h 1:SrSSKJrJr SSKJr SSKrSS/rSr Sr SS jr \RRS 5\R"S S0S S 9SSj55r\RRS 5\R"S S0S S 9SSj55rg)z Functions for hashing graphs to strings. Isomorphic graphs should be assigned identical hashes. For now, only Weisfeiler-Lehman hashing is implemented. )Counter defaultdict)blake2bNweisfeiler_lehman_graph_hash!weisfeiler_lehman_subgraph_hashescP[URS5US9R5$)Nascii) digest_size)rencode hexdigest)labelr s S/var/www/html/env/lib/python3.13/site-packages/networkx/algorithms/graph_hashing.py _hash_labelrs! 5<<(k B L L NNc $U(a0URSS9VVs0sHup4U[XB5_M snn$U(aUVs0sHo3S_M sn$UR5VVs0sHup5U[U5_M snn$s snnfs snfs snnf)NT)data)nodesstrdegree)G edge_attr node_attrudddegs r_init_node_labelsrs347773EF3E%!3r}%%3EFF  !q!2q!!*+((*5*3s8 *55 G!5sB B%B c/nURU5H1nUcSO[XUU5nURXbU-5 M3 X!SR[ U55-$)zW Compute new labels for given node by aggregating the labels of each node's neighbors. r) neighborsrappendjoinsorted)rnode node_labelsr label_listnbrprefixs r_neighborhood_aggregater(sl J{{4  (c!'#,y2I.J&s#334!  rwwvj'9: ::r multigraphrr) edge_attrs node_attrsc ^SU4Sjjn[XU5n/n[U5HKnU"XUS9n[UR55n UR [ U R 5SS95 MM [[[U55T5$)aS Return Weisfeiler Lehman (WL) graph hash. The function iteratively aggregates and hashes neighborhoods of each node. After each node's neighbors are hashed to obtain updated node labels, a hashed histogram of resulting labels is returned as the final hash. Hashes are identical for isomorphic graphs and strong guarantees that non-isomorphic graphs will get different hashes. See [1]_ for details. If no node or edge attributes are provided, the degree of each node is used as its initial label. Otherwise, node and/or edge labels are used to compute the hash. Parameters ---------- G : graph The graph to be hashed. Can have node and/or edge attributes. Can also have no attributes. edge_attr : string, optional (default=None) The key in edge attribute dictionary to be used for hashing. If None, edge labels are ignored. node_attr: string, optional (default=None) The key in node attribute dictionary to be used for hashing. If None, and no edge_attr given, use the degrees of the nodes as labels. iterations: int, optional (default=3) Number of neighbor aggregations to perform. Should be larger for larger graphs. digest_size: int, optional (default=16) Size (in bits) of blake2b hash digest to use for hashing node labels. Returns ------- h : string Hexadecimal string corresponding to hash of the input graph. Examples -------- Two graphs with edge attributes that are isomorphic, except for differences in the edge labels. >>> G1 = nx.Graph() >>> G1.add_edges_from( ... [ ... (1, 2, {"label": "A"}), ... (2, 3, {"label": "A"}), ... (3, 1, {"label": "A"}), ... (1, 4, {"label": "B"}), ... ] ... ) >>> G2 = nx.Graph() >>> G2.add_edges_from( ... [ ... (5, 6, {"label": "B"}), ... (6, 7, {"label": "A"}), ... (7, 5, {"label": "A"}), ... (7, 8, {"label": "A"}), ... ] ... ) Omitting the `edge_attr` option, results in identical hashes. >>> nx.weisfeiler_lehman_graph_hash(G1) '7bc4dde9a09d0b94c5097b219891d81a' >>> nx.weisfeiler_lehman_graph_hash(G2) '7bc4dde9a09d0b94c5097b219891d81a' With edge labels, the graphs are no longer assigned the same hash digest. >>> nx.weisfeiler_lehman_graph_hash(G1, edge_attr="label") 'c653d85538bcf041d88c011f4f905f10' >>> nx.weisfeiler_lehman_graph_hash(G2, edge_attr="label") '3dcd84af1ca855d0eff3c978d88e7ec7' Notes ----- To return the WL hashes of each subgraph of a graph, use `weisfeiler_lehman_subgraph_hashes` Similarity between hashes does not imply similarity between graphs. References ---------- .. [1] Shervashidze, Nino, Pascal Schweitzer, Erik Jan Van Leeuwen, Kurt Mehlhorn, and Karsten M. Borgwardt. Weisfeiler Lehman Graph Kernels. Journal of Machine Learning Research. 