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diff --git a/.venv/lib/python3.12/site-packages/networkx/algorithms/connectivity/disjoint_paths.py b/.venv/lib/python3.12/site-packages/networkx/algorithms/connectivity/disjoint_paths.py
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+"""Flow based node and edge disjoint paths."""
+
+import networkx as nx
+
+# Define the default maximum flow function to use for the underlying
+# maximum flow computations
+from networkx.algorithms.flow import (
+    edmonds_karp,
+    preflow_push,
+    shortest_augmenting_path,
+)
+from networkx.exception import NetworkXNoPath
+
+default_flow_func = edmonds_karp
+from itertools import filterfalse as _filterfalse
+
+# Functions to build auxiliary data structures.
+from .utils import build_auxiliary_edge_connectivity, build_auxiliary_node_connectivity
+
+__all__ = ["edge_disjoint_paths", "node_disjoint_paths"]
+
+
+@nx._dispatchable(
+    graphs={"G": 0, "auxiliary?": 5},
+    preserve_edge_attrs={"auxiliary": {"capacity": float("inf")}},
+)
+def edge_disjoint_paths(
+    G, s, t, flow_func=None, cutoff=None, auxiliary=None, residual=None
+):
+    """Returns the edges disjoint paths between source and target.
+
+    Edge disjoint paths are paths that do not share any edge. The
+    number of edge disjoint paths between source and target is equal
+    to their edge connectivity.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    s : node
+        Source node for the flow.
+
+    t : node
+        Sink node for the flow.
+
+    flow_func : function
+        A function for computing the maximum flow among a pair of nodes.
+        The function has to accept at least three parameters: a Digraph,
+        a source node, and a target node. And return a residual network
+        that follows NetworkX conventions (see :meth:`maximum_flow` for
+        details). If flow_func is None, the default maximum flow function
+        (:meth:`edmonds_karp`) is used. The choice of the default function
+        may change from version to version and should not be relied on.
+        Default value: None.
+
+    cutoff : integer or None (default: None)
+        Maximum number of paths to yield. If specified, the maximum flow
+        algorithm will terminate when the flow value reaches or exceeds the
+        cutoff. This only works for flows that support the cutoff parameter
+        (most do) and is ignored otherwise.
+
+    auxiliary : NetworkX DiGraph
+        Auxiliary digraph to compute flow based edge connectivity. It has
+        to have a graph attribute called mapping with a dictionary mapping
+        node names in G and in the auxiliary digraph. If provided
+        it will be reused instead of recreated. Default value: None.
+
+    residual : NetworkX DiGraph
+        Residual network to compute maximum flow. If provided it will be
+        reused instead of recreated. Default value: None.
+
+    Returns
+    -------
+    paths : generator
+        A generator of edge independent paths.
+
+    Raises
+    ------
+    NetworkXNoPath
+        If there is no path between source and target.
+
+    NetworkXError
+        If source or target are not in the graph G.
+
+    See also
+    --------
+    :meth:`node_disjoint_paths`
+    :meth:`edge_connectivity`
+    :meth:`maximum_flow`
+    :meth:`edmonds_karp`
+    :meth:`preflow_push`
+    :meth:`shortest_augmenting_path`
+
+    Examples
+    --------
+    We use in this example the platonic icosahedral graph, which has node
+    edge connectivity 5, thus there are 5 edge disjoint paths between any
+    pair of nodes.
+
+    >>> G = nx.icosahedral_graph()
+    >>> len(list(nx.edge_disjoint_paths(G, 0, 6)))
+    5
+
+
+    If you need to compute edge disjoint paths on several pairs of
+    nodes in the same graph, it is recommended that you reuse the
+    data structures that NetworkX uses in the computation: the
+    auxiliary digraph for edge connectivity, and the residual
+    network for the underlying maximum flow computation.
+
+    Example of how to compute edge disjoint paths among all pairs of
+    nodes of the platonic icosahedral graph reusing the data
+    structures.
+
+    >>> import itertools
+    >>> # You also have to explicitly import the function for
+    >>> # building the auxiliary digraph from the connectivity package
+    >>> from networkx.algorithms.connectivity import build_auxiliary_edge_connectivity
+    >>> H = build_auxiliary_edge_connectivity(G)
+    >>> # And the function for building the residual network from the
+    >>> # flow package
+    >>> from networkx.algorithms.flow import build_residual_network
+    >>> # Note that the auxiliary digraph has an edge attribute named capacity
+    >>> R = build_residual_network(H, "capacity")
+    >>> result = {n: {} for n in G}
+    >>> # Reuse the auxiliary digraph and the residual network by passing them
+    >>> # as arguments
+    >>> for u, v in itertools.combinations(G, 2):
+    ...     k = len(list(nx.edge_disjoint_paths(G, u, v, auxiliary=H, residual=R)))
+    ...     result[u][v] = k
+    >>> all(result[u][v] == 5 for u, v in itertools.combinations(G, 2))
+    True
+
+    You can also use alternative flow algorithms for computing edge disjoint
+    paths. For instance, in dense networks the algorithm
+    :meth:`shortest_augmenting_path` will usually perform better than
+    the default :meth:`edmonds_karp` which is faster for sparse
+    networks with highly skewed degree distributions. Alternative flow
+    functions have to be explicitly imported from the flow package.
