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diff --git a/.venv/lib/python3.12/site-packages/networkx/classes/function.py b/.venv/lib/python3.12/site-packages/networkx/classes/function.py
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+"""Functional interface to graph methods and assorted utilities."""
+
+from collections import Counter
+from itertools import chain
+
+import networkx as nx
+from networkx.utils import not_implemented_for, pairwise
+
+__all__ = [
+    "nodes",
+    "edges",
+    "degree",
+    "degree_histogram",
+    "neighbors",
+    "number_of_nodes",
+    "number_of_edges",
+    "density",
+    "is_directed",
+    "freeze",
+    "is_frozen",
+    "subgraph",
+    "induced_subgraph",
+    "edge_subgraph",
+    "restricted_view",
+    "to_directed",
+    "to_undirected",
+    "add_star",
+    "add_path",
+    "add_cycle",
+    "create_empty_copy",
+    "set_node_attributes",
+    "get_node_attributes",
+    "remove_node_attributes",
+    "set_edge_attributes",
+    "get_edge_attributes",
+    "remove_edge_attributes",
+    "all_neighbors",
+    "non_neighbors",
+    "non_edges",
+    "common_neighbors",
+    "is_weighted",
+    "is_negatively_weighted",
+    "is_empty",
+    "selfloop_edges",
+    "nodes_with_selfloops",
+    "number_of_selfloops",
+    "path_weight",
+    "is_path",
+]
+
+
+def nodes(G):
+    """Returns a NodeView over the graph nodes.
+
+    This function wraps the :func:`G.nodes <networkx.Graph.nodes>` property.
+    """
+    return G.nodes()
+
+
+def edges(G, nbunch=None):
+    """Returns an edge view of edges incident to nodes in nbunch.
+
+    Return all edges if nbunch is unspecified or nbunch=None.
+
+    For digraphs, edges=out_edges
+
+    This function wraps the :func:`G.edges <networkx.Graph.edges>` property.
+    """
+    return G.edges(nbunch)
+
+
+def degree(G, nbunch=None, weight=None):
+    """Returns a degree view of single node or of nbunch of nodes.
+    If nbunch is omitted, then return degrees of *all* nodes.
+
+    This function wraps the :func:`G.degree <networkx.Graph.degree>` property.
+    """
+    return G.degree(nbunch, weight)
+
+
+def neighbors(G, n):
+    """Returns an iterator over all neighbors of node n.
+
+    This function wraps the :func:`G.neighbors <networkx.Graph.neighbors>` function.
+    """
+    return G.neighbors(n)
+
+
+def number_of_nodes(G):
+    """Returns the number of nodes in the graph.
+
+    This function wraps the :func:`G.number_of_nodes <networkx.Graph.number_of_nodes>` function.
+    """
+    return G.number_of_nodes()
+
+
+def number_of_edges(G):
+    """Returns the number of edges in the graph.
+
+    This function wraps the :func:`G.number_of_edges <networkx.Graph.number_of_edges>` function.
+    """
+    return G.number_of_edges()
+
+
+def density(G):
+    r"""Returns the density of a graph.
+
+    The density for undirected graphs is
+
+    .. math::
+
+       d = \frac{2m}{n(n-1)},
+
+    and for directed graphs is
+
+    .. math::
+
+       d = \frac{m}{n(n-1)},
+
+    where `n` is the number of nodes and `m`  is the number of edges in `G`.
+
+    Notes
+    -----
+    The density is 0 for a graph without edges and 1 for a complete graph.
+    The density of multigraphs can be higher than 1.
+
+    Self loops are counted in the total number of edges so graphs with self
+    loops can have density higher than 1.
+    """
+    n = number_of_nodes(G)
+    m = number_of_edges(G)
+    if m == 0 or n <= 1:
+        return 0
+    d = m / (n * (n - 1))
+    if not G.is_directed():
+        d *= 2
+    return d
+
+
+def degree_histogram(G):
+    """Returns a list of the frequency of each degree value.
+
+    Parameters
+    ----------
+    G : Networkx graph
+       A graph
+
+    Returns
+    -------
+    hist : list
+       A list of frequencies of degrees.
+       The degree values are the index in the list.
+
+    Notes
+    -----
+    Note: the bins are width one, hence len(list) can be large
+    (Order(number_of_edges))
+    """
+    counts = Counter(d for n, d in G.degree())
+    return [counts.get(i, 0) for i in range(max(counts) + 1 if counts else 0)]
+
+
+def is_directed(G):
+    """Return True if graph is directed."""
+    return G.is_directed()
+
+
+def frozen(*args, **kwargs):
+    """Dummy method for raising errors when trying to modify frozen graphs"""
+    raise nx.NetworkXError("Frozen graph can't be modified")
+
+
+def freeze(G):
+    """Modify graph to prevent further change by adding or removing
+    nodes or edges.
+
+    Node and edge data can still be modified.