2011. http://www.jmlr.org/papers/volume12/shervashidze11a/shervashidze11a.pdf See also -------- weisfeiler_lehman_subgraph_hashes cj>0nUR5Hn[XXS9n[UT5X4'M U$)zl Apply neighborhood aggregation to each node in the graph. Computes a dictionary with labels for each node. r)rr(r)rlabelsr new_labelsr#r r s rweisfeiler_lehman_step.weisfeiler_lehman_steps=  GGID+AVQE*5+>J rr.c US$)Nr)xs r.weisfeiler_lehman_graph_hash..s!A$r)keyN) rrangervaluesextendr"itemsrrtuple) rrr iterationsr r1r$subgraph_hash_counts_counters ` rrr(sD $A)>> G1 = nx.Graph() >>> G1.add_edges_from([(1, 2), (2, 3), (2, 4), (3, 5), (4, 6), (5, 7), (6, 7)]) >>> G2 = nx.Graph() >>> G2.add_edges_from([(1, 3), (2, 3), (1, 6), (1, 5), (4, 6)]) >>> g1_hashes = nx.weisfeiler_lehman_subgraph_hashes( ... G1, iterations=3, digest_size=8 ... ) >>> g2_hashes = nx.weisfeiler_lehman_subgraph_hashes( ... G2, iterations=3, digest_size=8 ... ) Even though G1 and G2 are not isomorphic (they have different numbers of edges), the hash sequence of depth 3 for node 1 in G1 and node 5 in G2 are similar: >>> g1_hashes[1] ['a93b64973cfc8897', 'db1b43ae35a1878f', '57872a7d2059c1c0'] >>> g2_hashes[5] ['a93b64973cfc8897', 'db1b43ae35a1878f', '1716d2a4012fa4bc'] The first 2 WL subgraph hashes match. From this we can conclude that it's very likely the neighborhood of 2 hops around these nodes are isomorphic. However the 3-hop neighborhoods of ``G1`` and ``G2`` are not isomorphic since the 3rd hashes in the lists above are not equal. These nodes may be candidates to be classified together since their local topology is similar. Notes ----- To hash the full graph when subgraph hashes are not needed, use `weisfeiler_lehman_graph_hash` for efficiency. Similarity between hashes does not imply similarity between graphs. References ---------- .. [1] Shervashidze, Nino, Pascal Schweitzer, Erik Jan Van Leeuwen, Kurt Mehlhorn, and Karsten M. Borgwardt. Weisfeiler Lehman Graph Kernels. Journal of Machine Learning Research. 2011. http://www.jmlr.org/papers/volume12/shervashidze11a/shervashidze11a.pdf .. [2] Annamalai Narayanan, Mahinthan Chandramohan, Rajasekar Venkatesan, Lihui Chen, Yang Liu and Shantanu Jaiswa. graph2vec: Learning Distributed Representations of Graphs. arXiv. 2017 https://arxiv.org/pdf/1707.05005.pdf See also -------- weisfeiler_lehman_graph_hash c>0nUR5H0n[XXS9n[UT5nXtU'X%RU5 M2 U$)z Apply neighborhood aggregation to each node in the graph. Computes a dictionary with labels for each node. Appends the new hashed label to the dictionary of subgraph hashes originating from and indexed by each node in G r.)rr(rr ) rr/node_subgraph_hashesrr0r#r hashed_labelr s rr1Aweisfeiler_lehman_subgraph_hashes..weisfeiler_lehman_step+sS GGID+AVQE&uk:L+t  & - -l ;  rr9)rr=rrlistr:dict) rrrr?r include_initial_labelsr1r$kvrErAs ` rrrsN $A)rXs - )+N OO6 ;l+k40[IACwFJ,wFtl+k40[I b&J,b&r