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+"""Base class for MultiGraph."""
+
+from copy import deepcopy
+from functools import cached_property
+
+import networkx as nx
+from networkx import NetworkXError, convert
+from networkx.classes.coreviews import MultiAdjacencyView
+from networkx.classes.graph import Graph
+from networkx.classes.reportviews import MultiDegreeView, MultiEdgeView
+
+__all__ = ["MultiGraph"]
+
+
+class MultiGraph(Graph):
+    """
+    An undirected graph class that can store multiedges.
+
+    Multiedges are multiple edges between two nodes.  Each edge
+    can hold optional data or attributes.
+
+    A MultiGraph holds undirected edges.  Self loops are allowed.
+
+    Nodes can be arbitrary (hashable) Python objects with optional
+    key/value attributes. By convention `None` is not used as a node.
+
+    Edges are represented as links between nodes with optional
+    key/value attributes, in a MultiGraph each edge has a key to
+    distinguish between multiple edges that have the same source and
+    destination nodes.
+
+    Parameters
+    ----------
+    incoming_graph_data : input graph (optional, default: None)
+        Data to initialize graph. If None (default) an empty
+        graph is created.  The data can be any format that is supported
+        by the to_networkx_graph() function, currently including edge list,
+        dict of dicts, dict of lists, NetworkX graph, 2D NumPy array,
+        SciPy sparse array, or PyGraphviz graph.
+
+    multigraph_input : bool or None (default None)
+        Note: Only used when `incoming_graph_data` is a dict.
+        If True, `incoming_graph_data` is assumed to be a
+        dict-of-dict-of-dict-of-dict structure keyed by
+        node to neighbor to edge keys to edge data for multi-edges.
+        A NetworkXError is raised if this is not the case.
+        If False, :func:`to_networkx_graph` is used to try to determine
+        the dict's graph data structure as either a dict-of-dict-of-dict
+        keyed by node to neighbor to edge data, or a dict-of-iterable
+        keyed by node to neighbors.
+        If None, the treatment for True is tried, but if it fails,
+        the treatment for False is tried.
+
+    attr : keyword arguments, optional (default= no attributes)
+        Attributes to add to graph as key=value pairs.
+
+    See Also
+    --------
+    Graph
+    DiGraph
+    MultiDiGraph
+
+    Examples
+    --------
+    Create an empty graph structure (a "null graph") with no nodes and
+    no edges.
+
+    >>> G = nx.MultiGraph()
+
+    G can be grown in several ways.
+
+    **Nodes:**
+
+    Add one node at a time:
+
+    >>> G.add_node(1)
+
+    Add the nodes from any container (a list, dict, set or
+    even the lines from a file or the nodes from another graph).
+
+    >>> G.add_nodes_from([2, 3])
+    >>> G.add_nodes_from(range(100, 110))
+    >>> H = nx.path_graph(10)
+    >>> G.add_nodes_from(H)
+
+    In addition to strings and integers any hashable Python object
+    (except None) can represent a node, e.g. a customized node object,
+    or even another Graph.
+
+    >>> G.add_node(H)
+
+    **Edges:**
+
+    G can also be grown by adding edges.
+
+    Add one edge,
+
+    >>> key = G.add_edge(1, 2)
+
+    a list of edges,
+
+    >>> keys = G.add_edges_from([(1, 2), (1, 3)])
+
+    or a collection of edges,
+
+    >>> keys = G.add_edges_from(H.edges)
+
+    If some edges connect nodes not yet in the graph, the nodes
+    are added automatically.  If an edge already exists, an additional
+    edge is created and stored using a key to identify the edge.
+    By default the key is the lowest unused integer.
+
+    >>> keys = G.add_edges_from([(4, 5, {"route": 28}), (4, 5, {"route": 37})])
+    >>> G[4]
+    AdjacencyView({3: {0: {}}, 5: {0: {}, 1: {'route': 28}, 2: {'route': 37}}})
+
+    **Attributes:**
+
+    Each graph, node, and edge can hold key/value attribute pairs
+    in an associated attribute dictionary (the keys must be hashable).