+
+    Parameters
+    ----------
+    G : graph
+      A NetworkX graph
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4)
+    >>> G = nx.freeze(G)
+    >>> try:
+    ...     G.add_edge(4, 5)
+    ... except nx.NetworkXError as err:
+    ...     print(str(err))
+    Frozen graph can't be modified
+
+    Notes
+    -----
+    To "unfreeze" a graph you must make a copy by creating a new graph object:
+
+    >>> graph = nx.path_graph(4)
+    >>> frozen_graph = nx.freeze(graph)
+    >>> unfrozen_graph = nx.Graph(frozen_graph)
+    >>> nx.is_frozen(unfrozen_graph)
+    False
+
+    See Also
+    --------
+    is_frozen
+    """
+    G.add_node = frozen
+    G.add_nodes_from = frozen
+    G.remove_node = frozen
+    G.remove_nodes_from = frozen
+    G.add_edge = frozen
+    G.add_edges_from = frozen
+    G.add_weighted_edges_from = frozen
+    G.remove_edge = frozen
+    G.remove_edges_from = frozen
+    G.clear = frozen
+    G.clear_edges = frozen
+    G.frozen = True
+    return G
+
+
+def is_frozen(G):
+    """Returns True if graph is frozen.
+
+    Parameters
+    ----------
+    G : graph
+      A NetworkX graph
+
+    See Also
+    --------
+    freeze
+    """
+    try:
+        return G.frozen
+    except AttributeError:
+        return False
+
+
+def add_star(G_to_add_to, nodes_for_star, **attr):
+    """Add a star to Graph G_to_add_to.
+
+    The first node in `nodes_for_star` is the middle of the star.
+    It is connected to all other nodes.
+
+    Parameters
+    ----------
+    G_to_add_to : graph
+        A NetworkX graph
+    nodes_for_star : iterable container
+        A container of nodes.
+    attr : keyword arguments, optional (default= no attributes)
+        Attributes to add to every edge in star.
+
+    See Also
+    --------
+    add_path, add_cycle
+
+    Examples
+    --------
+    >>> G = nx.Graph()
+    >>> nx.add_star(G, [0, 1, 2, 3])
+    >>> nx.add_star(G, [10, 11, 12], weight=2)
+    """
+    nlist = iter(nodes_for_star)
+    try:
+        v = next(nlist)
+    except StopIteration:
+        return
+    G_to_add_to.add_node(v)
+    edges = ((v, n) for n in nlist)
+    G_to_add_to.add_edges_from(edges, **attr)
+
+
+def add_path(G_to_add_to, nodes_for_path, **attr):
+    """Add a path to the Graph G_to_add_to.
+
+    Parameters
+    ----------
+    G_to_add_to : graph
+        A NetworkX graph
+    nodes_for_path : iterable container
+        A container of nodes.  A path will be constructed from
+        the nodes (in order) and added to the graph.
+    attr : keyword arguments, optional (default= no attributes)
+        Attributes to add to every edge in path.
+
+    See Also
+    --------
+    add_star, add_cycle
+
+    Examples
+    --------
+    >>> G = nx.Graph()
+    >>> nx.add_path(G, [0, 1, 2, 3])
+    >>> nx.add_path(G, [10, 11, 12], weight=7)
+    """
+    nlist = iter(nodes_for_path)
+    try:
+        first_node = next(nlist)
+    except StopIteration:
+        return
+    G_to_add_to.add_node(first_node)
+    G_to_add_to.add_edges_from(pairwise(chain((first_node,), nlist)), **attr)
+
+
+def add_cycle(G_to_add_to, nodes_for_cycle, **attr):
+    """Add a cycle to the Graph G_to_add_to.
+
+    Parameters
+    ----------
+    G_to_add_to : graph
+        A NetworkX graph
+    nodes_for_cycle: iterable container
+        A container of nodes.  A cycle will be constructed from
+        the nodes (in order) and added to the graph.
+    attr : keyword arguments, optional (default= no attributes)
+        Attributes to add to every edge in cycle.
+
+    See Also
+    --------
+    add_path, add_star
+
+    Examples
+    --------
+    >>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
+    >>> nx.add_cycle(G, [0, 1, 2, 3])
+    >>> nx.add_cycle(G, [10, 11, 12], weight=7)
+    """
+    nlist = iter(nodes_for_cycle)
+    try:
+        first_node = next(nlist)
+    except StopIteration:
+        return
+    G_to_add_to.add_node(first_node)
+    G_to_add_to.add_edges_from(
+        pairwise(chain((first_node,), nlist), cyclic=True), **attr
+    )
+
+
+def subgraph(G, nbunch):
+    """Returns the subgraph induced on nodes in nbunch.
+
+    Parameters
+    ----------
+    G : graph
+       A NetworkX graph
+
+    nbunch : list, iterable
+       A container of nodes that will be iterated through once (thus
+       it should be an iterator or be iterable).  Each element of the
+       container should be a valid node type: any hashable type except
+       None.  If nbunch is None, return all edges data in the graph.
+       Nodes in nbunch that are not in the graph will be (quietly)
+       ignored.
+
+    Notes
+    -----
+    subgraph(G) calls G.subgraph()
+    """
+    return G.subgraph(nbunch)
+
+
+def induced_subgraph(G, nbunch):
+    """Returns a SubGraph view of `G` showing only nodes in nbunch.
