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<h1>Source code for networkx.algorithms.graph_hashing</h1><div class="highlight"><pre>
<span></span><span class="sd">"""</span>
<span class="sd">Functions for hashing graphs to strings.</span>
<span class="sd">Isomorphic graphs should be assigned identical hashes.</span>
<span class="sd">For now, only Weisfeiler-Lehman hashing is implemented.</span>
<span class="sd">"""</span>
<span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">Counter</span><span class="p">,</span> <span class="n">defaultdict</span>
<span class="kn">from</span> <span class="nn">hashlib</span> <span class="kn">import</span> <span class="n">blake2b</span>
<span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"weisfeiler_lehman_graph_hash"</span><span class="p">,</span> <span class="s2">"weisfeiler_lehman_subgraph_hashes"</span><span class="p">]</span>
<span class="k">def</span> <span class="nf">_hash_label</span><span class="p">(</span><span class="n">label</span><span class="p">,</span> <span class="n">digest_size</span><span class="p">):</span>
<span class="k">return</span> <span class="n">blake2b</span><span class="p">(</span><span class="n">label</span><span class="o">.</span><span class="n">encode</span><span class="p">(</span><span class="s2">"ascii"</span><span class="p">),</span> <span class="n">digest_size</span><span class="o">=</span><span class="n">digest_size</span><span class="p">)</span><span class="o">.</span><span class="n">hexdigest</span><span class="p">()</span>
<span class="k">def</span> <span class="nf">_init_node_labels</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">edge_attr</span><span class="p">,</span> <span class="n">node_attr</span><span class="p">):</span>
<span class="k">if</span> <span class="n">node_attr</span><span class="p">:</span>
<span class="k">return</span> <span class="p">{</span><span class="n">u</span><span class="p">:</span> <span class="nb">str</span><span class="p">(</span><span class="n">dd</span><span class="p">[</span><span class="n">node_attr</span><span class="p">])</span> <span class="k">for</span> <span class="n">u</span><span class="p">,</span> <span class="n">dd</span> <span class="ow">in</span> <span class="n">G</span><span class="o">.</span><span class="n">nodes</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="kc">True</span><span class="p">)}</span>
<span class="k">elif</span> <span class="n">edge_attr</span><span class="p">:</span>
<span class="k">return</span> <span class="p">{</span><span class="n">u</span><span class="p">:</span> <span class="s2">""</span> <span class="k">for</span> <span class="n">u</span> <span class="ow">in</span> <span class="n">G</span><span class="p">}</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="p">{</span><span class="n">u</span><span class="p">:</span> <span class="nb">str</span><span class="p">(</span><span class="n">deg</span><span class="p">)</span> <span class="k">for</span> <span class="n">u</span><span class="p">,</span> <span class="n">deg</span> <span class="ow">in</span> <span class="n">G</span><span class="o">.</span><span class="n">degree</span><span class="p">()}</span>
<span class="k">def</span> <span class="nf">_neighborhood_aggregate</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">node</span><span class="p">,</span> <span class="n">node_labels</span><span class="p">,</span> <span class="n">edge_attr</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Compute new labels for given node by aggregating</span>
<span class="sd"> the labels of each node's neighbors.</span>
<span class="sd"> """</span>
<span class="n">label_list</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">nbr</span> <span class="ow">in</span> <span class="n">G</span><span class="o">.</span><span class="n">neighbors</span><span class="p">(</span><span class="n">node</span><span class="p">):</span>
<span class="n">prefix</span> <span class="o">=</span> <span class="s2">""</span> <span class="k">if</span> <span class="n">edge_attr</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="nb">str</span><span class="p">(</span><span class="n">G</span><span class="p">[</span><span class="n">node</span><span class="p">][</span><span class="n">nbr</span><span class="p">][</span><span class="n">edge_attr</span><span class="p">])</span>
<span class="n">label_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">prefix</span> <span class="o">+</span> <span class="n">node_labels</span><span class="p">[</span><span class="n">nbr</span><span class="p">])</span>
<span class="k">return</span> <span class="n">node_labels</span><span class="p">[</span><span class="n">node</span><span class="p">]</span> <span class="o">+</span> <span class="s2">""</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">sorted</span><span class="p">(</span><span class="n">label_list</span><span class="p">))</span>