+    By default these are empty, but can be added or changed using
+    add_edge, add_node or direct manipulation of the attribute
+    dictionaries named graph, node and edge respectively.
+
+    >>> G = nx.MultiGraph(day="Friday")
+    >>> G.graph
+    {'day': 'Friday'}
+
+    Add node attributes using add_node(), add_nodes_from() or G.nodes
+
+    >>> G.add_node(1, time="5pm")
+    >>> G.add_nodes_from([3], time="2pm")
+    >>> G.nodes[1]
+    {'time': '5pm'}
+    >>> G.nodes[1]["room"] = 714
+    >>> del G.nodes[1]["room"]  # remove attribute
+    >>> list(G.nodes(data=True))
+    [(1, {'time': '5pm'}), (3, {'time': '2pm'})]
+
+    Add edge attributes using add_edge(), add_edges_from(), subscript
+    notation, or G.edges.
+
+    >>> key = G.add_edge(1, 2, weight=4.7)
+    >>> keys = G.add_edges_from([(3, 4), (4, 5)], color="red")
+    >>> keys = G.add_edges_from([(1, 2, {"color": "blue"}), (2, 3, {"weight": 8})])
+    >>> G[1][2][0]["weight"] = 4.7
+    >>> G.edges[1, 2, 0]["weight"] = 4
+
+    Warning: we protect the graph data structure by making `G.edges[1,
+    2, 0]` a read-only dict-like structure. However, you can assign to
+    attributes in e.g. `G.edges[1, 2, 0]`. Thus, use 2 sets of brackets
+    to add/change data attributes: `G.edges[1, 2, 0]['weight'] = 4`.
+
+    **Shortcuts:**
+
+    Many common graph features allow python syntax to speed reporting.
+
+    >>> 1 in G  # check if node in graph
+    True
+    >>> [n for n in G if n < 3]  # iterate through nodes
+    [1, 2]
+    >>> len(G)  # number of nodes in graph
+    5
+    >>> G[1]  # adjacency dict-like view mapping neighbor -> edge key -> edge attributes
+    AdjacencyView({2: {0: {'weight': 4}, 1: {'color': 'blue'}}})
+
+    Often the best way to traverse all edges of a graph is via the neighbors.
+    The neighbors are reported as an adjacency-dict `G.adj` or `G.adjacency()`.
+
+    >>> for n, nbrsdict in G.adjacency():
+    ...     for nbr, keydict in nbrsdict.items():
+    ...         for key, eattr in keydict.items():
+    ...             if "weight" in eattr:
+    ...                 # Do something useful with the edges
+    ...                 pass
+
+    But the edges() method is often more convenient:
+
+    >>> for u, v, keys, weight in G.edges(data="weight", keys=True):
+    ...     if weight is not None:
+    ...         # Do something useful with the edges
+    ...         pass
+
+    **Reporting:**
+
+    Simple graph information is obtained using methods and object-attributes.
+    Reporting usually provides views instead of containers to reduce memory
+    usage. The views update as the graph is updated similarly to dict-views.
+    The objects `nodes`, `edges` and `adj` provide access to data attributes
+    via lookup (e.g. `nodes[n]`, `edges[u, v, k]`, `adj[u][v]`) and iteration
+    (e.g. `nodes.items()`, `nodes.data('color')`,
+    `nodes.data('color', default='blue')` and similarly for `edges`)
+    Views exist for `nodes`, `edges`, `neighbors()`/`adj` and `degree`.
+
+    For details on these and other miscellaneous methods, see below.
+
+    **Subclasses (Advanced):**
+
+    The MultiGraph class uses a dict-of-dict-of-dict-of-dict data structure.
+    The outer dict (node_dict) holds adjacency information keyed by node.
+    The next dict (adjlist_dict) represents the adjacency information
+    and holds edge_key dicts keyed by neighbor. The edge_key dict holds
+    each edge_attr dict keyed by edge key. The inner dict
+    (edge_attr_dict) represents the edge data and holds edge attribute
+    values keyed by attribute names.