+
+    The induced subgraph of a graph on a set of nodes N is the
+    graph with nodes N and edges from G which have both ends in N.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+    nbunch : node, container of nodes or None (for all nodes)
+
+    Returns
+    -------
+    subgraph : SubGraph View
+        A read-only view of the subgraph in `G` induced by the nodes.
+        Changes to the graph `G` will be reflected in the view.
+
+    Notes
+    -----
+    To create a mutable subgraph with its own copies of nodes
+    edges and attributes use `subgraph.copy()` or `Graph(subgraph)`
+
+    For an inplace reduction of a graph to a subgraph you can remove nodes:
+    `G.remove_nodes_from(n in G if n not in set(nbunch))`
+
+    If you are going to compute subgraphs of your subgraphs you could
+    end up with a chain of views that can be very slow once the chain
+    has about 15 views in it. If they are all induced subgraphs, you
+    can short-cut the chain by making them all subgraphs of the original
+    graph. The graph class method `G.subgraph` does this when `G` is
+    a subgraph. In contrast, this function allows you to choose to build
+    chains or not, as you wish. The returned subgraph is a view on `G`.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
+    >>> H = nx.induced_subgraph(G, [0, 1, 3])
+    >>> list(H.edges)
+    [(0, 1)]
+    >>> list(H.nodes)
+    [0, 1, 3]
+    """
+    induced_nodes = nx.filters.show_nodes(G.nbunch_iter(nbunch))
+    return nx.subgraph_view(G, filter_node=induced_nodes)
+
+
+def edge_subgraph(G, edges):
+    """Returns a view of the subgraph induced by the specified edges.
+
+    The induced subgraph contains each edge in `edges` and each
+    node incident to any of those edges.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+    edges : iterable
+        An iterable of edges. Edges not present in `G` are ignored.
+
+    Returns
+    -------
+    subgraph : SubGraph View
+        A read-only edge-induced subgraph of `G`.
+        Changes to `G` are reflected in the view.
+
+    Notes
+    -----
+    To create a mutable subgraph with its own copies of nodes
+    edges and attributes use `subgraph.copy()` or `Graph(subgraph)`
+
+    If you create a subgraph of a subgraph recursively you can end up
+    with a chain of subgraphs that becomes very slow with about 15
+    nested subgraph views. Luckily the edge_subgraph filter nests
+    nicely so you can use the original graph as G in this function
+    to avoid chains. We do not rule out chains programmatically so
+    that odd cases like an `edge_subgraph` of a `restricted_view`
+    can be created.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(5)
+    >>> H = G.edge_subgraph([(0, 1), (3, 4)])
+    >>> list(H.nodes)
+    [0, 1, 3, 4]
+    >>> list(H.edges)
+    [(0, 1), (3, 4)]
+    """
+    nxf = nx.filters
+    edges = set(edges)
+    nodes = set()
+    for e in edges:
+        nodes.update(e[:2])
+    induced_nodes = nxf.show_nodes(nodes)
+    if G.is_multigraph():
+        if G.is_directed():
+            induced_edges = nxf.show_multidiedges(edges)
+        else:
+            induced_edges = nxf.show_multiedges(edges)
+    else:
+        if G.is_directed():
+            induced_edges = nxf.show_diedges(edges)
+        else:
+            induced_edges = nxf.show_edges(edges)
+    return nx.subgraph_view(G, filter_node=induced_nodes, filter_edge=induced_edges)
+
+
+def restricted_view(G, nodes, edges):
+    """Returns a view of `G` with hidden nodes and edges.
+
+    The resulting subgraph filters out node `nodes` and edges `edges`.
+    Filtered out nodes also filter out any of their edges.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+    nodes : iterable
+        An iterable of nodes. Nodes not present in `G` are ignored.
+    edges : iterable
+        An iterable of edges. Edges not present in `G` are ignored.
+
+    Returns
+    -------
+    subgraph : SubGraph View
+        A read-only restricted view of `G` filtering out nodes and edges.
+        Changes to `G` are reflected in the view.
+
+    Notes
+    -----
+    To create a mutable subgraph with its own copies of nodes
+    edges and attributes use `subgraph.copy()` or `Graph(subgraph)`
+
+    If you create a subgraph of a subgraph recursively you may end up
+    with a chain of subgraph views. Such chains can get quite slow
+    for lengths near 15. To avoid long chains, try to make your subgraph
+    based on the original graph.  We do not rule out chains programmatically
+    so that odd cases like an `edge_subgraph` of a `restricted_view`
+    can be created.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(5)
+    >>> H = nx.restricted_view(G, [0], [(1, 2), (3, 4)])
+    >>> list(H.nodes)
+    [1, 2, 3, 4]
+    >>> list(H.edges)
+    [(2, 3)]
+    """
+    nxf = nx.filters
+    hide_nodes = nxf.hide_nodes(nodes)
+    if G.is_multigraph():
+        if G.is_directed():
+            hide_edges = nxf.hide_multidiedges(edges)
+        else:
+            hide_edges = nxf.hide_multiedges(edges)
+    else:
+        if G.is_directed():
+            hide_edges = nxf.hide_diedges(edges)
+        else:
+            hide_edges = nxf.hide_edges(edges)
+    return nx.subgraph_view(G, filter_node=hide_nodes, filter_edge=hide_edges)
+
+
+def to_directed(graph):
+    """Returns a directed view of the graph `graph`.
