span class="n">in_2</span> <span class="o">=</span> <span class="p">{}</span>
<span class="bp">self</span><span class="o">.</span><span class="n">out_1</span> <span class="o">=</span> <span class="p">{}</span>
<span class="bp">self</span><span class="o">.</span><span class="n">out_2</span> <span class="o">=</span> <span class="p">{}</span>
<span class="bp">self</span><span class="o">.</span><span class="n">state</span> <span class="o">=</span> <span class="n">DiGMState</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span>
<span class="c1"># Provide a convenient way to access the isomorphism mapping.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">mapping</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_1</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span></div>
<div class="viewcode-block" id="DiGraphMatcher.syntactic_feasibility"><a class="viewcode-back" href="../../../../reference/algorithms/generated/networkx.algorithms.isomorphism.DiGraphMatcher.syntactic_feasibility.html#networkx.algorithms.isomorphism.DiGraphMatcher.syntactic_feasibility">[docs]</a> <span class="k">def</span> <span class="nf">syntactic_feasibility</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">G1_node</span><span class="p">,</span> <span class="n">G2_node</span><span class="p">):</span>
<span class="sd">"""Returns True if adding (G1_node, G2_node) is syntactically feasible.</span>
<span class="sd"> This function returns True if it is adding the candidate pair</span>
<span class="sd"> to the current partial isomorphism/monomorphism mapping is allowable.</span>
<span class="sd"> The addition is allowable if the inclusion of the candidate pair does</span>
<span class="sd"> not make it impossible for an isomorphism/monomorphism to be found.</span>
<span class="sd"> """</span>
<span class="c1"># The VF2 algorithm was designed to work with graphs having, at most,</span>
<span class="c1"># one edge connecting any two nodes. This is not the case when</span>
<span class="c1"># dealing with an MultiGraphs.</span>
<span class="c1">#</span>
<span class="c1"># Basically, when we test the look-ahead rules R_pred and R_succ, we</span>
<span class="c1"># will make sure that the number of edges are checked. We also add</span>
<span class="c1"># a R_self check to verify that the number of selfloops is acceptable.</span>
<span class="c1"># Users might be comparing DiGraph instances with MultiDiGraph</span>
<span class="c1"># instances. So the generic DiGraphMatcher class must work with</span>
<span class="c1"># MultiDiGraphs. Care must be taken since the value in the innermost</span>
<span class="c1"># dictionary is a singlet for DiGraph instances. For MultiDiGraphs,</span>
<span class="c1"># the value in the innermost dictionary is a list.</span>
<span class="c1">###</span>
<span class="c1"># Test at each step to get a return value as soon as possible.</span>
<span class="c1">###</span>
<span class="c1"># Look ahead 0</span>
<span class="c1"># R_self</span>
<span class="c1"># The number of selfloops for G1_node must equal the number of</span>
<span class="c1"># self-loops for G2_node. Without this check, we would fail on R_pred</span>
<span class="c1"># at the next recursion level. This should prune the tree even further.</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">test</span> <span class="o">==</span> <span class="s2">"mono"</span><span class="p">:</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="o">.</span><span class="n">number_of_edges</span><span class="p">(</span><span class="n">G1_node</span><span class="p">,</span> <span class="n">G1_node</span><span class="p">)</span> <span class="o"><</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="o">.</span><span class="n">number_of_edges</span><span class="p">(</span>
<span class="n">G2_node</span><span class="p">,</span> <span class="n">G2_node</span>
<span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="o">.</span><span class="n">number_of_edges</span><span class="p">(</span><span class="n">G1_node</span><span class="p">,</span> <span class="n">G1_node</span><span class="p">)</span> <span class="o">!=</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="o">.</span><span class="n">number_of_edges</span><span class="p">(</span>
<span class="n">G2_node</span><span class="p">,</span> <span class="n">G2_node</span>
<span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="c1"># R_pred</span>
<span class="c1"># For each predecessor n' of n in the partial mapping, the</span>
<span class="c1"># corresponding node m' is a predecessor of m, and vice versa. Also,</span>
<span class="c1"># the number of edges must be equal</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">test</span> <span class="o">!=</span> <span class="s2">"mono"</span><span class="p">:</span>
<span class="k">for</span> <span class="n">predecessor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="o">.</span><span class="n">pred</span><span class="p">[</span><span class="n">G1_node</span><span class="p">]:</span>
<span class="k">if</span> <span class="n">predecessor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_1</span><span class="p">:</span>
<span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">core_1</span><span class="p">[</span><span class="n">predecessor</span><span class="p">]</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="o">.</span><span class="n">pred</span><span class="p">[</span><span class="n">G2_node</span><span class="p">]):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="o">.</span><span class="n">number_of_edges</span><span class="p">(</span>
<span class="n">predecessor</span><span class="p">,</span> <span class="n">G1_node</span>