<div class="viewcode-block" id="weisfeiler_lehman_graph_hash"><a class="viewcode-back" href="../../../reference/algorithms/generated/networkx.algorithms.graph_hashing.weisfeiler_lehman_graph_hash.html#networkx.algorithms.graph_hashing.weisfeiler_lehman_graph_hash">[docs]</a><span class="k">def</span> <span class="nf">weisfeiler_lehman_graph_hash</span><span class="p">(</span>
<span class="n">G</span><span class="p">,</span> <span class="n">edge_attr</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">node_attr</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">iterations</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">digest_size</span><span class="o">=</span><span class="mi">16</span>
<span class="p">):</span>
<span class="w"> </span><span class="sd">"""Return Weisfeiler Lehman (WL) graph hash.</span>
<span class="sd"> The function iteratively aggregates and hashes neighbourhoods of each node.</span>
<span class="sd"> After each node's neighbors are hashed to obtain updated node labels,</span>
<span class="sd"> a hashed histogram of resulting labels is returned as the final hash.</span>
<span class="sd"> Hashes are identical for isomorphic graphs and strong guarantees that</span>
<span class="sd"> non-isomorphic graphs will get different hashes. See [1]_ for details.</span>
<span class="sd"> If no node or edge attributes are provided, the degree of each node</span>
<span class="sd"> is used as its initial label.</span>
<span class="sd"> Otherwise, node and/or edge labels are used to compute the hash.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G: graph</span>
<span class="sd"> The graph to be hashed.</span>
<span class="sd"> Can have node and/or edge attributes. Can also have no attributes.</span>
<span class="sd"> edge_attr: string, default=None</span>
<span class="sd"> The key in edge attribute dictionary to be used for hashing.</span>
<span class="sd"> If None, edge labels are ignored.</span>
<span class="sd"> node_attr: string, default=None</span>
<span class="sd"> The key in node attribute dictionary to be used for hashing.</span>
<span class="sd"> If None, and no edge_attr given, use the degrees of the nodes as labels.</span>
<span class="sd"> iterations: int, default=3</span>
<span class="sd"> Number of neighbor aggregations to perform.</span>
<span class="sd"> Should be larger for larger graphs.</span>
<span class="sd"> digest_size: int, default=16</span>
<span class="sd"> Size (in bits) of blake2b hash digest to use for hashing node labels.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> h : string</span>
<span class="sd"> Hexadecimal string corresponding to hash of the input graph.</span>
<span class="sd"> Examples</span>
<span class="sd"> --------</span>
<span class="sd"> Two graphs with edge attributes that are isomorphic, except for</span>
<span class="sd"> differences in the edge labels.</span>
<span class="sd"> >>> G1 = nx.Graph()</span>
<span class="sd"> >>> G1.add_edges_from(</span>
<span class="sd"> ... [</span>
<span class="sd"> ... (1, 2, {"label": "A"}),</span>
<span class="sd"> ... (2, 3, {"label": "A"}),</span>
<span class="sd"> ... (3, 1, {"label": "A"}),</span>
<span class="sd"> ... (1, 4, {"label": "B"}),</span>
<span class="sd"> ... ]</span>
<span class="sd"> ... )</span>
<span class="sd"> >>> G2 = nx.Graph()</span>
<span class="sd"> >>> G2.add_edges_from(</span>
<span class="sd"> ... [</span>
<span class="sd"> ... (5, 6, {"label": "B"}),</span>
<span class="sd"> ... (6, 7, {"label": "A"}),</span>
<span class="sd"> ... (7, 5, {"label": "A"}),</span>
<span class="sd"> ... (7, 8, {"label": "A"}),</span>
<span class="sd"> ... ]</span>
<span class="sd"> ... )</span>
<span class="sd"> Omitting the `edge_attr` option, results in identical hashes.</span>
<span class="sd"> >>> nx.weisfeiler_lehman_graph_hash(G1)</span>
<span class="sd"> '7bc4dde9a09d0b94c5097b219891d81a'</span>
<span class="sd"> >>> nx.weisfeiler_lehman_graph_hash(G2)</span>
<span class="sd"> '7bc4dde9a09d0b94c5097b219891d81a'</span>
<span class="sd"> With edge labels, the graphs are no longer assigned</span>
<span class="sd"> the same hash digest.</span>
<span class="sd"> >>> nx.weisfeiler_lehman_graph_hash(G1, edge_attr="label")</span>
<span class="sd"> 'c653d85538bcf041d88c011f4f905f10'</span>
<span class="sd"> >>> nx.weisfeiler_lehman_graph_hash(G2, edge_attr="label")</span>
<span class="sd"> '3dcd84af1ca855d0eff3c978d88e7ec7'</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> To return the WL hashes of each subgraph of a graph, use</span>
<span class="sd"> `weisfeiler_lehman_subgraph_hashes`</span>