+
+    Identical to graph.to_directed(as_view=True)
+    Note that graph.to_directed defaults to `as_view=False`
+    while this function always provides a view.
+    """
+    return graph.to_directed(as_view=True)
+
+
+def to_undirected(graph):
+    """Returns an undirected view of the graph `graph`.
+
+    Identical to graph.to_undirected(as_view=True)
+    Note that graph.to_undirected defaults to `as_view=False`
+    while this function always provides a view.
+    """
+    return graph.to_undirected(as_view=True)
+
+
+def create_empty_copy(G, with_data=True):
+    """Returns a copy of the graph G with all of the edges removed.
+
+    Parameters
+    ----------
+    G : graph
+       A NetworkX graph
+
+    with_data :  bool (default=True)
+       Propagate Graph and Nodes data to the new graph.
+
+    See Also
+    --------
+    empty_graph
+
+    """
+    H = G.__class__()
+    H.add_nodes_from(G.nodes(data=with_data))
+    if with_data:
+        H.graph.update(G.graph)
+    return H
+
+
+def set_node_attributes(G, values, name=None):
+    """Sets node attributes from a given value or dictionary of values.
+
+    .. Warning:: The call order of arguments `values` and `name`
+        switched between v1.x & v2.x.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+
+    values : scalar value, dict-like
+        What the node attribute should be set to.  If `values` is
+        not a dictionary, then it is treated as a single attribute value
+        that is then applied to every node in `G`.  This means that if
+        you provide a mutable object, like a list, updates to that object
+        will be reflected in the node attribute for every node.
+        The attribute name will be `name`.
+
+        If `values` is a dict or a dict of dict, it should be keyed
+        by node to either an attribute value or a dict of attribute key/value
+        pairs used to update the node's attributes.
+
+    name : string (optional, default=None)
+        Name of the node attribute to set if values is a scalar.
+
+    Examples
+    --------
+    After computing some property of the nodes of a graph, you may want
+    to assign a node attribute to store the value of that property for
+    each node::
+
+        >>> G = nx.path_graph(3)
+        >>> bb = nx.betweenness_centrality(G)
+        >>> isinstance(bb, dict)
+        True
+        >>> nx.set_node_attributes(G, bb, "betweenness")
+        >>> G.nodes[1]["betweenness"]
+        1.0
+
+    If you provide a list as the second argument, updates to the list
+    will be reflected in the node attribute for each node::
+
+        >>> G = nx.path_graph(3)
+        >>> labels = []
+        >>> nx.set_node_attributes(G, labels, "labels")
+        >>> labels.append("foo")
+        >>> G.nodes[0]["labels"]
+        ['foo']
+        >>> G.nodes[1]["labels"]
+        ['foo']
+        >>> G.nodes[2]["labels"]
+        ['foo']
+
+    If you provide a dictionary of dictionaries as the second argument,
+    the outer dictionary is assumed to be keyed by node to an inner
+    dictionary of node attributes for that node::
+
+        >>> G = nx.path_graph(3)
+        >>> attrs = {0: {"attr1": 20, "attr2": "nothing"}, 1: {"attr2": 3}}
+        >>> nx.set_node_attributes(G, attrs)
+        >>> G.nodes[0]["attr1"]
+        20
+        >>> G.nodes[0]["attr2"]
+        'nothing'
+        >>> G.nodes[1]["attr2"]
+        3
+        >>> G.nodes[2]
+        {}
+
+    Note that if the dictionary contains nodes that are not in `G`, the
+    values are silently ignored::
+
+        >>> G = nx.Graph()
+        >>> G.add_node(0)
+        >>> nx.set_node_attributes(G, {0: "red", 1: "blue"}, name="color")
+        >>> G.nodes[0]["color"]
+        'red'
+        >>> 1 in G.nodes
+        False
+
+    """
+    # Set node attributes based on type of `values`
+    if name is not None:  # `values` must not be a dict of dict
+        try:  # `values` is a dict
+            for n, v in values.items():
+                try:
+                    G.nodes[n][name] = values[n]
+                except KeyError:
+                    pass
+        except AttributeError:  # `values` is a constant
+            for n in G:
+                G.nodes[n][name] = values
+    else:  # `values` must be dict of dict
+        for n, d in values.items():
+            try:
+                G.nodes[n].update(d)
+            except KeyError:
+                pass
+    nx._clear_cache(G)
+
+
+def get_node_attributes(G, name, default=None):
+    """Get node attributes from graph
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+
+    name : string
+       Attribute name
+
+    default: object (default=None)
+       Default value of the node attribute if there is no value set for that
+       node in graph. If `None` then nodes without this attribute are not
+       included in the returned dict.
+
+    Returns
+    -------
+    Dictionary of attributes keyed by node.