<span class="p">)</span> <span class="o">!=</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="o">.</span><span class="n">number_of_edges</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">core_1</span><span class="p">[</span><span class="n">predecessor</span><span class="p">],</span> <span class="n">G2_node</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">for</span> <span class="n">predecessor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="o">.</span><span class="n">pred</span><span class="p">[</span><span class="n">G2_node</span><span class="p">]:</span>
<span class="k">if</span> <span class="n">predecessor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_2</span><span class="p">:</span>
<span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">core_2</span><span class="p">[</span><span class="n">predecessor</span><span class="p">]</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="o">.</span><span class="n">pred</span><span class="p">[</span><span class="n">G1_node</span><span class="p">]):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">test</span> <span class="o">==</span> <span class="s2">"mono"</span><span class="p">:</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="o">.</span><span class="n">number_of_edges</span><span class="p">(</span>
<span class="bp">self</span><span class="o">.</span><span class="n">core_2</span><span class="p">[</span><span class="n">predecessor</span><span class="p">],</span> <span class="n">G1_node</span>
<span class="p">)</span> <span class="o"><</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="o">.</span><span class="n">number_of_edges</span><span class="p">(</span><span class="n">predecessor</span><span class="p">,</span> <span class="n">G2_node</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="o">.</span><span class="n">number_of_edges</span><span class="p">(</span>
<span class="bp">self</span><span class="o">.</span><span class="n">core_2</span><span class="p">[</span><span class="n">predecessor</span><span class="p">],</span> <span class="n">G1_node</span>
<span class="p">)</span> <span class="o">!=</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="o">.</span><span class="n">number_of_edges</span><span class="p">(</span><span class="n">predecessor</span><span class="p">,</span> <span class="n">G2_node</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="c1"># R_succ</span>
<span class="c1"># For each successor n' of n in the partial mapping, the corresponding</span>
<span class="c1"># node m' is a successor of m, and vice versa. Also, the number of</span>
<span class="c1"># edges must be equal.</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">test</span> <span class="o">!=</span> <span class="s2">"mono"</span><span class="p">:</span>
<span class="k">for</span> <span class="n">successor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="p">[</span><span class="n">G1_node</span><span class="p">]:</span>
<span class="k">if</span> <span class="n">successor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_1</span><span class="p">:</span>
<span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">core_1</span><span class="p">[</span><span class="n">successor</span><span class="p">]</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="p">[</span><span class="n">G2_node</span><span class="p">]):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="o">.</span><span class="n">number_of_edges</span><span class="p">(</span>
<span class="n">G1_node</span><span class="p">,</span> <span class="n">successor</span>
<span class="p">)</span> <span class="o">!=</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="o">.</span><span class="n">number_of_edges</span><span class="p">(</span><span class="n">G2_node</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_1</span><span class="p">[</span><span class="n">successor</span><span class="p">]):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">for</span> <span class="n">successor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="p">[</span><span class="n">G2_node</span><span class="p">]:</span>
<span class="k">if</span> <span class="n">successor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_2</span><span class="p">:</span>
<span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">core_2</span><span class="p">[</span><span class="n">successor</span><span class="p">]</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="p">[</span><span class="n">G1_node</span><span class="p">]):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">test</span> <span class="o">==</span> <span class="s2">"mono"</span><span class="p">:</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="o">.</span><span class="n">number_of_edges</span><span class="p">(</span>
<span class="n">G1_node</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_2</span><span class="p">[</span><span class="n">successor</span><span class="p">]</span>
<span class="p">)</span> <span class="o"><</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="o">.</span><span class="n">number_of_edges</span><span class="p">(</span><span class="n">G2_node</span><span class="p">,</span> <span class="n">successor</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="o">.</span><span class="n">number_of_edges</span><span class="p">(</span>
<span class="n">G1_node</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_2</span><span class="p">[</span><span class="n">successor</span><span class="p">]</span>
<span class="p">)</span> <span class="o">!=</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="o">.</span><span class="n">number_of_edges</span><span class="p">(</span><span class="n">G2_node</span><span class="p">,</span> <span class="n">successor</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">test</span> <span class="o">!=</span> <span class="s2">"mono"</span><span class="p">:</span>
<span class="c1"># Look ahead 1</span>