+
+    Each of these four dicts in the dict-of-dict-of-dict-of-dict
+    structure can be replaced by a user defined dict-like object.
+    In general, the dict-like features should be maintained but
+    extra features can be added. To replace one of the dicts create
+    a new graph class by changing the class(!) variable holding the
+    factory for that dict-like structure. The variable names are
+    node_dict_factory, node_attr_dict_factory, adjlist_inner_dict_factory,
+    adjlist_outer_dict_factory, edge_key_dict_factory, edge_attr_dict_factory
+    and graph_attr_dict_factory.
+
+    node_dict_factory : function, (default: dict)
+        Factory function to be used to create the dict containing node
+        attributes, keyed by node id.
+        It should require no arguments and return a dict-like object
+
+    node_attr_dict_factory: function, (default: dict)
+        Factory function to be used to create the node attribute
+        dict which holds attribute values keyed by attribute name.
+        It should require no arguments and return a dict-like object
+
+    adjlist_outer_dict_factory : function, (default: dict)
+        Factory function to be used to create the outer-most dict
+        in the data structure that holds adjacency info keyed by node.
+        It should require no arguments and return a dict-like object.
+
+    adjlist_inner_dict_factory : function, (default: dict)
+        Factory function to be used to create the adjacency list
+        dict which holds multiedge key dicts keyed by neighbor.
+        It should require no arguments and return a dict-like object.
+
+    edge_key_dict_factory : function, (default: dict)
+        Factory function to be used to create the edge key dict
+        which holds edge data keyed by edge key.
+        It should require no arguments and return a dict-like object.
+
+    edge_attr_dict_factory : function, (default: dict)
+        Factory function to be used to create the edge attribute
+        dict which holds attribute values keyed by attribute name.
+        It should require no arguments and return a dict-like object.
+
+    graph_attr_dict_factory : function, (default: dict)
+        Factory function to be used to create the graph attribute
+        dict which holds attribute values keyed by attribute name.
+        It should require no arguments and return a dict-like object.
+
+    Typically, if your extension doesn't impact the data structure all
+    methods will inherited without issue except: `to_directed/to_undirected`.
+    By default these methods create a DiGraph/Graph class and you probably
+    want them to create your extension of a DiGraph/Graph. To facilitate
+    this we define two class variables that you can set in your subclass.
+
+    to_directed_class : callable, (default: DiGraph or MultiDiGraph)
+        Class to create a new graph structure in the `to_directed` method.
+        If `None`, a NetworkX class (DiGraph or MultiDiGraph) is used.
+
+    to_undirected_class : callable, (default: Graph or MultiGraph)
+        Class to create a new graph structure in the `to_undirected` method.
+        If `None`, a NetworkX class (Graph or MultiGraph) is used.
+
+    **Subclassing Example**
+
+    Create a low memory graph class that effectively disallows edge
+    attributes by using a single attribute dict for all edges.
+    This reduces the memory used, but you lose edge attributes.
+
+    >>> class ThinGraph(nx.Graph):
+    ...     all_edge_dict = {"weight": 1}
+    ...
+    ...     def single_edge_dict(self):
+    ...         return self.all_edge_dict
+    ...
+    ...     edge_attr_dict_factory = single_edge_dict
+    >>> G = ThinGraph()
+    >>> G.add_edge(2, 1)
+    >>> G[2][1]
+    {'weight': 1}
+    >>> G.add_edge(2, 2)
+    >>> G[2][1] is G[2][2]
+    True
+    """
+
+    # node_dict_factory = dict    # already assigned in Graph
+    # adjlist_outer_dict_factory = dict
+    # adjlist_inner_dict_factory = dict
+    edge_key_dict_factory = dict
+    # edge_attr_dict_factory = dict
+
+    def to_directed_class(self):
+        """Returns the class to use for empty directed copies.
+
+        If you subclass the base classes, use this to designate
+        what directed class to use for `to_directed()` copies.
+        """
+        return nx.MultiDiGraph
+
+    def to_undirected_class(self):
+        """Returns the class to use for empty undirected copies.
