VhA)6dZddlZddlmZddlZddlmZgdZejdddd d d Z d Z ejdddd Z dZ ejddddZdZejdddddddZy)z Graph isomorphism functions. N)Counter) NetworkXError)could_be_isomorphicfast_could_be_isomorphicfaster_could_be_isomorphic is_isomorphic)G1G2)graphsdtc) propertiesc jjk7ryt|}ggcfd}d|vrFjjjj|syd|vrPjt j jt j |syd|vrjt tjjt jjt tjjt j|syy)aReturns False if graphs are definitely not isomorphic. True does NOT guarantee isomorphism. Parameters ---------- G1, G2 : graphs The two graphs `G1` and `G2` must be the same type. properties : str, default="dct" Determines which properties of the graph are checked. Each character indicates a particular property as follows: - if ``"d"`` in `properties`: degree of each node - if ``"t"`` in `properties`: number of triangles for each node - if ``"c"`` in `properties`: number of maximal cliques for each node Unrecognized characters are ignored. The default is ``"dtc"``, which compares the sequence of ``(degree, num_triangles, num_cliques)`` properties between `G1` and `G2`. Generally, ``properties="dt"`` would be faster, and ``properties="d"`` faster still. See Notes for additional details on property selection. Returns ------- bool A Boolean value representing whether `G1` could be isomorphic with `G2` according to the specified `properties`. Notes ----- The triangle sequence contains the number of triangles each node is part of. The clique sequence contains for each node the number of maximal cliques involving that node. Some properties are faster to compute than others. And there are other properties we could include and don't. But of the three properties listed here, comparing the degree distributions is the fastest. The "triangles" property is slower (and also a stricter version of "could") and the "maximal cliques" property is slower still, but usually faster than doing a full isomorphism check. FcDcgc]tfdD}}Dcgc]tfdD}}t|t|k(Scc}wcc}w)Nc3(K|] }| ywN.0pns X/home/dcms/DCMS/lib/python3.12/site-packages/networkx/algorithms/isomorphism/isomorph.py zFcould_be_isomorphic.._properties_consistent..H2A1Q42c3(K|] }| ywrrrs rrzFcould_be_isomorphic.._properties_consistent..Irr)tuplesorted)r G1_ptable G2_ptabler G1_propsr G2_propss` r_properties_consistentz3could_be_isomorphic.._properties_consistentFs]<>?qU222? ?<>?qU222? ?i F9$555@?s AA#dtcT) ordersetappenddegreenx trianglesr itertoolschain from_iterable find_cliques)r r rproperties_to_checkr#r!r"s`` @@rrrsZ xxzRXXZj/RHh6 !! $ $%' !! R() R()%' !!  = =boob>Q RST  = =boob>Q RST%' cRddl}|jdtdt||S)z .. deprecated:: 3.5 `graph_could_be_isomorphic` is a deprecated alias for `could_be_isomorphic`. Use `could_be_isomorphic` instead. rNzKgraph_could_be_isomorphic is deprecated, use `could_be_isomorphic` instead.category stacklevel)warningswarnDeprecationWarningrr r r8s rgraph_could_be_isomorphicr<js0 MMU# r2 &&r2c|j|jk7ry|j}tj|}|Dcgc] \}}|||g}}}|j |j}tj|}|Dcgc] \}}|||g} }}| j || k7ryycc}}wcc}}w)alReturns False if graphs are definitely not isomorphic. True does NOT guarantee isomorphism. Parameters ---------- G1, G2 : graphs The two graphs G1 and G2 must be the same type. Notes ----- Checks for matching degree and triangle sequences. The triangle sequence contains the number of triangles each node is part of. FT)r'r*r+r,sort) r r d1t1vr$props1d2t2props2s rrr{s" xxzRXXZ B b B%' (TQq"Q%j (F ( KKM B b B%' (TQq"Q%j (F ( KKM  ) )s CC cRddl}|jdtdt||S)z .. deprecated:: 3.5 `fast_graph_could_be_isomorphic` is a deprecated alias for `fast_could_be_isomorphic`. Use `fast_could_be_isomorphic` instead. rNzRfast_graph_could_be_isomorphic is deprecated, use fast_could_be_isomorphic insteadr4r5)r8r9r:rr;s rfast_graph_could_be_isomorphicrGs0 MM\# $B ++r2c|j|jk7rytd|jD}td|jD}||k7ryy)aReturns False if graphs are definitely not isomorphic. True does NOT guarantee isomorphism. Parameters ---------- G1, G2 : graphs The two graphs G1 and G2 must be the same type. Notes ----- Checks for matching degree sequences. Fc3&K|] \}}| ywrrrrr$s rrz-faster_could_be_isomorphic..