<span class="c1"># R_termin</span>
<span class="c1"># The number of predecessors of n that are in T_1^{in} is equal to the</span>
<span class="c1"># number of predecessors of m that are in T_2^{in}.</span>
<span class="n">num1</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">predecessor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="o">.</span><span class="n">pred</span><span class="p">[</span><span class="n">G1_node</span><span class="p">]:</span>
<span class="k">if</span> <span class="p">(</span><span class="n">predecessor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">in_1</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">predecessor</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_1</span><span class="p">):</span>
<span class="n">num1</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">num2</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">predecessor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="o">.</span><span class="n">pred</span><span class="p">[</span><span class="n">G2_node</span><span class="p">]:</span>
<span class="k">if</span> <span class="p">(</span><span class="n">predecessor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">in_2</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">predecessor</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_2</span><span class="p">):</span>
<span class="n">num2</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">test</span> <span class="o">==</span> <span class="s2">"graph"</span><span class="p">:</span>
<span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">num1</span> <span class="o">==</span> <span class="n">num2</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">else</span><span class="p">:</span> <span class="c1"># self.test == 'subgraph'</span>
<span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">num1</span> <span class="o">>=</span> <span class="n">num2</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="c1"># The number of successors of n that are in T_1^{in} is equal to the</span>
<span class="c1"># number of successors of m that are in T_2^{in}.</span>
<span class="n">num1</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">successor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="p">[</span><span class="n">G1_node</span><span class="p">]:</span>
<span class="k">if</span> <span class="p">(</span><span class="n">successor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">in_1</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">successor</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_1</span><span class="p">):</span>
<span class="n">num1</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">num2</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">successor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="p">[</span><span class="n">G2_node</span><span class="p">]:</span>
<span class="k">if</span> <span class="p">(</span><span class="n">successor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">in_2</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">successor</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_2</span><span class="p">):</span>
<span class="n">num2</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">test</span> <span class="o">==</span> <span class="s2">"graph"</span><span class="p">:</span>
<span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">num1</span> <span class="o">==</span> <span class="n">num2</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">else</span><span class="p">:</span> <span class="c1"># self.test == 'subgraph'</span>
<span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">num1</span> <span class="o">>=</span> <span class="n">num2</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="c1"># R_termout</span>
<span class="c1"># The number of predecessors of n that are in T_1^{out} is equal to the</span>
<span class="c1"># number of predecessors of m that are in T_2^{out}.</span>
<span class="n">num1</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">predecessor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="o">.</span><span class="n">pred</span><span class="p">[</span><span class="n">G1_node</span><span class="p">]:</span>
<span class="k">if</span> <span class="p">(</span><span class="n">predecessor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">out_1</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">predecessor</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_1</span><span class="p">):</span>
<span class="n">num1</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">num2</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">predecessor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="o">.</span><span class="n">pred</span><span class="p">[</span><span class="n">G2_node</span><span class="p">]:</span>
<span class="k">if</span> <span class="p">(</span><span class="n">predecessor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">out_2</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">predecessor</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_2</span><span class="p">):</span>
<span class="n">num2</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">test</span> <span class="o">==</span> <span class="s2">"graph"</span><span class="p">:</span>
<span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">num1</span> <span class="o">==</span> <span class="n">num2</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">else</span><span class="p">:</span> <span class="c1"># self.test == 'subgraph'</span>
<span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">num1</span> <span class="o">>=</span> <span class="n">num2</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="c1"># The number of successors of n that are in T_1^{out} is equal to the</span>