+
+        If you subclass the base classes, use this to designate
+        what directed class to use for `to_directed()` copies.
+        """
+        return MultiGraph
+
+    def __init__(self, incoming_graph_data=None, multigraph_input=None, **attr):
+        """Initialize a graph with edges, name, or graph attributes.
+
+        Parameters
+        ----------
+        incoming_graph_data : input graph
+            Data to initialize graph.  If incoming_graph_data=None (default)
+            an empty graph is created.  The data can be an edge list, or any
+            NetworkX graph object.  If the corresponding optional Python
+            packages are installed the data can also be a 2D NumPy array, a
+            SciPy sparse array, or a PyGraphviz graph.
+
+        multigraph_input : bool or None (default None)
+            Note: Only used when `incoming_graph_data` is a dict.
+            If True, `incoming_graph_data` is assumed to be a
+            dict-of-dict-of-dict-of-dict structure keyed by
+            node to neighbor to edge keys to edge data for multi-edges.
+            A NetworkXError is raised if this is not the case.
+            If False, :func:`to_networkx_graph` is used to try to determine
+            the dict's graph data structure as either a dict-of-dict-of-dict
+            keyed by node to neighbor to edge data, or a dict-of-iterable
+            keyed by node to neighbors.
+            If None, the treatment for True is tried, but if it fails,
+            the treatment for False is tried.
+
+        attr : keyword arguments, optional (default= no attributes)
+            Attributes to add to graph as key=value pairs.
+
+        See Also
+        --------
+        convert
+
+        Examples
+        --------
+        >>> G = nx.MultiGraph()
+        >>> G = nx.MultiGraph(name="my graph")
+        >>> e = [(1, 2), (1, 2), (2, 3), (3, 4)]  # list of edges
+        >>> G = nx.MultiGraph(e)
+
+        Arbitrary graph attribute pairs (key=value) may be assigned
+
+        >>> G = nx.MultiGraph(e, day="Friday")
+        >>> G.graph
+        {'day': 'Friday'}
+
+        """
+        # multigraph_input can be None/True/False. So check "is not False"
+        if isinstance(incoming_graph_data, dict) and multigraph_input is not False:
+            Graph.__init__(self)
+            try:
+                convert.from_dict_of_dicts(
+                    incoming_graph_data, create_using=self, multigraph_input=True
+                )
+                self.graph.update(attr)
+            except Exception as err:
+                if multigraph_input is True:
+                    raise nx.NetworkXError(
+                        f"converting multigraph_input raised:\n{type(err)}: {err}"
+                    )
+                Graph.__init__(self, incoming_graph_data, **attr)
+        else:
+            Graph.__init__(self, incoming_graph_data, **attr)
+
+    @cached_property
+    def adj(self):
+        """Graph adjacency object holding the neighbors of each node.
+
+        This object is a read-only dict-like structure with node keys
+        and neighbor-dict values.  The neighbor-dict is keyed by neighbor
+        to the edgekey-data-dict.  So `G.adj[3][2][0]['color'] = 'blue'` sets
+        the color of the edge `(3, 2, 0)` to `"blue"`.
+
+        Iterating over G.adj behaves like a dict. Useful idioms include
+        `for nbr, edgesdict in G.adj[n].items():`.
+
+        The neighbor information is also provided by subscripting the graph.
+
+        Examples
+        --------
+        >>> e = [(1, 2), (1, 2), (1, 3), (3, 4)]  # list of edges
+        >>> G = nx.MultiGraph(e)
+        >>> G.edges[1, 2, 0]["weight"] = 3
+        >>> result = set()
+        >>> for edgekey, data in G[1][2].items():
+        ...     result.add(data.get("weight", 1))
+        >>> result
+        {1, 3}
+
+        For directed graphs, `G.adj` holds outgoing (successor) info.
+        """
+        return MultiAdjacencyView(self._adj)
+
+    def new_edge_key(self, u, v):
+        """Returns an unused key for edges between nodes `u` and `v`.
