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diff --git a/.venv/lib/python3.12/site-packages/networkx/generators/line.py b/.venv/lib/python3.12/site-packages/networkx/generators/line.py
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+"""Functions for generating line graphs."""
+
+from collections import defaultdict
+from functools import partial
+from itertools import combinations
+
+import networkx as nx
+from networkx.utils import arbitrary_element
+from networkx.utils.decorators import not_implemented_for
+
+__all__ = ["line_graph", "inverse_line_graph"]
+
+
+@nx._dispatchable(returns_graph=True)
+def line_graph(G, create_using=None):
+    r"""Returns the line graph of the graph or digraph `G`.
+
+    The line graph of a graph `G` has a node for each edge in `G` and an
+    edge joining those nodes if the two edges in `G` share a common node. For
+    directed graphs, nodes are adjacent exactly when the edges they represent
+    form a directed path of length two.
+
+    The nodes of the line graph are 2-tuples of nodes in the original graph (or
+    3-tuples for multigraphs, with the key of the edge as the third element).
+
+    For information about self-loops and more discussion, see the **Notes**
+    section below.
+
+    Parameters
+    ----------
+    G : graph
+        A NetworkX Graph, DiGraph, MultiGraph, or MultiDigraph.
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+       Graph type to create. If graph instance, then cleared before populated.
+
+    Returns
+    -------
+    L : graph
+        The line graph of G.
+
+    Examples
+    --------
+    >>> G = nx.star_graph(3)
+    >>> L = nx.line_graph(G)
+    >>> print(sorted(map(sorted, L.edges())))  # makes a 3-clique, K3
+    [[(0, 1), (0, 2)], [(0, 1), (0, 3)], [(0, 2), (0, 3)]]
+
+    Edge attributes from `G` are not copied over as node attributes in `L`, but
+    attributes can be copied manually:
+
+    >>> G = nx.path_graph(4)
+    >>> G.add_edges_from((u, v, {"tot": u + v}) for u, v in G.edges)
+    >>> G.edges(data=True)
+    EdgeDataView([(0, 1, {'tot': 1}), (1, 2, {'tot': 3}), (2, 3, {'tot': 5})])
+    >>> H = nx.line_graph(G)
+    >>> H.add_nodes_from((node, G.edges[node]) for node in H)
+    >>> H.nodes(data=True)
+    NodeDataView({(0, 1): {'tot': 1}, (2, 3): {'tot': 5}, (1, 2): {'tot': 3}})
+
+    Notes
+    -----
+    Graph, node, and edge data are not propagated to the new graph. For
+    undirected graphs, the nodes in G must be sortable, otherwise the
+    constructed line graph may not be correct.
+
+    *Self-loops in undirected graphs*
+
+    For an undirected graph `G` without multiple edges, each edge can be
+    written as a set `\{u, v\}`.  Its line graph `L` has the edges of `G` as
+    its nodes. If `x` and `y` are two nodes in `L`, then `\{x, y\}` is an edge
+    in `L` if and only if the intersection of `x` and `y` is nonempty. Thus,
+    the set of all edges is determined by the set of all pairwise intersections
+    of edges in `G`.
+
+    Trivially, every edge in G would have a nonzero intersection with itself,
+    and so every node in `L` should have a self-loop. This is not so
+    interesting, and the original context of line graphs was with simple
+    graphs, which had no self-loops or multiple edges. The line graph was also
+    meant to be a simple graph and thus, self-loops in `L` are not part of the
+    standard definition of a line graph. In a pairwise intersection matrix,
+    this is analogous to excluding the diagonal entries from the line graph
+    definition.
+
+    Self-loops and multiple edges in `G` add nodes to `L` in a natural way, and
+    do not require any fundamental changes to the definition. It might be
+    argued that the self-loops we excluded before should now be included.
+    However, the self-loops are still "trivial" in some sense and thus, are
+    usually excluded.
+
+    *Self-loops in directed graphs*
+
+    For a directed graph `G` without multiple edges, each edge can be written
+    as a tuple `(u, v)`. Its line graph `L` has the edges of `G` as its
+    nodes. If `x` and `y` are two nodes in `L`, then `(x, y)` is an edge in `L`
+    if and only if the tail of `x` matches the head of `y`, for example, if `x
+    = (a, b)` and `y = (b, c)` for some vertices `a`, `b`, and `c` in `G`.