<span class="c1"># number of successors of m that are in T_2^{out}.</span>
<span class="n">num1</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">successor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="p">[</span><span class="n">G1_node</span><span class="p">]:</span>
<span class="k">if</span> <span class="p">(</span><span class="n">successor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">out_1</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">successor</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_1</span><span class="p">):</span>
<span class="n">num1</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">num2</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">successor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="p">[</span><span class="n">G2_node</span><span class="p">]:</span>
<span class="k">if</span> <span class="p">(</span><span class="n">successor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">out_2</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">successor</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">core_2</span><span class="p">):</span>
<span class="n">num2</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">test</span> <span class="o">==</span> <span class="s2">"graph"</span><span class="p">:</span>
<span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">num1</span> <span class="o">==</span> <span class="n">num2</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">else</span><span class="p">:</span> <span class="c1"># self.test == 'subgraph'</span>
<span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">num1</span> <span class="o">>=</span> <span class="n">num2</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="c1"># Look ahead 2</span>
<span class="c1"># R_new</span>
<span class="c1"># The number of predecessors of n that are neither in the core_1 nor</span>
<span class="c1"># T_1^{in} nor T_1^{out} is equal to the number of predecessors of m</span>
<span class="c1"># that are neither in core_2 nor T_2^{in} nor T_2^{out}.</span>
<span class="n">num1</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">predecessor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="o">.</span><span class="n">pred</span><span class="p">[</span><span class="n">G1_node</span><span class="p">]:</span>
<span class="k">if</span> <span class="p">(</span><span class="n">predecessor</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">in_1</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">predecessor</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">out_1</span><span class="p">):</span>
<span class="n">num1</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">num2</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">predecessor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="o">.</span><span class="n">pred</span><span class="p">[</span><span class="n">G2_node</span><span class="p">]:</span>
<span class="k">if</span> <span class="p">(</span><span class="n">predecessor</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">in_2</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">predecessor</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">out_2</span><span class="p">):</span>
<span class="n">num2</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">test</span> <span class="o">==</span> <span class="s2">"graph"</span><span class="p">:</span>
<span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">num1</span> <span class="o">==</span> <span class="n">num2</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">else</span><span class="p">:</span> <span class="c1"># self.test == 'subgraph'</span>
<span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">num1</span> <span class="o">>=</span> <span class="n">num2</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="c1"># The number of successors of n that are neither in the core_1 nor</span>
<span class="c1"># T_1^{in} nor T_1^{out} is equal to the number of successors of m</span>
<span class="c1"># that are neither in core_2 nor T_2^{in} nor T_2^{out}.</span>
<span class="n">num1</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">successor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1</span><span class="p">[</span><span class="n">G1_node</span><span class="p">]:</span>
<span class="k">if</span> <span class="p">(</span><span class="n">successor</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">in_1</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">successor</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">out_1</span><span class="p">):</span>
<span class="n">num1</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">num2</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">successor</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2</span><span class="p">[</span><span class="n">G2_node</span><span class="p">]:</span>
<span class="k">if</span> <span class="p">(</span><span class="n">successor</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">in_2</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">successor</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">out_2</span><span class="p">):</span>
<span class="n">num2</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">test</span> <span class="o">==</span> <span class="s2">"graph"</span><span class="p">:</span>
<span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">num1</span> <span class="o">==</span> <span class="n">num2</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">else</span><span class="p">:</span> <span class="c1"># self.test == 'subgraph'</span>
<span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">num1</span> <span class="o">>=</span> <span class="n">num2</span><span class="p">):</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="c1"># Otherwise, this node pair is syntactically feasible!</span>
