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+"""
+Functions for hashing graphs to strings.
+Isomorphic graphs should be assigned identical hashes.
+For now, only Weisfeiler-Lehman hashing is implemented.
+"""
+
+import warnings
+from collections import Counter, defaultdict
+from hashlib import blake2b
+
+import networkx as nx
+
+__all__ = ["weisfeiler_lehman_graph_hash", "weisfeiler_lehman_subgraph_hashes"]
+
+
+def _hash_label(label, digest_size):
+    return blake2b(label.encode("ascii"), digest_size=digest_size).hexdigest()
+
+
+def _init_node_labels(G, edge_attr, node_attr):
+    if node_attr:
+        return {u: str(dd[node_attr]) for u, dd in G.nodes(data=True)}
+    elif edge_attr:
+        return dict.fromkeys(G, "")
+    else:
+        warnings.warn(
+            "The hashes produced for graphs without node or edge attributes"
+            "changed in v3.5 due to a bugfix (see documentation).",
+            UserWarning,
+            stacklevel=2,
+        )
+        if nx.is_directed(G):
+            return {u: str(G.in_degree(u)) + "_" + str(G.out_degree(u)) for u in G}
+        else:
+            return {u: str(deg) for u, deg in G.degree()}
+
+
+def _neighborhood_aggregate_undirected(G, node, node_labels, edge_attr=None):
+    """
+    Compute new labels for given node in an undirected graph by aggregating
+    the labels of each node's neighbors.
+    """
+    label_list = []
+    for nbr in G.neighbors(node):
+        prefix = "" if edge_attr is None else str(G[node][nbr][edge_attr])
+        label_list.append(prefix + node_labels[nbr])
+    return node_labels[node] + "".join(sorted(label_list))
+
+
+def _neighborhood_aggregate_directed(G, node, node_labels, edge_attr=None):
+    """
+    Compute new labels for given node in a directed graph by aggregating
+    the labels of each node's neighbors.
+    """
+    successor_labels = []
+    for nbr in G.successors(node):
+        prefix = "s_" + "" if edge_attr is None else str(G[node][nbr][edge_attr])
+        successor_labels.append(prefix + node_labels[nbr])
+
+    predecessor_labels = []
+    for nbr in G.predecessors(node):
+        prefix = "p_" + "" if edge_attr is None else str(G[nbr][node][edge_attr])
+        predecessor_labels.append(prefix + node_labels[nbr])
+    return (
+        node_labels[node]
+        + "".join(sorted(successor_labels))
+        + "".join(sorted(predecessor_labels))
+    )
+
+
+@nx.utils.not_implemented_for("multigraph")
+@nx._dispatchable(edge_attrs={"edge_attr": None}, node_attrs="node_attr")
+def weisfeiler_lehman_graph_hash(
+    G, edge_attr=None, node_attr=None, iterations=3, digest_size=16
+):
+    """Return Weisfeiler Lehman (WL) graph hash.
+
+    .. Warning:: Hash values for directed graphs and graphs without edge or
+        node attributes have changed in v3.5. In previous versions,
+        directed graphs did not distinguish in- and outgoing edges. Also,
+        graphs without attributes set initial states such that effectively
+        one extra iteration of WL occurred than indicated by `iterations`.
+        For undirected graphs without node or edge labels, the old
+        hashes can be obtained by increasing the iteration count by one.
+        For more details, see `issue #7806
+        <https://github.com/networkx/networkx/issues/7806>`_.
+
+    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 bytes) of blake2b hash digest to use for hashing node labels.
+
+    Returns
+    -------
+    h : string
+        Hexadecimal string corresponding to hash of `G` (length ``2 * digest_size``).
+
+    Raises
+    ------
+    ValueError
+        If `iterations` is not a positve number.
+
+    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)
+    'c045439172215f49e0bef8c3d26c6b61'
+    >>> nx.weisfeiler_lehman_graph_hash(G2)
+    'c045439172215f49e0bef8c3d26c6b61'
+
+    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
+    """
+
+    if G.is_directed():
+        _neighborhood_aggregate = _neighborhood_aggregate_directed
+        warnings.warn(
+            "The hashes produced for directed graphs changed in version v3.5"
+            " due to a bugfix to track in and out edges separately (see documentation).",
+            UserWarning,
+            stacklevel=2,
+        )
+    else:
+        _neighborhood_aggregate = _neighborhood_aggregate_undirected
+
+    def weisfeiler_lehman_step(G, labels, edge_attr=None):
+        """
+        Apply neighborhood aggregation to each node
+        in the graph.
+        Computes a dictionary with labels for each node.