<span class="sd"> Similarity between hashes does not imply similarity between graphs.</span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> .. [1] Shervashidze, Nino, Pascal Schweitzer, Erik Jan Van Leeuwen,</span>
<span class="sd"> Kurt Mehlhorn, and Karsten M. Borgwardt. Weisfeiler Lehman</span>
<span class="sd"> Graph Kernels. Journal of Machine Learning Research. 2011.</span>
<span class="sd"> http://www.jmlr.org/papers/volume12/shervashidze11a/shervashidze11a.pdf</span>
<span class="sd"> See also</span>
<span class="sd"> --------</span>
<span class="sd"> weisfeiler_lehman_subgraph_hashes</span>
<span class="sd"> """</span>
<span class="k">def</span> <span class="nf">weisfeiler_lehman_step</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">labels</span><span class="p">,</span> <span class="n">edge_attr</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Apply neighborhood aggregation to each node</span>
<span class="sd"> in the graph.</span>
<span class="sd"> Computes a dictionary with labels for each node.</span>
<span class="sd"> """</span>
<span class="n">new_labels</span> <span class="o">=</span> <span class="p">{}</span>
<span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="n">G</span><span class="o">.</span><span class="n">nodes</span><span class="p">():</span>
<span class="n">label</span> <span class="o">=</span> <span class="n">_neighborhood_aggregate</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">node</span><span class="p">,</span> <span class="n">labels</span><span class="p">,</span> <span class="n">edge_attr</span><span class="o">=</span><span class="n">edge_attr</span><span class="p">)</span>
<span class="n">new_labels</span><span class="p">[</span><span class="n">node</span><span class="p">]</span> <span class="o">=</span> <span class="n">_hash_label</span><span class="p">(</span><span class="n">label</span><span class="p">,</span> <span class="n">digest_size</span><span class="p">)</span>
<span class="k">return</span> <span class="n">new_labels</span>
<span class="c1"># set initial node labels</span>
<span class="n">node_labels</span> <span class="o">=</span> <span class="n">_init_node_labels</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">edge_attr</span><span class="p">,</span> <span class="n">node_attr</span><span class="p">)</span>
<span class="n">subgraph_hash_counts</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">iterations</span><span class="p">):</span>
<span class="n">node_labels</span> <span class="o">=</span> <span class="n">weisfeiler_lehman_step</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">node_labels</span><span class="p">,</span> <span class="n">edge_attr</span><span class="o">=</span><span class="n">edge_attr</span><span class="p">)</span>
<span class="n">counter</span> <span class="o">=</span> <span class="n">Counter</span><span class="p">(</span><span class="n">node_labels</span><span class="o">.</span><span class="n">values</span><span class="p">())</span>
<span class="c1"># sort the counter, extend total counts</span>
<span class="n">subgraph_hash_counts</span><span class="o">.</span><span class="n">extend</span><span class="p">(</span><span class="nb">sorted</span><span class="p">(</span><span class="n">counter</span><span class="o">.</span><span class="n">items</span><span class="p">(),</span> <span class="n">key</span><span class="o">=</span><span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">]))</span>
<span class="c1"># hash the final counter</span>
<span class="k">return</span> <span class="n">_hash_label</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="nb">tuple</span><span class="p">(</span><span class="n">subgraph_hash_counts</span><span class="p">)),</span> <span class="n">digest_size</span><span class="p">)</span></div>
<div class="viewcode-block" id="weisfeiler_lehman_subgraph_hashes"><a class="viewcode-back" href="../../../reference/algorithms/generated/networkx.algorithms.graph_hashing.weisfeiler_lehman_subgraph_hashes.html#networkx.algorithms.graph_hashing.weisfeiler_lehman_subgraph_hashes">[docs]</a><span class="k">def</span> <span class="nf">weisfeiler_lehman_subgraph_hashes</span><span class="p">(</span>
<span class="n">G</span><span class="p">,</span> <span class="n">edge_attr</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">node_attr</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">iterations</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">digest_size</span><span class="o">=</span><span class="mi">16</span>
<span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Return a dictionary of subgraph hashes by node.</span>
<span class="sd"> The dictionary is keyed by node to a list of hashes in increasingly</span>