*da*c3&K|] \}}| ywrrrJs rrz-faster_could_be_isomorphic..rKrLT)r'rr*)r r r?rCs rrrsX  xxzRXXZ *biik* *B *biik* *B Rx r2cRddl}|jdtdt||S)z .. deprecated:: 3.5 `faster_graph_could_be_isomorphic` is a deprecated alias for `faster_could_be_isomorphic`. Use `faster_could_be_isomorphic` instead. rNzVfaster_graph_could_be_isomorphic is deprecated, use faster_could_be_isomorphic insteadr4r5)r8r9r:rr;s r faster_graph_could_be_isomorphicrOs0 MM`# &b" --r2 edge_match node_match)r preserve_edge_attrspreserve_node_attrscd|jr5|jr%tjjj}nP|js5|js%tjjj }n t d|||||}|jS)a2 Returns True if the graphs G1 and G2 are isomorphic and False otherwise. Parameters ---------- G1, G2: graphs The two graphs G1 and G2 must be the same type. node_match : callable A function that returns True if node n1 in G1 and n2 in G2 should be considered equal during the isomorphism test. If node_match is not specified then node attributes are not considered. The function will be called like node_match(G1.nodes[n1], G2.nodes[n2]). That is, the function will receive the node attribute dictionaries for n1 and n2 as inputs. edge_match : callable A function that returns True if the edge attribute dictionary for the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should be considered equal during the isomorphism test. If edge_match is not specified then edge attributes are not considered. The function will be called like edge_match(G1[u1][v1], G2[u2][v2]). That is, the function will receive the edge attribute dictionaries of the edges under consideration. Notes ----- Uses the vf2 algorithm [1]_. Examples -------- >>> import networkx.algorithms.isomorphism as iso For digraphs G1 and G2, using 'weight' edge attribute (default: 1) >>> G1 = nx.DiGraph() >>> G2 = nx.DiGraph() >>> nx.add_path(G1, [1, 2, 3, 4], weight=1) >>> nx.add_path(G2, [10, 20, 30, 40], weight=2) >>> em = iso.numerical_edge_match("weight", 1) >>> nx.is_isomorphic(G1, G2) # no weights considered True >>> nx.is_isomorphic(G1, G2, edge_match=em) # match weights False For multidigraphs G1 and G2, using 'fill' node attribute (default: '') >>> G1 = nx.MultiDiGraph() >>> G2 = nx.MultiDiGraph() >>> G1.add_nodes_from([1, 2, 3], fill="red") >>> G2.add_nodes_from([10, 20, 30, 40], fill="red") >>> nx.add_path(G1, [1, 2, 3, 4], weight=3, linewidth=2.5) >>> nx.add_path(G2, [10, 20, 30, 40], weight=3) >>> nm = iso.categorical_node_match("fill", "red") >>> nx.is_isomorphic(G1, G2, node_match=nm) True For multidigraphs G1 and G2, using 'weight' edge attribute (default: 7) >>> G1.add_edge(1, 2, weight=7) 1 >>> G2.add_edge(10, 20) 1 >>> em = iso.numerical_multiedge_match("weight", 7, rtol=1e-6) >>> nx.is_isomorphic(G1, G2, edge_match=em) True For multigraphs G1 and G2, using 'weight' and 'linewidth' edge attributes with default values 7 and 2.5. Also using 'fill' node attribute with default value 'red'. >>> em = iso.numerical_multiedge_match(["weight", "linewidth"], [7, 2.5]) >>> nm = iso.categorical_node_match("fill", "red") >>> nx.is_isomorphic(G1, G2, edge_match=em, node_match=nm) True See Also -------- numerical_node_match, numerical_edge_match, numerical_multiedge_match categorical_node_match, categorical_edge_match, categorical_multiedge_match References ---------- .. [1] L. P. Cordella, P. Foggia, C. Sansone, M. Vento, "An Improved Algorithm for Matching Large Graphs", 3rd IAPR-TC15 Workshop on Graph-based Representations in Pattern Recognition, Cuen, pp. 149-159, 2001. https://www.researchgate.net/publication/200034365_An_Improved_Algorithm_for_Matching_Large_Graphs z*Graphs G1 and G2 are not of the same type.)rQrP) is_directedr+ algorithms isomorphismDiGraphMatcher GraphMatcherrr)r r rQrPGMgms rrrsL ~~BNN, ]] & & 5 5nn)9 ]] & & 3 3HII Bzj AB   r2)NN)__doc__r- collectionsrnetworkxr+networkx.exceptionr__all__ _dispatchablerr<rrGrrOrrr2rrbs, +,.3S-Sl'"+,"-"J,"+,-:."1 $$ j  jr2