o ]Zh 1@sdZddlmZmZddlmZddlZddgZddZ d d Z dd d Z ej d ejddidd dddZej d ejddidd     dddZdS)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_hashescCst|d|dS)Nascii digest_size)rencode hexdigest)labelr r P/var/www/auris/lib/python3.10/site-packages/networkx/algorithms/graph_hashing.py _hash_labelsrcsBrfdd|jddDS|rdd|DSdd|DS)Ncsi|] \}}|t|qSr str).0udd node_attrr r sz%_init_node_labels..T)datacSsi|]}|dqS)r )rrr r rrscSsi|] \}}|t|qSr r)rrdegr r rrs)nodesZdegree)G edge_attrrr rr_init_node_labelss rcCs\g}||D]}|durdn t||||}||||q||dt|S)zc Compute new labels for given node by aggregating the labels of each node's neighbors. Nr)Z neighborsrappendjoinsorted)rnode node_labelsrZ label_listZnbrprefixr r r_neighborhood_aggregates  r%Z multigraphrr)Z edge_attrsZ node_attrsc srdfdd }t|||}g}t|D]}||||d}t|} |t| dddqttt |S) a 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 Ncs4i}|D]}t||||d}t|||<q|S)z Apply neighborhood aggregation to each node in the graph. Computes a dictionary with labels for each node. r)rr%r)rlabelsr new_labelsr"r rr rweisfeiler_lehman_steps  z.weisfeiler_lehman_stepr(cSs|dS)Nrr )xr r rsz.weisfeiler_lehman_graph_hash..)keyN) rrangervaluesextendr!itemsrrtuple) rrr iterationsr r+r#Zsubgraph_hash_counts_counterr rrr(sb   Fc sbdfdd }t|||}|rfdd|D}ntt}t|D] } |||||}q#t|S)a Return a dictionary of subgraph hashes by node. Dictionary keys are nodes in `G`, and values are a list of hashes. Each hash corresponds to a subgraph rooted at a given node u in `G`. Lists of subgraph hashes are sorted in increasing order of depth from their root node, with the hash at index i corresponding to a subgraph of nodes at most i edges distance from u. Thus, each list will contain `iterations` elements - a hash for a subgraph at each depth. If `include_initial_labels` is set to `True`, each list will additionally have contain a hash of the initial node label (or equivalently a subgraph of depth 0) prepended, totalling ``iterations + 1`` elements. The function iteratively aggregates and hashes neighborhoods of each node. This is achieved for each step by replacing for each node its label from the previous iteration with its hashed 1-hop neighborhood aggregate. The new node label is then appended to a list of node labels for each node. To aggregate neighborhoods for a node $u$ at each step, all labels of nodes adjacent to $u$ are concatenated. If the `edge_attr` parameter is set, labels for each neighboring node are prefixed with the value of this attribute along the connecting edge from this neighbor to node $u$. The resulting string is then hashed to compress this information into a fixed digest size. Thus, at the $i$-th iteration, nodes within $i$ hops influence any given hashed node label. We can therefore say that at depth $i$ for node $u$ we have a hash for a subgraph induced by the $i$-hop neighborhood of $u$. The output can be used to create general Weisfeiler-Lehman graph kernels, or generate features for graphs or nodes - for example to generate 'words' in a graph as seen in the 'graph2vec' algorithm. See [1]_ & [2]_ respectively for details. Hashes are identical for isomorphic subgraphs and there exist 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. If None, and edge_attr is given, each node starts with an identical label. 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. The default size is 16 bits. include_initial_labels : bool, optional (default=False) If True, include the hashed initial node label as the first subgraph hash for each node. Returns ------- node_subgraph_hashes : dict A dictionary with each key given by a node in G, and each value given by the subgraph hashes in order of depth from the key node. Examples -------- Finding similar nodes in different graphs: >>> 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 NcsFi}|D]}t||||d}t|}|||<|||q|S)a  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_hashesrr*r"r Z hashed_labelrr rr++s  zAweisfeiler_lehman_subgraph_hashes..weisfeiler_lehman_stepcsi|] \}}|t|gqSr )r)rkvrr rr=sz5weisfeiler_lehman_subgraph_hashes..r/)rr3rlistr0dict) rrrr5r Zinclude_initial_labelsr+r#r8r6r rrrs   r/)NNr&r')NNr&r'F)__doc__ collectionsrrhashlibrZnetworkxnx__all__rrr%utilsZnot_implemented_forZ _dispatchablerrr r r rs(   z