+        """
+        new_labels = {}
+        for node in G.nodes():
+            label = _neighborhood_aggregate(G, node, labels, edge_attr=edge_attr)
+            new_labels[node] = _hash_label(label, digest_size)
+        return new_labels
+
+    if iterations <= 0:
+        raise ValueError("The WL algorithm requires that `iterations` be positive")
+
+    # set initial node labels
+    node_labels = _init_node_labels(G, edge_attr, node_attr)
+
+    # If the graph has no attributes, initial labels are the nodes' degrees.
+    # This is equivalent to doing the first iterations of WL.
+    if not edge_attr and not node_attr:
+        iterations -= 1
+
+    subgraph_hash_counts = []
+    for _ in range(iterations):
+        node_labels = weisfeiler_lehman_step(G, node_labels, edge_attr=edge_attr)
+        counter = Counter(node_labels.values())
+        # sort the counter, extend total counts
+        subgraph_hash_counts.extend(sorted(counter.items(), key=lambda x: x[0]))
+
+    # hash the final counter
+    return _hash_label(str(tuple(subgraph_hash_counts)), digest_size)
+
+
+@nx.utils.not_implemented_for("multigraph")
+@nx._dispatchable(edge_attrs={"edge_attr": None}, node_attrs="node_attr")
+def weisfeiler_lehman_subgraph_hashes(
+    G,
+    edge_attr=None,
+    node_attr=None,
+    iterations=3,
+    digest_size=16,
+    include_initial_labels=False,
+):
+    """
+    Return a dictionary of subgraph hashes by node.
+
+    .. Warning:: Hash values for directed graphs have changed in version
+        v3.5. In previous versions, directed graphs did not distinguish in-
+        and outgoing edges.
+        Graphs without attributes previously performed an extra iteration of
+        WL at initialisation, which was not visible in the output of this
+        function. This hash value is now included in the returned dictionary,
+        shifting the other calculated hashes one position to the right. To
+        obtain the same last subgraph hash, increase the number of iterations
+        by one.
+        For more details, see `issue #7806
+        <https://github.com/networkx/networkx/issues/7806>`_.
+
+    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-hops (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 bytes) of blake2b hash digest to use for hashing node labels.
+        The default size is 16 bytes.
+    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.
+        Hashes are hexadecimal strings (hence ``2 * digest_size`` long).
+
+
+    Raises
+    ------
+    ValueError
+        If `iterations` is not a positve number.
+
+    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=4, digest_size=8
+    ... )
+    >>> g2_hashes = nx.weisfeiler_lehman_subgraph_hashes(
+    ...     G2, iterations=4, 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]
+    ['f6fc42039fba3776', 'a93b64973cfc8897', 'db1b43ae35a1878f', '57872a7d2059c1c0']
+    >>> g2_hashes[5]
+    ['f6fc42039fba3776', 'a93b64973cfc8897', 'db1b43ae35a1878f', '1716d2a4012fa4bc']
+
+    The first 3 WL subgraph hashes match. From this we can conclude that it's very
+    likely the neighborhood of 3 hops around these nodes are isomorphic.
+
+    However the 4-hop neighborhoods of ``G1`` and ``G2`` are not isomorphic since the
+    4th 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
+    """
+
+    if G.is_directed():
+        _neighborhood_aggregate = _neighborhood_aggregate_directed
+        warnings.warn(
+            "The hashes produced for directed graphs changed in v3.5"
+            " due to a bugfix (see documentation).",
+            UserWarning,
+            stacklevel=2,
+        )
+    else:
+        _neighborhood_aggregate = _neighborhood_aggregate_undirected
+
+    def weisfeiler_lehman_step(G, labels, node_subgraph_hashes, edge_attr=None):
+        """
+        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
+        """
+        new_labels = {}
+        for node in G.nodes():
+            label = _neighborhood_aggregate(G, node, labels, edge_attr=edge_attr)
+            hashed_label = _hash_label(label, digest_size)
+            new_labels[node] = hashed_label
+            node_subgraph_hashes[node].append(hashed_label)
+        return new_labels
+
+    if iterations <= 0:
+        raise ValueError("The WL algorithm requires that `iterations` be positive")
+
+    node_labels = _init_node_labels(G, edge_attr, node_attr)
+
+    if include_initial_labels:
+        node_subgraph_hashes = {
+            k: [_hash_label(v, digest_size)] for k, v in node_labels.items()
+        }
+    else:
+        node_subgraph_hashes = defaultdict(list)
+
+    # If the graph has no attributes, initial labels are the nodes' degrees.
+    # This is equivalent to doing the first iterations of WL.
+    if not edge_attr and not node_attr:
+        iterations -= 1
+        for node in G.nodes():
+            hashed_label = _hash_label(node_labels[node], digest_size)
+            node_subgraph_hashes[node].append(hashed_label)
+
+    for _ in range(iterations):
+        node_labels = weisfeiler_lehman_step(
+            G, node_labels, node_subgraph_hashes, edge_attr
+        )
+
+    return dict(node_subgraph_hashes)