<span class="sd"> sized induced subgraphs containing the nodes within 2*k edges</span>
<span class="sd"> of the key node for increasing integer k until all nodes are included.</span>
<span class="sd"> The function iteratively aggregates and hashes neighbourhoods of each node.</span>
<span class="sd"> This is achieved for each step by replacing for each node its label from</span>
<span class="sd"> the previous iteration with its hashed 1-hop neighborhood aggregate.</span>
<span class="sd"> The new node label is then appended to a list of node labels for each</span>
<span class="sd"> node.</span>
<span class="sd"> To aggregate neighborhoods at each step for a node $n$, all labels of</span>
<span class="sd"> nodes adjacent to $n$ are concatenated. If the `edge_attr` parameter is set,</span>
<span class="sd"> labels for each neighboring node are prefixed with the value of this attribute</span>
<span class="sd"> along the connecting edge from this neighbor to node $n$. The resulting string</span>
<span class="sd"> is then hashed to compress this information into a fixed digest size.</span>
<span class="sd"> Thus, at the $i$th iteration nodes within $2i$ distance influence any given</span>
<span class="sd"> hashed node label. We can therefore say that at depth $i$ for node $n$</span>
<span class="sd"> we have a hash for a subgraph induced by the $2i$-hop neighborhood of $n$.</span>
<span class="sd"> Can be used to to create general Weisfeiler-Lehman graph kernels, or</span>
<span class="sd"> generate features for graphs or nodes, for example to generate 'words' in a</span>
<span class="sd"> graph as seen in the 'graph2vec' algorithm.</span>
<span class="sd"> See [1]_ & [2]_ respectively for details.</span>
<span class="sd"> Hashes are identical for isomorphic subgraphs and there exist strong</span>
<span class="sd"> guarantees that non-isomorphic graphs will get different hashes.</span>
<span class="sd"> See [1]_ for details.</span>
<span class="sd"> If no node or edge attributes are provided, the degree of each node</span>
<span class="sd"> is used as its initial label.</span>
<span class="sd"> Otherwise, node and/or edge labels are used to compute the hash.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> G: graph</span>
<span class="sd"> The graph to be hashed.</span>
<span class="sd"> Can have node and/or edge attributes. Can also have no attributes.</span>
<span class="sd"> edge_attr: string, default=None</span>
<span class="sd"> The key in edge attribute dictionary to be used for hashing.</span>
<span class="sd"> If None, edge labels are ignored.</span>
<span class="sd"> node_attr: string, default=None</span>
<span class="sd"> The key in node attribute dictionary to be used for hashing.</span>
<span class="sd"> If None, and no edge_attr given, use the degrees of the nodes as labels.</span>
<span class="sd"> iterations: int, default=3</span>
<span class="sd"> Number of neighbor aggregations to perform.</span>
<span class="sd"> Should be larger for larger graphs.</span>
<span class="sd"> digest_size: int, default=16</span>
<span class="sd"> Size (in bits) of blake2b hash digest to use for hashing node labels.</span>
<span class="sd"> The default size is 16 bits</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> node_subgraph_hashes : dict</span>
<span class="sd"> A dictionary with each key given by a node in G, and each value given</span>
<span class="sd"> by the subgraph hashes in order of depth from the key node.</span>
<span class="sd"> Examples</span>
<span class="sd"> --------</span>
<span class="sd"> Finding similar nodes in different graphs:</span>
<span class="sd"> >>> G1 = nx.Graph()</span>
<span class="sd"> >>> G1.add_edges_from([</span>
<span class="sd"> ... (1, 2), (2, 3), (2, 4), (3, 5), (4, 6), (5, 7), (6, 7)</span>
<span class="sd"> ... ])</span>
<span class="sd"> >>> G2 = nx.Graph()</span>
<span class="sd"> >>> G2.add_edges_from([</span>
<span class="sd"> ... (1, 3), (2, 3), (1, 6), (1, 5), (4, 6)</span>
<span class="sd"> ... ])</span>
<span class="sd"> >>> g1_hashes = nx.weisfeiler_lehman_subgraph_hashes(G1, iterations=3, digest_size=8)</span>
<span class="sd"> >>> g2_hashes = nx.weisfeiler_lehman_subgraph_hashes(G2, iterations=3, digest_size=8)</span>
<span class="sd"> Even though G1 and G2 are not isomorphic (they have different numbers of edges),</span>
<span class="sd"> the hash sequence of depth 3 for node 1 in G1 and node 5 in G2 are similar:</span>
<span class="sd"> >>> g1_hashes[1]</span>
<span class="sd"> ['a93b64973cfc8897', 'db1b43ae35a1878f', '57872a7d2059c1c0']</span>
<span class="sd"> >>> g2_hashes[5]</span>
<span class="sd"> ['a93b64973cfc8897', 'db1b43ae35a1878f', '1716d2a4012fa4bc']</span>
<span class="sd"> The first 2 WL subgraph hashes match. From this we can conclude that it's very</span>