+
+    Due to the directed nature of the edges, it is no longer the case that
+    every edge in `G` should have a self-loop in `L`. Now, the only time
+    self-loops arise is if a node in `G` itself has a self-loop.  So such
+    self-loops are no longer "trivial" but instead, represent essential
+    features of the topology of `G`. For this reason, the historical
+    development of line digraphs is such that self-loops are included. When the
+    graph `G` has multiple edges, once again only superficial changes are
+    required to the definition.
+
+    References
+    ----------
+    * Harary, Frank, and Norman, Robert Z., "Some properties of line digraphs",
+      Rend. Circ. Mat. Palermo, II. Ser. 9 (1960), 161--168.
+    * Hemminger, R. L.; Beineke, L. W. (1978), "Line graphs and line digraphs",
+      in Beineke, L. W.; Wilson, R. J., Selected Topics in Graph Theory,
+      Academic Press Inc., pp. 271--305.
+
+    """
+    if G.is_directed():
+        L = _lg_directed(G, create_using=create_using)
+    else:
+        L = _lg_undirected(G, selfloops=False, create_using=create_using)
+    return L
+
+
+def _lg_directed(G, create_using=None):
+    """Returns the line graph L of the (multi)digraph G.
+
+    Edges in G appear as nodes in L, represented as tuples of the form (u,v)
+    or (u,v,key) if G is a multidigraph. A node in L corresponding to the edge
+    (u,v) is connected to every node corresponding to an edge (v,w).
+
+    Parameters
+    ----------
+    G : digraph
+        A directed graph or directed multigraph.
+    create_using : NetworkX graph constructor, optional
+       Graph type to create. If graph instance, then cleared before populated.
+       Default is to use the same graph class as `G`.
+
+    """
+    L = nx.empty_graph(0, create_using, default=G.__class__)
+
+    # Create a graph specific edge function.
+    get_edges = partial(G.edges, keys=True) if G.is_multigraph() else G.edges
+
+    for from_node in get_edges():
+        # from_node is: (u,v) or (u,v,key)
+        L.add_node(from_node)
+        for to_node in get_edges(from_node[1]):
+            L.add_edge(from_node, to_node)
+
+    return L
+
+
+def _lg_undirected(G, selfloops=False, create_using=None):
+    """Returns the line graph L of the (multi)graph G.
+
+    Edges in G appear as nodes in L, represented as sorted tuples of the form
+    (u,v), or (u,v,key) if G is a multigraph. A node in L corresponding to
+    the edge {u,v} is connected to every node corresponding to an edge that
+    involves u or v.
+
+    Parameters
+    ----------
+    G : graph
+        An undirected graph or multigraph.
+    selfloops : bool
+        If `True`, then self-loops are included in the line graph. If `False`,
+        they are excluded.
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+       Graph type to create. If graph instance, then cleared before populated.
+
+    Notes
+    -----
+    The standard algorithm for line graphs of undirected graphs does not
+    produce self-loops.
+
+    """
+    L = nx.empty_graph(0, create_using, default=G.__class__)
+
+    # Graph specific functions for edges.
+    get_edges = partial(G.edges, keys=True) if G.is_multigraph() else G.edges
+
+    # Determine if we include self-loops or not.
+    shift = 0 if selfloops else 1
+
+    # Introduce numbering of nodes
+    node_index = {n: i for i, n in enumerate(G)}
+
+    # Lift canonical representation of nodes to edges in line graph
+    edge_key_function = lambda edge: (node_index[edge[0]], node_index[edge[1]])
+
+    edges = set()
+    for u in G:
+        # Label nodes as a sorted tuple of nodes in original graph.
+        # Decide on representation of {u, v} as (u, v) or (v, u) depending on node_index.
+        # -> This ensures a canonical representation and avoids comparing values of different types.
+        nodes = [tuple(sorted(x[:2], key=node_index.get)) + x[2:] for x in get_edges(u)]
+
+        if len(nodes) == 1:
+            # Then the edge will be an isolated node in L.
+            L.add_node(nodes[0])
+
+        # Add a clique of `nodes` to graph. To prevent double adding edges,
+        # especially important for multigraphs, we store the edges in
+        # canonical form in a set.
+        for i, a in enumerate(nodes):
+            edges.update(
+                [
+                    tuple(sorted((a, b), key=edge_key_function))
+                    for b in nodes[i + shift :]
+                ]
+            )
+
+    L.add_edges_from(edges)
+    return L
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatchable(returns_graph=True)
+def inverse_line_graph(G):
+    """Returns the inverse line graph of graph G.
+
+    If H is a graph, and G is the line graph of H, such that G = L(H).