+
+        The nodes `u` and `v` do not need to be already in the graph.
+
+        Notes
+        -----
+        In the standard MultiGraph class the new key is the number of existing
+        edges between `u` and `v` (increased if necessary to ensure unused).
+        The first edge will have key 0, then 1, etc. If an edge is removed
+        further new_edge_keys may not be in this order.
+
+        Parameters
+        ----------
+        u, v : nodes
+
+        Returns
+        -------
+        key : int
+        """
+        try:
+            keydict = self._adj[u][v]
+        except KeyError:
+            return 0
+        key = len(keydict)
+        while key in keydict:
+            key += 1
+        return key
+
+    def add_edge(self, u_for_edge, v_for_edge, key=None, **attr):
+        """Add an edge between u and v.
+
+        The nodes u and v will be automatically added if they are
+        not already in the graph.
+
+        Edge attributes can be specified with keywords or by directly
+        accessing the edge's attribute dictionary. See examples below.
+
+        Parameters
+        ----------
+        u_for_edge, v_for_edge : nodes
+            Nodes can be, for example, strings or numbers.
+            Nodes must be hashable (and not None) Python objects.
+        key : hashable identifier, optional (default=lowest unused integer)
+            Used to distinguish multiedges between a pair of nodes.
+        attr : keyword arguments, optional
+            Edge data (or labels or objects) can be assigned using
+            keyword arguments.
+
+        Returns
+        -------
+        The edge key assigned to the edge.
+
+        See Also
+        --------
+        add_edges_from : add a collection of edges
+
+        Notes
+        -----
+        To replace/update edge data, use the optional key argument
+        to identify a unique edge.  Otherwise a new edge will be created.
+
+        NetworkX algorithms designed for weighted graphs cannot use
+        multigraphs directly because it is not clear how to handle
+        multiedge weights.  Convert to Graph using edge attribute
+        'weight' to enable weighted graph algorithms.
+
+        Default keys are generated using the method `new_edge_key()`.
+        This method can be overridden by subclassing the base class and
+        providing a custom `new_edge_key()` method.
+
+        Examples
+        --------
+        The following each add an additional edge e=(1, 2) to graph G:
+
+        >>> G = nx.MultiGraph()
+        >>> e = (1, 2)
+        >>> ekey = G.add_edge(1, 2)  # explicit two-node form
+        >>> G.add_edge(*e)  # single edge as tuple of two nodes
+        1
+        >>> G.add_edges_from([(1, 2)])  # add edges from iterable container
+        [2]
+
+        Associate data to edges using keywords:
+
+        >>> ekey = G.add_edge(1, 2, weight=3)
+        >>> ekey = G.add_edge(1, 2, key=0, weight=4)  # update data for key=0
+        >>> ekey = G.add_edge(1, 3, weight=7, capacity=15, length=342.7)
+
+        For non-string attribute keys, use subscript notation.
+
+        >>> ekey = G.add_edge(1, 2)
+        >>> G[1][2][0].update({0: 5})
+        >>> G.edges[1, 2, 0].update({0: 5})
+        """
+        u, v = u_for_edge, v_for_edge
+        # add nodes
+        if u not in self._adj:
+            if u is None:
+                raise ValueError("None cannot be a node")
+            self._adj[u] = self.adjlist_inner_dict_factory()
+            self._node[u] = self.node_attr_dict_factory()
+        if v not in self._adj:
+            if v is None:
+                raise ValueError("None cannot be a node")
+            self._adj[v] = self.adjlist_inner_dict_factory()
+            self._node[v] = self.node_attr_dict_factory()
+        if key is None:
+            key = self.new_edge_key(u, v)
+        if v in self._adj[u]:
+            keydict = self._adj[u][v]
+            datadict = keydict.get(key, self.edge_attr_dict_factory())
+            datadict.update(attr)
+            keydict[key] = datadict
+        else:
+            # selfloops work this way without special treatment
+            datadict = self.edge_attr_dict_factory()
+            datadict.update(attr)
+            keydict = self.edge_key_dict_factory()
+            keydict[key] = datadict
+            self._adj[u][v] = keydict
+            self._adj[v][u] = keydict
+        nx._clear_cache(self)
+        return key
+
+    def add_edges_from(self, ebunch_to_add, **attr):
+        """Add all the edges in ebunch_to_add.