<span class="k">return</span> <span class="kc">True</span></div>
<span class="k">class</span> <span class="nc">GMState</span><span class="p">:</span>
<span class="sd">"""Internal representation of state for the GraphMatcher class.</span>
<span class="sd"> This class is used internally by the GraphMatcher class. It is used</span>
<span class="sd"> only to store state specific data. There will be at most G2.order() of</span>
<span class="sd"> these objects in memory at a time, due to the depth-first search</span>
<span class="sd"> strategy employed by the VF2 algorithm.</span>
<span class="sd"> """</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">GM</span><span class="p">,</span> <span class="n">G1_node</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">G2_node</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="sd">"""Initializes GMState object.</span>
<span class="sd"> Pass in the GraphMatcher to which this GMState belongs and the</span>
<span class="sd"> new node pair that will be added to the GraphMatcher's current</span>
<span class="sd"> isomorphism mapping.</span>
<span class="sd"> """</span>
<span class="bp">self</span><span class="o">.</span><span class="n">GM</span> <span class="o">=</span> <span class="n">GM</span>
<span class="c1"># Initialize the last stored node pair.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">G1_node</span> <span class="o">=</span> <span class="kc">None</span>
<span class="bp">self</span><span class="o">.</span><span class="n">G2_node</span> <span class="o">=</span> <span class="kc">None</span>
<span class="bp">self</span><span class="o">.</span><span class="n">depth</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">GM</span><span class="o">.</span><span class="n">core_1</span><span class="p">)</span>
<span class="k">if</span> <span class="n">G1_node</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">G2_node</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="c1"># Then we reset the class variables</span>
<span class="n">GM</span><span class="o">.</span><span class="n">core_1</span> <span class="o">=</span> <span class="p">{}</span>
<span class="n">GM</span><span class="o">.</span><span class="n">core_2</span> <span class="o">=</span> <span class="p">{}</span>
<span class="n">GM</span><span class="o">.</span><span class="n">inout_1</span> <span class="o">=</span> <span class="p">{}</span>
<span class="n">GM</span><span class="o">.</span><span class="n">inout_2</span> <span class="o">=</span> <span class="p">{}</span>
<span class="c1"># Watch out! G1_node == 0 should evaluate to True.</span>
<span class="k">if</span> <span class="n">G1_node</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span> <span class="ow">and</span> <span class="n">G2_node</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="c1"># Add the node pair to the isomorphism mapping.</span>
<span class="n">GM</span><span class="o">.</span><span class="n">core_1</span><span class="p">[</span><span class="n">G1_node</span><span class="p">]</span> <span class="o">=</span> <span class="n">G2_node</span>
<span class="n">GM</span><span class="o">.</span><span class="n">core_2</span><span class="p">[</span><span class="n">G2_node</span><span class="p">]</span> <span class="o">=</span> <span class="n">G1_node</span>
<span class="c1"># Store the node that was added last.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">G1_node</span> <span class="o">=</span> <span class="n">G1_node</span>
<span class="bp">self</span><span class="o">.</span><span class="n">G2_node</span> <span class="o">=</span> <span class="n">G2_node</span>
<span class="c1"># Now we must update the other two vectors.</span>
<span class="c1"># We will add only if it is not in there already!</span>
<span class="bp">self</span><span class="o">.</span><span class="n">depth</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">GM</span><span class="o">.</span><span class="n">core_1</span><span class="p">)</span>
<span class="c1"># First we add the new nodes...</span>
<span class="k">if</span> <span class="n">G1_node</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">GM</span><span class="o">.</span><span class="n">inout_1</span><span class="p">:</span>
<span class="n">GM</span><span class="o">.</span><span class="n">inout_1</span><span class="p">[</span><span class="n">G1_node</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">depth</span>
<span class="k">if</span> <span class="n">G2_node</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">GM</span><span class="o">.</span><span class="n">inout_2</span><span class="p">:</span>
<span class="n">GM</span><span class="o">.</span><span class="n">inout_2</span><span class="p">[</span><span class="n">G2_node</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">depth</span>
<span class="c1"># Now we add every other node...</span>
<span class="c1"># Updates for T_1^{inout}</span>
<span class="n">new_nodes</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
<span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="n">GM</span><span class="o">.</span><span class="n">core_1</span><span class="p">:</span>
<span class="n">new_nodes</span><span class="o">.</span><span class="n">update</span><span class="p">(</span>
<span class="p">[</span><span class="n">neighbor</span> <span class="k">for</span> <span class="n">neighbor</span> <span class="ow">in</span> <span class="n">GM</span><span class="o">.</span><span class="n">G1</span><span class="p">[</span><span class="n">node</span><span class="p">]</span> <span class="k">if</span> <span class="n">neighbor</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">GM</span><span class="o">.</span><span class="n">core_1</span><span class="p">]</span>