+
+    Examples
+    --------
+    >>> G = nx.Graph()
+    >>> G.add_nodes_from([1, 2, 3], color="red")
+    >>> color = nx.get_node_attributes(G, "color")
+    >>> color[1]
+    'red'
+    >>> G.add_node(4)
+    >>> color = nx.get_node_attributes(G, "color", default="yellow")
+    >>> color[4]
+    'yellow'
+    """
+    if default is not None:
+        return {n: d.get(name, default) for n, d in G.nodes.items()}
+    return {n: d[name] for n, d in G.nodes.items() if name in d}
+
+
+def remove_node_attributes(G, *attr_names, nbunch=None):
+    """Remove node attributes from all nodes in the graph.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+
+    *attr_names : List of Strings
+        The attribute names to remove from the graph.
+
+    nbunch : List of Nodes
+        Remove the node attributes only from the nodes in this list.
+
+    Examples
+    --------
+    >>> G = nx.Graph()
+    >>> G.add_nodes_from([1, 2, 3], color="blue")
+    >>> nx.get_node_attributes(G, "color")
+    {1: 'blue', 2: 'blue', 3: 'blue'}
+    >>> nx.remove_node_attributes(G, "color")
+    >>> nx.get_node_attributes(G, "color")
+    {}
+    """
+
+    if nbunch is None:
+        nbunch = G.nodes()
+
+    for attr in attr_names:
+        for n, d in G.nodes(data=True):
+            if n in nbunch:
+                try:
+                    del d[attr]
+                except KeyError:
+                    pass
+
+
+def set_edge_attributes(G, values, name=None):
+    """Sets edge attributes from a given value or dictionary of values.
+
+    .. Warning:: The call order of arguments `values` and `name`
+        switched between v1.x & v2.x.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+
+    values : scalar value, dict-like
+        What the edge attribute should be set to.  If `values` is
+        not a dictionary, then it is treated as a single attribute value
+        that is then applied to every edge in `G`.  This means that if
+        you provide a mutable object, like a list, updates to that object
+        will be reflected in the edge attribute for each edge.  The attribute
+        name will be `name`.
+
+        If `values` is a dict or a dict of dict, it should be keyed
+        by edge tuple to either an attribute value or a dict of attribute
+        key/value pairs used to update the edge's attributes.
+        For multigraphs, the edge tuples must be of the form ``(u, v, key)``,
+        where `u` and `v` are nodes and `key` is the edge key.
+        For non-multigraphs, the keys must be tuples of the form ``(u, v)``.
+
+    name : string (optional, default=None)
+        Name of the edge attribute to set if values is a scalar.
+
+    Examples
+    --------
+    After computing some property of the edges of a graph, you may want
+    to assign a edge attribute to store the value of that property for
+    each edge::
+
+        >>> G = nx.path_graph(3)
+        >>> bb = nx.edge_betweenness_centrality(G, normalized=False)
+        >>> nx.set_edge_attributes(G, bb, "betweenness")
+        >>> G.edges[1, 2]["betweenness"]
+        2.0
+
+    If you provide a list as the second argument, updates to the list
+    will be reflected in the edge attribute for each edge::
+
+        >>> labels = []
+        >>> nx.set_edge_attributes(G, labels, "labels")
+        >>> labels.append("foo")
+        >>> G.edges[0, 1]["labels"]
+        ['foo']
+        >>> G.edges[1, 2]["labels"]
+        ['foo']
+
+    If you provide a dictionary of dictionaries as the second argument,
+    the entire dictionary will be used to update edge attributes::
+
+        >>> G = nx.path_graph(3)
+        >>> attrs = {(0, 1): {"attr1": 20, "attr2": "nothing"}, (1, 2): {"attr2": 3}}
+        >>> nx.set_edge_attributes(G, attrs)
+        >>> G[0][1]["attr1"]
+        20
+        >>> G[0][1]["attr2"]
+        'nothing'
+        >>> G[1][2]["attr2"]
+        3
+
+    The attributes of one Graph can be used to set those of another.
+
+        >>> H = nx.path_graph(3)
+        >>> nx.set_edge_attributes(H, G.edges)
+
+    Note that if the dict contains edges that are not in `G`, they are
+    silently ignored::
+
+        >>> G = nx.Graph([(0, 1)])
+        >>> nx.set_edge_attributes(G, {(1, 2): {"weight": 2.0}})
+        >>> (1, 2) in G.edges()
+        False
+
+    For multigraphs, the `values` dict is expected to be keyed by 3-tuples
+    including the edge key::
+
+        >>> MG = nx.MultiGraph()
+        >>> edges = [(0, 1), (0, 1)]
+        >>> MG.add_edges_from(edges)  # Returns list of edge keys
+        [0, 1]
+        >>> attributes = {(0, 1, 0): {"cost": 21}, (0, 1, 1): {"cost": 7}}
+        >>> nx.set_edge_attributes(MG, attributes)
+        >>> MG[0][1][0]["cost"]
+        21
+        >>> MG[0][1][1]["cost"]
+        7
+
+    If MultiGraph attributes are desired for a Graph, you must convert the 3-tuple
+    multiedge to a 2-tuple edge and the last multiedge's attribute value will
+    overwrite the previous values. Continuing from the previous case we get::
+
+        >>> H = nx.path_graph([0, 1, 2])
+        >>> nx.set_edge_attributes(H, {(u, v): ed for u, v, ed in MG.edges.data()})
+        >>> nx.get_edge_attributes(H, "cost")
+        {(0, 1): 7}
+
+    """
+    if name is not None:
+        # `values` does not contain attribute names
+        try:
+            # if `values` is a dict using `.items()` => {edge: value}
+            if G.is_multigraph():
+                for (u, v, key), value in values.items():
+                    try:
+                        G._adj[u][v][key][name] = value
+                    except KeyError:
+                        pass
+            else:
+                for (u, v), value in values.items():
+                    try:
+                        G._adj[u][v][name] = value
+                    except KeyError:
+                        pass
+        except AttributeError:
+            # treat `values` as a constant
+            for u, v, data in G.edges(data=True):
+                data[name] = values
+    else:
+        # `values` consists of doct-of-dict {edge: {attr: value}} shape
+        if G.is_multigraph():
+            for (u, v, key), d in values.items():
+                try:
+                    G._adj[u][v][key].update(d)
+                except KeyError:
+                    pass
+        else:
+            for (u, v), d in values.items():
+                try:
+                    G._adj[u][v].update(d)
+                except KeyError:
+                    pass
+    nx._clear_cache(G)
+
+
+def get_edge_attributes(G, name, default=None):
+    """Get edge attributes from graph
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+
+    name : string
+       Attribute name
+
+    default: object (default=None)
+       Default value of the edge attribute if there is no value set for that
+       edge in graph. If `None` then edges without this attribute are not
+       included in the returned dict.