+
+    >>> from networkx.algorithms.flow import shortest_augmenting_path
+    >>> len(list(nx.edge_disjoint_paths(G, 0, 6, flow_func=shortest_augmenting_path)))
+    5
+
+    Notes
+    -----
+    This is a flow based implementation of edge disjoint paths. We compute
+    the maximum flow between source and target on an auxiliary directed
+    network. The saturated edges in the residual network after running the
+    maximum flow algorithm correspond to edge disjoint paths between source
+    and target in the original network. This function handles both directed
+    and undirected graphs, and can use all flow algorithms from NetworkX flow
+    package.
+
+    """
+    if s not in G:
+        raise nx.NetworkXError(f"node {s} not in graph")
+    if t not in G:
+        raise nx.NetworkXError(f"node {t} not in graph")
+
+    if flow_func is None:
+        flow_func = default_flow_func
+
+    if auxiliary is None:
+        H = build_auxiliary_edge_connectivity(G)
+    else:
+        H = auxiliary
+
+    # Maximum possible edge disjoint paths
+    possible = min(H.out_degree(s), H.in_degree(t))
+    if not possible:
+        raise NetworkXNoPath
+
+    if cutoff is None:
+        cutoff = possible
+    else:
+        cutoff = min(cutoff, possible)
+
+    # Compute maximum flow between source and target. Flow functions in
+    # NetworkX return a residual network.
+    kwargs = {
+        "capacity": "capacity",
+        "residual": residual,
+        "cutoff": cutoff,
+        "value_only": True,
+    }
+    if flow_func is preflow_push:
+        del kwargs["cutoff"]
+    if flow_func is shortest_augmenting_path:
+        kwargs["two_phase"] = True
+    R = flow_func(H, s, t, **kwargs)
+
+    if R.graph["flow_value"] == 0:
+        raise NetworkXNoPath
+
+    # Saturated edges in the residual network form the edge disjoint paths
+    # between source and target
+    cutset = [
+        (u, v)
+        for u, v, d in R.edges(data=True)
+        if d["capacity"] == d["flow"] and d["flow"] > 0
+    ]
+    # This is equivalent of what flow.utils.build_flow_dict returns, but
+    # only for the nodes with saturated edges and without reporting 0 flows.
+    flow_dict = {n: {} for edge in cutset for n in edge}
+    for u, v in cutset:
+        flow_dict[u][v] = 1
+
+    # Rebuild the edge disjoint paths from the flow dictionary.
+    paths_found = 0
+    for v in list(flow_dict[s]):
+        if paths_found >= cutoff:
+            # preflow_push does not support cutoff: we have to
+            # keep track of the paths founds and stop at cutoff.
+            break
+        path = [s]
+        if v == t:
+            path.append(v)
+            yield path
+            continue
+        u = v
+        while u != t:
+            path.append(u)
+            try:
+                u, _ = flow_dict[u].popitem()
+            except KeyError:
+                break
+        else:
+            path.append(t)
+            yield path
+            paths_found += 1
+
+
+@nx._dispatchable(
+    graphs={"G": 0, "auxiliary?": 5},
+    preserve_node_attrs={"auxiliary": {"id": None}},
+    preserve_graph_attrs={"auxiliary"},
+)
+def node_disjoint_paths(
+    G, s, t, flow_func=None, cutoff=None, auxiliary=None, residual=None
+):
+    r"""Computes node disjoint paths between source and target.
+
+    Node disjoint paths are paths that only share their first and last
+    nodes. The number of node independent paths between two nodes is
+    equal to their local node connectivity.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    s : node
+        Source node.
+
+    t : node
+        Target node.
+
+    flow_func : function
+        A function for computing the maximum flow among a pair of nodes.
+        The function has to accept at least three parameters: a Digraph,
+        a source node, and a target node. And return a residual network
+        that follows NetworkX conventions (see :meth:`maximum_flow` for
+        details). If flow_func is None, the default maximum flow function
+        (:meth:`edmonds_karp`) is used. See below for details. The choice
+        of the default function may change from version to version and
+        should not be relied on. Default value: None.
+
+    cutoff : integer or None (default: None)
+        Maximum number of paths to yield. If specified, the maximum flow
+        algorithm will terminate when the flow value reaches or exceeds the
+        cutoff. This only works for flows that support the cutoff parameter
+        (most do) and is ignored otherwise.
+
+    auxiliary : NetworkX DiGraph
+        Auxiliary digraph to compute flow based node connectivity. It has
+        to have a graph attribute called mapping with a dictionary mapping
+        node names in G and in the auxiliary digraph. If provided
+        it will be reused instead of recreated. Default value: None.