<span class="p">)</span>
<span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="n">new_nodes</span><span class="p">:</span>
<span class="k">if</span> <span class="n">node</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">GM</span><span class="o">.</span><span class="n">inout_1</span><span class="p">:</span>
<span class="n">GM</span><span class="o">.</span><span class="n">inout_1</span><span class="p">[</span><span class="n">node</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">depth</span>
<span class="c1"># Updates for T_2^{inout}</span>
<span class="n">new_nodes</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
<span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="n">GM</span><span class="o">.</span><span class="n">core_2</span><span class="p">:</span>
<span class="n">new_nodes</span><span class="o">.</span><span class="n">update</span><span class="p">(</span>
<span class="p">[</span><span class="n">neighbor</span> <span class="k">for</span> <span class="n">neighbor</span> <span class="ow">in</span> <span class="n">GM</span><span class="o">.</span><span class="n">G2</span><span class="p">[</span><span class="n">node</span><span class="p">]</span> <span class="k">if</span> <span class="n">neighbor</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">GM</span><span class="o">.</span><span class="n">core_2</span><span class="p">]</span>
<span class="p">)</span>
<span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="n">new_nodes</span><span class="p">:</span>
<span class="k">if</span> <span class="n">node</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">GM</span><span class="o">.</span><span class="n">inout_2</span><span class="p">:</span>
<span class="n">GM</span><span class="o">.</span><span class="n">inout_2</span><span class="p">[</span><span class="n">node</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">depth</span>
<span class="k">def</span> <span class="nf">restore</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">"""Deletes the GMState object and restores the class variables."""</span>
<span class="c1"># First we remove the node that was added from the core vectors.</span>
<span class="c1"># Watch out! G1_node == 0 should evaluate to True.</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1_node</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span> <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2_node</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">del</span> <span class="bp">self</span><span class="o">.</span><span class="n">GM</span><span class="o">.</span><span class="n">core_1</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">G1_node</span><span class="p">]</span>
<span class="k">del</span> <span class="bp">self</span><span class="o">.</span><span class="n">GM</span><span class="o">.</span><span class="n">core_2</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">G2_node</span><span class="p">]</span>
<span class="c1"># Now we revert the other two vectors.</span>
<span class="c1"># Thus, we delete all entries which have this depth level.</span>
<span class="k">for</span> <span class="n">vector</span> <span class="ow">in</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">GM</span><span class="o">.</span><span class="n">inout_1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">GM</span><span class="o">.</span><span class="n">inout_2</span><span class="p">):</span>
<span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="nb">list</span><span class="p">(</span><span class="n">vector</span><span class="o">.</span><span class="n">keys</span><span class="p">()):</span>
<span class="k">if</span> <span class="n">vector</span><span class="p">[</span><span class="n">node</span><span class="p">]</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">depth</span><span class="p">:</span>
<span class="k">del</span> <span class="n">vector</span><span class="p">[</span><span class="n">node</span><span class="p">]</span>
<span class="k">class</span> <span class="nc">DiGMState</span><span class="p">:</span>
<span class="sd">"""Internal representation of state for the DiGraphMatcher class.</span>
<span class="sd"> This class is used internally by the DiGraphMatcher class. It is used</span>
<span class="sd"> only to store state specific data. There will be at most G2.order() of</span>
<span class="sd"> these objects in memory at a time, due to the depth-first search</span>
<span class="sd"> strategy employed by the VF2 algorithm.</span>
<span class="sd"> """</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">GM</span><span class="p">,</span> <span class="n">G1_node</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">G2_node</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="sd">"""Initializes DiGMState object.</span>
<span class="sd"> Pass in the DiGraphMatcher to which this DiGMState belongs and the</span>
<span class="sd"> new node pair that will be added to the GraphMatcher's current</span>
<span class="sd"> isomorphism mapping.</span>
<span class="sd"> """</span>
<span class="bp">self</span><span class="o">.</span><span class="n">GM</span> <span class="o">=</span> <span class="n">GM</span>
<span class="c1"># Initialize the last stored node pair.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">G1_node</span> <span class="o">=</span> <span class="kc">None</span>
<span class="bp">self</span><span class="o">.</span><span class="n">G2_node</span> <span class="o">=</span> <span class="kc">None</span>
<span class="bp">self</span><span class="o">.</span><span class="n">depth</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">GM</span><span class="o">.</span><span class="n">core_1</span><span class="p">)</span>
<span class="k">if</span> <span class="n">G1_node</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">G2_node</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="c1"># Then we reset the class variables</span>