+
+    Returns
+    -------
+    Dictionary of attributes keyed by edge. For (di)graphs, the keys are
+    2-tuples of the form: (u, v). For multi(di)graphs, the keys are 3-tuples of
+    the form: (u, v, key).
+
+    Examples
+    --------
+    >>> G = nx.Graph()
+    >>> nx.add_path(G, [1, 2, 3], color="red")
+    >>> color = nx.get_edge_attributes(G, "color")
+    >>> color[(1, 2)]
+    'red'
+    >>> G.add_edge(3, 4)
+    >>> color = nx.get_edge_attributes(G, "color", default="yellow")
+    >>> color[(3, 4)]
+    'yellow'
+    """
+    if G.is_multigraph():
+        edges = G.edges(keys=True, data=True)
+    else:
+        edges = G.edges(data=True)
+    if default is not None:
+        return {x[:-1]: x[-1].get(name, default) for x in edges}
+    return {x[:-1]: x[-1][name] for x in edges if name in x[-1]}
+
+
+def remove_edge_attributes(G, *attr_names, ebunch=None):
+    """Remove edge attributes from all edges in the graph.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+
+    *attr_names : List of Strings
+        The attribute names to remove from the graph.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(3)
+    >>> nx.set_edge_attributes(G, {(u, v): u + v for u, v in G.edges()}, name="weight")
+    >>> nx.get_edge_attributes(G, "weight")
+    {(0, 1): 1, (1, 2): 3}
+    >>> remove_edge_attributes(G, "weight")
+    >>> nx.get_edge_attributes(G, "weight")
+    {}
+    """
+    if ebunch is None:
+        ebunch = G.edges(keys=True) if G.is_multigraph() else G.edges()
+
+    for attr in attr_names:
+        edges = (
+            G.edges(keys=True, data=True) if G.is_multigraph() else G.edges(data=True)
+        )
+        for *e, d in edges:
+            if tuple(e) in ebunch:
+                try:
+                    del d[attr]
+                except KeyError:
+                    pass
+
+
+def all_neighbors(graph, node):
+    """Returns all of the neighbors of a node in the graph.
+
+    If the graph is directed returns predecessors as well as successors.
+
+    Parameters
+    ----------
+    graph : NetworkX graph
+        Graph to find neighbors.
+
+    node : node
+        The node whose neighbors will be returned.
+
+    Returns
+    -------
+    neighbors : iterator
+        Iterator of neighbors
+    """
+    if graph.is_directed():
+        values = chain(graph.predecessors(node), graph.successors(node))
+    else:
+        values = graph.neighbors(node)
+    return values
+
+
+def non_neighbors(graph, node):
+    """Returns the non-neighbors of the node in the graph.
+
+    Parameters
+    ----------
+    graph : NetworkX graph
+        Graph to find neighbors.
+
+    node : node
+        The node whose neighbors will be returned.
+
+    Returns
+    -------
+    non_neighbors : set
+        Set of nodes in the graph that are not neighbors of the node.
+    """
+    return graph._adj.keys() - graph._adj[node].keys() - {node}
+
+
+def non_edges(graph):
+    """Returns the nonexistent edges in the graph.
+
+    Parameters
+    ----------
+    graph : NetworkX graph.
+        Graph to find nonexistent edges.
+
+    Returns
+    -------
+    non_edges : iterator
+        Iterator of edges that are not in the graph.
+    """
+    if graph.is_directed():
+        for u in graph:
+            for v in non_neighbors(graph, u):
+                yield (u, v)
+    else:
+        nodes = set(graph)
+        while nodes:
+            u = nodes.pop()
+            for v in nodes - set(graph[u]):
+                yield (u, v)
+
+
+@not_implemented_for("directed")
+def common_neighbors(G, u, v):
+    """Returns the common neighbors of two nodes in a graph.