+    Then H is the inverse line graph of G.
+
+    Not all graphs are line graphs and these do not have an inverse line graph.
+    In these cases this function raises a NetworkXError.
+
+    Parameters
+    ----------
+    G : graph
+        A NetworkX Graph
+
+    Returns
+    -------
+    H : graph
+        The inverse line graph of G.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is directed or a multigraph
+
+    NetworkXError
+        If G is not a line graph
+
+    Notes
+    -----
+    This is an implementation of the Roussopoulos algorithm[1]_.
+
+    If G consists of multiple components, then the algorithm doesn't work.
+    You should invert every component separately:
+
+    >>> K5 = nx.complete_graph(5)
+    >>> P4 = nx.Graph([("a", "b"), ("b", "c"), ("c", "d")])
+    >>> G = nx.union(K5, P4)
+    >>> root_graphs = []
+    >>> for comp in nx.connected_components(G):
+    ...     root_graphs.append(nx.inverse_line_graph(G.subgraph(comp)))
+    >>> len(root_graphs)
+    2
+
+    References
+    ----------
+    .. [1] Roussopoulos, N.D. , "A max {m, n} algorithm for determining the graph H from
+       its line graph G", Information Processing Letters 2, (1973), 108--112, ISSN 0020-0190,
+       `DOI link <https://doi.org/10.1016/0020-0190(73)90029-X>`_
+
+    """
+    if G.number_of_nodes() == 0:
+        return nx.empty_graph(1)
+    elif G.number_of_nodes() == 1:
+        v = arbitrary_element(G)
+        a = (v, 0)
+        b = (v, 1)
+        H = nx.Graph([(a, b)])
+        return H
+    elif G.number_of_nodes() > 1 and G.number_of_edges() == 0:
+        msg = (
+            "inverse_line_graph() doesn't work on an edgeless graph. "
+            "Please use this function on each component separately."
+        )
+        raise nx.NetworkXError(msg)
+
+    if nx.number_of_selfloops(G) != 0:
+        msg = (
+            "A line graph as generated by NetworkX has no selfloops, so G has no "
+            "inverse line graph. Please remove the selfloops from G and try again."
+        )
+        raise nx.NetworkXError(msg)
+
+    starting_cell = _select_starting_cell(G)
+    P = _find_partition(G, starting_cell)
+    # count how many times each vertex appears in the partition set
+    P_count = {u: 0 for u in G.nodes}
+    for p in P:
+        for u in p:
+            P_count[u] += 1
+
+    if max(P_count.values()) > 2:
+        msg = "G is not a line graph (vertex found in more than two partition cells)"
+        raise nx.NetworkXError(msg)
+    W = tuple((u,) for u in P_count if P_count[u] == 1)
+    H = nx.Graph()
+    H.add_nodes_from(P)
+    H.add_nodes_from(W)
+    for a, b in combinations(H.nodes, 2):
+        if any(a_bit in b for a_bit in a):
+            H.add_edge(a, b)
+    return H
+
+
+def _triangles(G, e):
+    """Return list of all triangles containing edge e"""
+    u, v = e
+    if u not in G:
+        raise nx.NetworkXError(f"Vertex {u} not in graph")
+    if v not in G[u]:
+        raise nx.NetworkXError(f"Edge ({u}, {v}) not in graph")
+    triangle_list = []
+    for x in G[u]:
+        if x in G[v]:
+            triangle_list.append((u, v, x))
+    return triangle_list
+
+
+def _odd_triangle(G, T):
+    """Test whether T is an odd triangle in G
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+    T : 3-tuple of vertices forming triangle in G
+
+    Returns
+    -------
+    True is T is an odd triangle
+    False otherwise
+
+    Raises
+    ------
+    NetworkXError
+        T is not a triangle in G
+
+    Notes
+    -----
+    An odd triangle is one in which there exists another vertex in G which is
+    adjacent to either exactly one or exactly all three of the vertices in the
+    triangle.