<span class="n">GM</span><span class="o">.</span><span class="n">core_1</span> <span class="o">=</span> <span class="p">{}</span>
<span class="n">GM</span><span class="o">.</span><span class="n">core_2</span> <span class="o">=</span> <span class="p">{}</span>
<span class="n">GM</span><span class="o">.</span><span class="n">in_1</span> <span class="o">=</span> <span class="p">{}</span>
<span class="n">GM</span><span class="o">.</span><span class="n">in_2</span> <span class="o">=</span> <span class="p">{}</span>
<span class="n">GM</span><span class="o">.</span><span class="n">out_1</span> <span class="o">=</span> <span class="p">{}</span>
<span class="n">GM</span><span class="o">.</span><span class="n">out_2</span> <span class="o">=</span> <span class="p">{}</span>
<span class="c1"># Watch out! G1_node == 0 should evaluate to True.</span>
<span class="k">if</span> <span class="n">G1_node</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span> <span class="ow">and</span> <span class="n">G2_node</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="c1"># Add the node pair to the isomorphism mapping.</span>
<span class="n">GM</span><span class="o">.</span><span class="n">core_1</span><span class="p">[</span><span class="n">G1_node</span><span class="p">]</span> <span class="o">=</span> <span class="n">G2_node</span>
<span class="n">GM</span><span class="o">.</span><span class="n">core_2</span><span class="p">[</span><span class="n">G2_node</span><span class="p">]</span> <span class="o">=</span> <span class="n">G1_node</span>
<span class="c1"># Store the node that was added last.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">G1_node</span> <span class="o">=</span> <span class="n">G1_node</span>
<span class="bp">self</span><span class="o">.</span><span class="n">G2_node</span> <span class="o">=</span> <span class="n">G2_node</span>
<span class="c1"># Now we must update the other four vectors.</span>
<span class="c1"># We will add only if it is not in there already!</span>
<span class="bp">self</span><span class="o">.</span><span class="n">depth</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">GM</span><span class="o">.</span><span class="n">core_1</span><span class="p">)</span>
<span class="c1"># First we add the new nodes...</span>
<span class="k">for</span> <span class="n">vector</span> <span class="ow">in</span> <span class="p">(</span><span class="n">GM</span><span class="o">.</span><span class="n">in_1</span><span class="p">,</span> <span class="n">GM</span><span class="o">.</span><span class="n">out_1</span><span class="p">):</span>
<span class="k">if</span> <span class="n">G1_node</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">vector</span><span class="p">:</span>
<span class="n">vector</span><span class="p">[</span><span class="n">G1_node</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">depth</span>
<span class="k">for</span> <span class="n">vector</span> <span class="ow">in</span> <span class="p">(</span><span class="n">GM</span><span class="o">.</span><span class="n">in_2</span><span class="p">,</span> <span class="n">GM</span><span class="o">.</span><span class="n">out_2</span><span class="p">):</span>
<span class="k">if</span> <span class="n">G2_node</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">vector</span><span class="p">:</span>
<span class="n">vector</span><span class="p">[</span><span class="n">G2_node</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">depth</span>
<span class="c1"># Now we add every other node...</span>
<span class="c1"># Updates for T_1^{in}</span>
<span class="n">new_nodes</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
<span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="n">GM</span><span class="o">.</span><span class="n">core_1</span><span class="p">:</span>
<span class="n">new_nodes</span><span class="o">.</span><span class="n">update</span><span class="p">(</span>
<span class="p">[</span>
<span class="n">predecessor</span>
<span class="k">for</span> <span class="n">predecessor</span> <span class="ow">in</span> <span class="n">GM</span><span class="o">.</span><span class="n">G1</span><span class="o">.</span><span class="n">predecessors</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<span class="k">if</span> <span class="n">predecessor</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">GM</span><span class="o">.</span><span class="n">core_1</span>
<span class="p">]</span>
<span class="p">)</span>
<span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="n">new_nodes</span><span class="p">:</span>
<span class="k">if</span> <span class="n">node</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">GM</span><span class="o">.</span><span class="n">in_1</span><span class="p">:</span>
<span class="n">GM</span><span class="o">.</span><span class="n">in_1</span><span class="p">[</span><span class="n">node</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">depth</span>
<span class="c1"># Updates for T_2^{in}</span>
<span class="n">new_nodes</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
<span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="n">GM</span><span class="o">.</span><span class="n">core_2</span><span class="p">:</span>
<span class="n">new_nodes</span><span class="o">.</span><span class="n">update</span><span class="p">(</span>
<span class="p">[</span>
<span class="n">predecessor</span>
<span class="k">for</span> <span class="n">predecessor</span> <span class="ow">in</span> <span class="n">GM</span><span class="o">.</span><span class="n">G2</span><span class="o">.</span><span class="n">predecessors</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<span class="k">if</span> <span class="n">predecessor</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">GM</span><span class="o">.</span><span class="n">core_2</span>