+
+    residual : NetworkX DiGraph
+        Residual network to compute maximum flow. If provided it will be
+        reused instead of recreated. Default value: None.
+
+    Returns
+    -------
+    paths : generator
+        Generator of node disjoint paths.
+
+    Raises
+    ------
+    NetworkXNoPath
+        If there is no path between source and target.
+
+    NetworkXError
+        If source or target are not in the graph G.
+
+    Examples
+    --------
+    We use in this example the platonic icosahedral graph, which has node
+    connectivity 5, thus there are 5 node disjoint paths between any pair
+    of non neighbor nodes.
+
+    >>> G = nx.icosahedral_graph()
+    >>> len(list(nx.node_disjoint_paths(G, 0, 6)))
+    5
+
+    If you need to compute node disjoint paths between several pairs of
+    nodes in the same graph, it is recommended that you reuse the
+    data structures that NetworkX uses in the computation: the
+    auxiliary digraph for node connectivity and node cuts, and the
+    residual network for the underlying maximum flow computation.
+
+    Example of how to compute node disjoint paths reusing the data
+    structures:
+
+    >>> # You also have to explicitly import the function for
+    >>> # building the auxiliary digraph from the connectivity package
+    >>> from networkx.algorithms.connectivity import build_auxiliary_node_connectivity
+    >>> H = build_auxiliary_node_connectivity(G)
+    >>> # And the function for building the residual network from the
+    >>> # flow package
+    >>> from networkx.algorithms.flow import build_residual_network
+    >>> # Note that the auxiliary digraph has an edge attribute named capacity
+    >>> R = build_residual_network(H, "capacity")
+    >>> # Reuse the auxiliary digraph and the residual network by passing them
+    >>> # as arguments
+    >>> len(list(nx.node_disjoint_paths(G, 0, 6, auxiliary=H, residual=R)))
+    5
+
+    You can also use alternative flow algorithms for computing node disjoint
+    paths. For instance, in dense networks the algorithm
+    :meth:`shortest_augmenting_path` will usually perform better than
+    the default :meth:`edmonds_karp` which is faster for sparse
+    networks with highly skewed degree distributions. Alternative flow
+    functions have to be explicitly imported from the flow package.
+
+    >>> from networkx.algorithms.flow import shortest_augmenting_path
+    >>> len(list(nx.node_disjoint_paths(G, 0, 6, flow_func=shortest_augmenting_path)))
+    5
+
+    Notes
+    -----
+    This is a flow based implementation of node disjoint paths. We compute
+    the maximum flow between source and target on an auxiliary directed
+    network. The saturated edges in the residual network after running the
+    maximum flow algorithm correspond to node disjoint paths between source
+    and target in the original network. This function handles both directed
+    and undirected graphs, and can use all flow algorithms from NetworkX flow
+    package.
+
+    See also
+    --------
+    :meth:`edge_disjoint_paths`
+    :meth:`node_connectivity`
+    :meth:`maximum_flow`
+    :meth:`edmonds_karp`
+    :meth:`preflow_push`
+    :meth:`shortest_augmenting_path`
+
+    """
+    if s not in G:
+        raise nx.NetworkXError(f"node {s} not in graph")
+    if t not in G:
+        raise nx.NetworkXError(f"node {t} not in graph")
+
+    if auxiliary is None:
+        H = build_auxiliary_node_connectivity(G)
+    else:
+        H = auxiliary
+
+    mapping = H.graph.get("mapping", None)
+    if mapping is None:
+        raise nx.NetworkXError("Invalid auxiliary digraph.")
+
+    # Maximum possible edge disjoint paths
+    possible = min(H.out_degree(f"{mapping[s]}B"), H.in_degree(f"{mapping[t]}A"))
+    if not possible:
+        raise NetworkXNoPath
+
+    if cutoff is None:
+        cutoff = possible
+    else:
+        cutoff = min(cutoff, possible)
+
+    kwargs = {
+        "flow_func": flow_func,
+        "residual": residual,
+        "auxiliary": H,
+        "cutoff": cutoff,
+    }
+
+    # The edge disjoint paths in the auxiliary digraph correspond to the node
+    # disjoint paths in the original graph.
+    paths_edges = edge_disjoint_paths(H, f"{mapping[s]}B", f"{mapping[t]}A", **kwargs)
+    for path in paths_edges:
+        # Each node in the original graph maps to two nodes in auxiliary graph
+        yield list(_unique_everseen(H.nodes[node]["id"] for node in path))
+
+
+def _unique_everseen(iterable):
+    # Adapted from https://docs.python.org/3/library/itertools.html examples
+    "List unique elements, preserving order. Remember all elements ever seen."
+    # unique_everseen('AAAABBBCCDAABBB') --> A B C D
+    seen = set()
+    seen_add = seen.add
+    for element in _filterfalse(seen.__contains__, iterable):
+        seen_add(element)
+        yield element