+
+    """
+    for u in T:
+        if u not in G.nodes():
+            raise nx.NetworkXError(f"Vertex {u} not in graph")
+    for e in list(combinations(T, 2)):
+        if e[0] not in G[e[1]]:
+            raise nx.NetworkXError(f"Edge ({e[0]}, {e[1]}) not in graph")
+
+    T_nbrs = defaultdict(int)
+    for t in T:
+        for v in G[t]:
+            if v not in T:
+                T_nbrs[v] += 1
+    return any(T_nbrs[v] in [1, 3] for v in T_nbrs)
+
+
+def _find_partition(G, starting_cell):
+    """Find a partition of the vertices of G into cells of complete graphs
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+    starting_cell : tuple of vertices in G which form a cell
+
+    Returns
+    -------
+    List of tuples of vertices of G
+
+    Raises
+    ------
+    NetworkXError
+        If a cell is not a complete subgraph then G is not a line graph
+    """
+    G_partition = G.copy()
+    P = [starting_cell]  # partition set
+    G_partition.remove_edges_from(list(combinations(starting_cell, 2)))
+    # keep list of partitioned nodes which might have an edge in G_partition
+    partitioned_vertices = list(starting_cell)
+    while G_partition.number_of_edges() > 0:
+        # there are still edges left and so more cells to be made
+        u = partitioned_vertices.pop()
+        deg_u = len(G_partition[u])
+        if deg_u != 0:
+            # if u still has edges then we need to find its other cell
+            # this other cell must be a complete subgraph or else G is
+            # not a line graph
+            new_cell = [u] + list(G_partition[u])
+            for u in new_cell:
+                for v in new_cell:
+                    if (u != v) and (v not in G_partition[u]):
+                        msg = (
+                            "G is not a line graph "
+                            "(partition cell not a complete subgraph)"
+                        )
+                        raise nx.NetworkXError(msg)
+            P.append(tuple(new_cell))
+            G_partition.remove_edges_from(list(combinations(new_cell, 2)))
+            partitioned_vertices += new_cell
+    return P
+
+
+def _select_starting_cell(G, starting_edge=None):
+    """Select a cell to initiate _find_partition
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+    starting_edge: an edge to build the starting cell from
+
+    Returns
+    -------
+    Tuple of vertices in G
+
+    Raises
+    ------
+    NetworkXError
+        If it is determined that G is not a line graph
+
+    Notes
+    -----
+    If starting edge not specified then pick an arbitrary edge - doesn't
+    matter which. However, this function may call itself requiring a
+    specific starting edge. Note that the r, s notation for counting
+    triangles is the same as in the Roussopoulos paper cited above.
+    """
+    if starting_edge is None:
+        e = arbitrary_element(G.edges())
+    else:
+        e = starting_edge
+        if e[0] not in G.nodes():
+            raise nx.NetworkXError(f"Vertex {e[0]} not in graph")
+        if e[1] not in G[e[0]]:
+            msg = f"starting_edge ({e[0]}, {e[1]}) is not in the Graph"
+            raise nx.NetworkXError(msg)
+    e_triangles = _triangles(G, e)
+    r = len(e_triangles)
+    if r == 0:
+        # there are no triangles containing e, so the starting cell is just e
+        starting_cell = e
+    elif r == 1:
+        # there is exactly one triangle, T, containing e. If other 2 edges
+        # of T belong only to this triangle then T is starting cell
+        T = e_triangles[0]
+        a, b, c = T
+        # ab was original edge so check the other 2 edges
+        ac_edges = len(_triangles(G, (a, c)))
+        bc_edges = len(_triangles(G, (b, c)))
+        if ac_edges == 1:
+            if bc_edges == 1:
+                starting_cell = T
+            else:
+                return _select_starting_cell(G, starting_edge=(b, c))
+        else:
+            return _select_starting_cell(G, starting_edge=(a, c))
+    else:
+        # r >= 2 so we need to count the number of odd triangles, s
+        s = 0
+        odd_triangles = []
+        for T in e_triangles:
+            if _odd_triangle(G, T):
+                s += 1
+                odd_triangles.append(T)
+        if r == 2 and s == 0:
+            # in this case either triangle works, so just use T
+            starting_cell = T
+        elif r - 1 <= s <= r:
+            # check if odd triangles containing e form complete subgraph
+            triangle_nodes = set()
+            for T in odd_triangles:
+                for x in T:
+                    triangle_nodes.add(x)
+
+            for u in triangle_nodes:
+                for v in triangle_nodes:
+                    if u != v and (v not in G[u]):
+                        msg = (
+                            "G is not a line graph (odd triangles "
+                            "do not form complete subgraph)"
+                        )
+                        raise nx.NetworkXError(msg)
+            # otherwise then we can use this as the starting cell
+            starting_cell = tuple(triangle_nodes)
+
+        else:
+            msg = (
+                "G is not a line graph (incorrect number of "
+                "odd triangles around starting edge)"
+            )
+            raise nx.NetworkXError(msg)
+    return starting_cell