<span class="p">]</span>
<span class="p">)</span>
<span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="n">new_nodes</span><span class="p">:</span>
<span class="k">if</span> <span class="n">node</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">GM</span><span class="o">.</span><span class="n">in_2</span><span class="p">:</span>
<span class="n">GM</span><span class="o">.</span><span class="n">in_2</span><span class="p">[</span><span class="n">node</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">depth</span>
<span class="c1"># Updates for T_1^{out}</span>
<span class="n">new_nodes</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
<span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="n">GM</span><span class="o">.</span><span class="n">core_1</span><span class="p">:</span>
<span class="n">new_nodes</span><span class="o">.</span><span class="n">update</span><span class="p">(</span>
<span class="p">[</span>
<span class="n">successor</span>
<span class="k">for</span> <span class="n">successor</span> <span class="ow">in</span> <span class="n">GM</span><span class="o">.</span><span class="n">G1</span><span class="o">.</span><span class="n">successors</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<span class="k">if</span> <span class="n">successor</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">GM</span><span class="o">.</span><span class="n">core_1</span>
<span class="p">]</span>
<span class="p">)</span>
<span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="n">new_nodes</span><span class="p">:</span>
<span class="k">if</span> <span class="n">node</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">GM</span><span class="o">.</span><span class="n">out_1</span><span class="p">:</span>
<span class="n">GM</span><span class="o">.</span><span class="n">out_1</span><span class="p">[</span><span class="n">node</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">depth</span>
<span class="c1"># Updates for T_2^{out}</span>
<span class="n">new_nodes</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
<span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="n">GM</span><span class="o">.</span><span class="n">core_2</span><span class="p">:</span>
<span class="n">new_nodes</span><span class="o">.</span><span class="n">update</span><span class="p">(</span>
<span class="p">[</span>
<span class="n">successor</span>
<span class="k">for</span> <span class="n">successor</span> <span class="ow">in</span> <span class="n">GM</span><span class="o">.</span><span class="n">G2</span><span class="o">.</span><span class="n">successors</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<span class="k">if</span> <span class="n">successor</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">GM</span><span class="o">.</span><span class="n">core_2</span>
<span class="p">]</span>
<span class="p">)</span>
<span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="n">new_nodes</span><span class="p">:</span>
<span class="k">if</span> <span class="n">node</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">GM</span><span class="o">.</span><span class="n">out_2</span><span class="p">:</span>
<span class="n">GM</span><span class="o">.</span><span class="n">out_2</span><span class="p">[</span><span class="n">node</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">depth</span>
<span class="k">def</span> <span class="nf">restore</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">"""Deletes the DiGMState object and restores the class variables."""</span>
<span class="c1"># First we remove the node that was added from the core vectors.</span>
<span class="c1"># Watch out! G1_node == 0 should evaluate to True.</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">G1_node</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span> <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">G2_node</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">del</span> <span class="bp">self</span><span class="o">.</span><span class="n">GM</span><span class="o">.</span><span class="n">core_1</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">G1_node</span><span class="p">]</span>
<span class="k">del</span> <span class="bp">self</span><span class="o">.</span><span class="n">GM</span><span class="o">.</span><span class="n">core_2</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">G2_node</span><span class="p">]</span>
<span class="c1"># Now we revert the other four vectors.</span>
<span class="c1"># Thus, we delete all entries which have this depth level.</span>
<span class="k">for</span> <span class="n">vector</span> <span class="ow">in</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">GM</span><span class="o">.</span><span class="n">in_1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">GM</span><span class="o">.</span><span class="n">in_2</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">GM</span><span class="o">.</span><span class="n">out_1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">GM</span><span class="o">.</span><span class="n">out_2</span><span class="p">):</span>
<span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="nb">list</span><span class="p">(</span><span class="n">vector</span><span class="o">.</span><span class="n">keys</span><span class="p">()):</span>
<span class="k">if</span> <span class="n">vector</span><span class="p">[</span><span class="n">node</span><span class="p">]</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">depth</span><span class="p">:</span>
<span class="k">del</span> <span class="n">vector</span><span class="p">[</span><span class="n">node</span><span class="p">]</span>
</pre></div>
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