+
+    Parameters
+    ----------
+    G : graph
+        A NetworkX undirected graph.
+
+    u, v : nodes
+        Nodes in the graph.
+
+    Returns
+    -------
+    cnbors : set
+        Set of common neighbors of u and v in the graph.
+
+    Raises
+    ------
+    NetworkXError
+        If u or v is not a node in the graph.
+
+    Examples
+    --------
+    >>> G = nx.complete_graph(5)
+    >>> sorted(nx.common_neighbors(G, 0, 1))
+    [2, 3, 4]
+    """
+    if u not in G:
+        raise nx.NetworkXError("u is not in the graph.")
+    if v not in G:
+        raise nx.NetworkXError("v is not in the graph.")
+
+    return G._adj[u].keys() & G._adj[v].keys() - {u, v}
+
+
+def is_weighted(G, edge=None, weight="weight"):
+    """Returns True if `G` has weighted edges.
+
+    Parameters
+    ----------
+    G : graph
+        A NetworkX graph.
+
+    edge : tuple, optional
+        A 2-tuple specifying the only edge in `G` that will be tested. If
+        None, then every edge in `G` is tested.
+
+    weight: string, optional
+        The attribute name used to query for edge weights.
+
+    Returns
+    -------
+    bool
+        A boolean signifying if `G`, or the specified edge, is weighted.
+
+    Raises
+    ------
+    NetworkXError
+        If the specified edge does not exist.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4)
+    >>> nx.is_weighted(G)
+    False
+    >>> nx.is_weighted(G, (2, 3))
+    False
+
+    >>> G = nx.DiGraph()
+    >>> G.add_edge(1, 2, weight=1)
+    >>> nx.is_weighted(G)
+    True
+
+    """
+    if edge is not None:
+        data = G.get_edge_data(*edge)
+        if data is None:
+            msg = f"Edge {edge!r} does not exist."
+            raise nx.NetworkXError(msg)
+        return weight in data
+
+    if is_empty(G):
+        # Special handling required since: all([]) == True
+        return False
+
+    return all(weight in data for u, v, data in G.edges(data=True))
+
+
+@nx._dispatchable(edge_attrs="weight")
+def is_negatively_weighted(G, edge=None, weight="weight"):
+    """Returns True if `G` has negatively weighted edges.
+
+    Parameters
+    ----------
+    G : graph
+        A NetworkX graph.
+
+    edge : tuple, optional
+        A 2-tuple specifying the only edge in `G` that will be tested. If
+        None, then every edge in `G` is tested.
+
+    weight: string, optional
+        The attribute name used to query for edge weights.
+
+    Returns
+    -------
+    bool
+        A boolean signifying if `G`, or the specified edge, is negatively
+        weighted.
+
+    Raises
+    ------
+    NetworkXError
+        If the specified edge does not exist.
+
+    Examples
+    --------
+    >>> G = nx.Graph()
+    >>> G.add_edges_from([(1, 3), (2, 4), (2, 6)])
+    >>> G.add_edge(1, 2, weight=4)
+    >>> nx.is_negatively_weighted(G, (1, 2))
+    False
+    >>> G[2][4]["weight"] = -2
+    >>> nx.is_negatively_weighted(G)
+    True
+    >>> G = nx.DiGraph()
+    >>> edges = [("0", "3", 3), ("0", "1", -5), ("1", "0", -2)]
+    >>> G.add_weighted_edges_from(edges)
+    >>> nx.is_negatively_weighted(G)
+    True
+
+    """
+    if edge is not None:
+        data = G.get_edge_data(*edge)
+        if data is None:
+            msg = f"Edge {edge!r} does not exist."
+            raise nx.NetworkXError(msg)
+        return weight in data and data[weight] < 0
+
+    return any(weight in data and data[weight] < 0 for u, v, data in G.edges(data=True))
+
+
+def is_empty(G):
+    """Returns True if `G` has no edges.
+
+    Parameters
+    ----------
+    G : graph
+        A NetworkX graph.
+
+    Returns
+    -------
+    bool
+        True if `G` has no edges, and False otherwise.
+
+    Notes
+    -----
+    An empty graph can have nodes but not edges. The empty graph with zero
+    nodes is known as the null graph. This is an $O(n)$ operation where n
+    is the number of nodes in the graph.
+
+    """
+    return not any(G._adj.values())
+
+
+def nodes_with_selfloops(G):
+    """Returns an iterator over nodes with self loops.
+
+    A node with a self loop has an edge with both ends adjacent
+    to that node.
+
+    Returns
+    -------
+    nodelist : iterator
+        A iterator over nodes with self loops.
+
+    See Also
+    --------
+    selfloop_edges, number_of_selfloops
+
+    Examples
+    --------
+    >>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
+    >>> G.add_edge(1, 1)
+    >>> G.add_edge(1, 2)
+    >>> list(nx.nodes_with_selfloops(G))
+    [1]
+
+    """
+    return (n for n, nbrs in G._adj.items() if n in nbrs)
+
+
+def selfloop_edges(G, data=False, keys=False, default=None):
+    """Returns an iterator over selfloop edges.
+
+    A selfloop edge has the same node at both ends.