<span class="sd"> likely the neighborhood of 4 hops around these nodes are isomorphic: each</span>
<span class="sd"> iteration aggregates 1-hop neighbourhoods meaning hashes at depth $n$ are influenced</span>
<span class="sd"> by every node within $2n$ hops.</span>
<span class="sd"> However the neighborhood of 6 hops is no longer isomorphic since their 3rd hash does</span>
<span class="sd"> not match.</span>
<span class="sd"> These nodes may be candidates to be classified together since their local topology</span>
<span class="sd"> is similar.</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> To hash the full graph when subgraph hashes are not needed, use</span>
<span class="sd"> `weisfeiler_lehman_graph_hash` for efficiency.</span>
<span class="sd"> Similarity between hashes does not imply similarity between graphs.</span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> .. [1] Shervashidze, Nino, Pascal Schweitzer, Erik Jan Van Leeuwen,</span>
<span class="sd"> Kurt Mehlhorn, and Karsten M. Borgwardt. Weisfeiler Lehman</span>
<span class="sd"> Graph Kernels. Journal of Machine Learning Research. 2011.</span>
<span class="sd"> http://www.jmlr.org/papers/volume12/shervashidze11a/shervashidze11a.pdf</span>
<span class="sd"> .. [2] Annamalai Narayanan, Mahinthan Chandramohan, Rajasekar Venkatesan,</span>
<span class="sd"> Lihui Chen, Yang Liu and Shantanu Jaiswa. graph2vec: Learning</span>
<span class="sd"> Distributed Representations of Graphs. arXiv. 2017</span>
<span class="sd"> https://arxiv.org/pdf/1707.05005.pdf</span>
<span class="sd"> See also</span>
<span class="sd"> --------</span>
<span class="sd"> weisfeiler_lehman_graph_hash</span>
<span class="sd"> """</span>
<span class="k">def</span> <span class="nf">weisfeiler_lehman_step</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">labels</span><span class="p">,</span> <span class="n">node_subgraph_hashes</span><span class="p">,</span> <span class="n">edge_attr</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Apply neighborhood aggregation to each node</span>
<span class="sd"> in the graph.</span>
<span class="sd"> Computes a dictionary with labels for each node.</span>
<span class="sd"> Appends the new hashed label to the dictionary of subgraph hashes</span>
<span class="sd"> originating from and indexed by each node in G</span>
<span class="sd"> """</span>
<span class="n">new_labels</span> <span class="o">=</span> <span class="p">{}</span>
<span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="n">G</span><span class="o">.</span><span class="n">nodes</span><span class="p">():</span>
<span class="n">label</span> <span class="o">=</span> <span class="n">_neighborhood_aggregate</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">node</span><span class="p">,</span> <span class="n">labels</span><span class="p">,</span> <span class="n">edge_attr</span><span class="o">=</span><span class="n">edge_attr</span><span class="p">)</span>
<span class="n">hashed_label</span> <span class="o">=</span> <span class="n">_hash_label</span><span class="p">(</span><span class="n">label</span><span class="p">,</span> <span class="n">digest_size</span><span class="p">)</span>
<span class="n">new_labels</span><span class="p">[</span><span class="n">node</span><span class="p">]</span> <span class="o">=</span> <span class="n">hashed_label</span>
<span class="n">node_subgraph_hashes</span><span class="p">[</span><span class="n">node</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">hashed_label</span><span class="p">)</span>
<span class="k">return</span> <span class="n">new_labels</span>
<span class="n">node_labels</span> <span class="o">=</span> <span class="n">_init_node_labels</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="n">edge_attr</span><span class="p">,</span> <span class="n">node_attr</span><span class="p">)</span>
<span class="n">node_subgraph_hashes</span> <span class="o">=</span> <span class="n">defaultdict</span><span class="p">(</span><span class="nb">list</span><span class="p">)</span>
<span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">iterations</span><span class="p">):</span>
<span class="n">node_labels</span> <span class="o">=</span> <span class="n">weisfeiler_lehman_step</span><span class="p">(</span>
<span class="n">G</span><span class="p">,</span> <span class="n">node_labels</span><span class="p">,</span> <span class="n">node_subgraph_hashes</span><span class="p">,</span> <span class="n">edge_attr</span>
<span class="p">)</span>
<span class="k">return</span> <span class="nb">dict</span><span class="p">(</span><span class="n">node_subgraph_hashes</span><span class="p">)</span></div>
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