+
+    Parameters
+    ----------
+    G : graph
+        A NetworkX graph.
+    data : string or bool, optional (default=False)
+        Return selfloop edges as two tuples (u, v) (data=False)
+        or three-tuples (u, v, datadict) (data=True)
+        or three-tuples (u, v, datavalue) (data='attrname')
+    keys : bool, optional (default=False)
+        If True, return edge keys with each edge.
+    default : value, optional (default=None)
+        Value used for edges that don't have the requested attribute.
+        Only relevant if data is not True or False.
+
+    Returns
+    -------
+    edgeiter : iterator over edge tuples
+        An iterator over all selfloop edges.
+
+    See Also
+    --------
+    nodes_with_selfloops, number_of_selfloops
+
+    Examples
+    --------
+    >>> G = nx.MultiGraph()  # or Graph, DiGraph, MultiDiGraph, etc
+    >>> ekey = G.add_edge(1, 1)
+    >>> ekey = G.add_edge(1, 2)
+    >>> list(nx.selfloop_edges(G))
+    [(1, 1)]
+    >>> list(nx.selfloop_edges(G, data=True))
+    [(1, 1, {})]
+    >>> list(nx.selfloop_edges(G, keys=True))
+    [(1, 1, 0)]
+    >>> list(nx.selfloop_edges(G, keys=True, data=True))
+    [(1, 1, 0, {})]
+    """
+    if data is True:
+        if G.is_multigraph():
+            if keys is True:
+                return (
+                    (n, n, k, d)
+                    for n, nbrs in G._adj.items()
+                    if n in nbrs
+                    for k, d in nbrs[n].items()
+                )
+            else:
+                return (
+                    (n, n, d)
+                    for n, nbrs in G._adj.items()
+                    if n in nbrs
+                    for d in nbrs[n].values()
+                )
+        else:
+            return ((n, n, nbrs[n]) for n, nbrs in G._adj.items() if n in nbrs)
+    elif data is not False:
+        if G.is_multigraph():
+            if keys is True:
+                return (
+                    (n, n, k, d.get(data, default))
+                    for n, nbrs in G._adj.items()
+                    if n in nbrs
+                    for k, d in nbrs[n].items()
+                )
+            else:
+                return (
+                    (n, n, d.get(data, default))
+                    for n, nbrs in G._adj.items()
+                    if n in nbrs
+                    for d in nbrs[n].values()
+                )
+        else:
+            return (
+                (n, n, nbrs[n].get(data, default))
+                for n, nbrs in G._adj.items()
+                if n in nbrs
+            )
+    else:
+        if G.is_multigraph():
+            if keys is True:
+                return (
+                    (n, n, k)
+                    for n, nbrs in G._adj.items()
+                    if n in nbrs
+                    for k in nbrs[n]
+                )
+            else:
+                return (
+                    (n, n)
+                    for n, nbrs in G._adj.items()
+                    if n in nbrs
+                    for i in range(len(nbrs[n]))  # for easy edge removal (#4068)
+                )
+        else:
+            return ((n, n) for n, nbrs in G._adj.items() if n in nbrs)
+
+
+def number_of_selfloops(G):
+    """Returns the number of selfloop edges.
+
+    A selfloop edge has the same node at both ends.
+
+    Returns
+    -------
+    nloops : int
+        The number of selfloops.
+
+    See Also
+    --------
+    nodes_with_selfloops, selfloop_edges
+
+    Examples
+    --------
+    >>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
+    >>> G.add_edge(1, 1)
+    >>> G.add_edge(1, 2)
+    >>> nx.number_of_selfloops(G)
+    1
+    """
+    return sum(1 for _ in nx.selfloop_edges(G))
+
+
+def is_path(G, path):
+    """Returns whether or not the specified path exists.
+
+    For it to return True, every node on the path must exist and
+    each consecutive pair must be connected via one or more edges.
+
+    Parameters
+    ----------
+    G : graph
+        A NetworkX graph.
+
+    path : list
+        A list of nodes which defines the path to traverse
+
+    Returns
+    -------
+    bool
+        True if `path` is a valid path in `G`
+
+    """
+    try:
+        return all(nbr in G._adj[node] for node, nbr in nx.utils.pairwise(path))
+    except (KeyError, TypeError):
+        return False
+
+
+def path_weight(G, path, weight):
+    """Returns total cost associated with specified path and weight
+
+    Parameters
+    ----------
+    G : graph
+        A NetworkX graph.
+
+    path: list
+        A list of node labels which defines the path to traverse
+
+    weight: string
+        A string indicating which edge attribute to use for path cost
+
+    Returns
+    -------
+    cost: int or float
+        An integer or a float representing the total cost with respect to the
+        specified weight of the specified path
+
+    Raises
+    ------
+    NetworkXNoPath
+        If the specified edge does not exist.
+    """
+    multigraph = G.is_multigraph()
+    cost = 0
+
+    if not nx.is_path(G, path):
+        raise nx.NetworkXNoPath("path does not exist")
+    for node, nbr in nx.utils.pairwise(path):
+        if multigraph:
+            cost += min(v[weight] for v in G._adj[node][nbr].values())
+        else:
+            cost += G._adj[node][nbr][weight]
+    return cost