+
+        Parameters
+        ----------
+        ebunch_to_add : container of edges
+            Each edge given in the container will be added to the
+            graph. The edges can be:
+
+                - 2-tuples (u, v) or
+                - 3-tuples (u, v, d) for an edge data dict d, or
+                - 3-tuples (u, v, k) for not iterable key k, or
+                - 4-tuples (u, v, k, d) for an edge with data and key k
+
+        attr : keyword arguments, optional
+            Edge data (or labels or objects) can be assigned using
+            keyword arguments.
+
+        Returns
+        -------
+        A list of edge keys assigned to the edges in `ebunch`.
+
+        See Also
+        --------
+        add_edge : add a single edge
+        add_weighted_edges_from : convenient way to add weighted edges
+
+        Notes
+        -----
+        Adding the same edge twice has no effect but any edge data
+        will be updated when each duplicate edge is added.
+
+        Edge attributes specified in an ebunch take precedence over
+        attributes specified via keyword arguments.
+
+        Default keys are generated using the method ``new_edge_key()``.
+        This method can be overridden by subclassing the base class and
+        providing a custom ``new_edge_key()`` method.
+
+        When adding edges from an iterator over the graph you are changing,
+        a `RuntimeError` can be raised with message:
+        `RuntimeError: dictionary changed size during iteration`. This
+        happens when the graph's underlying dictionary is modified during
+        iteration. To avoid this error, evaluate the iterator into a separate
+        object, e.g. by using `list(iterator_of_edges)`, and pass this
+        object to `G.add_edges_from`.
+
+        Examples
+        --------
+        >>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> G.add_edges_from([(0, 1), (1, 2)])  # using a list of edge tuples
+        >>> e = zip(range(0, 3), range(1, 4))
+        >>> G.add_edges_from(e)  # Add the path graph 0-1-2-3
+
+        Associate data to edges
+
+        >>> G.add_edges_from([(1, 2), (2, 3)], weight=3)
+        >>> G.add_edges_from([(3, 4), (1, 4)], label="WN2898")
+
+        Evaluate an iterator over a graph if using it to modify the same graph
+
+        >>> G = nx.MultiGraph([(1, 2), (2, 3), (3, 4)])
+        >>> # Grow graph by one new node, adding edges to all existing nodes.
+        >>> # wrong way - will raise RuntimeError
+        >>> # G.add_edges_from(((5, n) for n in G.nodes))
+        >>> # right way - note that there will be no self-edge for node 5
+        >>> assigned_keys = G.add_edges_from(list((5, n) for n in G.nodes))
+        """
+        keylist = []
+        for e in ebunch_to_add:
+            ne = len(e)
+            if ne == 4:
+                u, v, key, dd = e
+            elif ne == 3:
+                u, v, dd = e
+                key = None
+            elif ne == 2:
+                u, v = e
+                dd = {}
+                key = None
+            else:
+                msg = f"Edge tuple {e} must be a 2-tuple, 3-tuple or 4-tuple."
+                raise NetworkXError(msg)
+            ddd = {}
+            ddd.update(attr)
+            try:
+                ddd.update(dd)
+            except (TypeError, ValueError):
+                if ne != 3:
+                    raise
+                key = dd  # ne == 3 with 3rd value not dict, must be a key
+            key = self.add_edge(u, v, key)
+            self[u][v][key].update(ddd)
+            keylist.append(key)
+        nx._clear_cache(self)
+        return keylist
+
+    def remove_edge(self, u, v, key=None):
+        """Remove an edge between u and v.
+
+        Parameters
+        ----------
+        u, v : nodes
+            Remove an edge between nodes u and v.
+        key : hashable identifier, optional (default=None)
+            Used to distinguish multiple edges between a pair of nodes.
+            If None, remove a single edge between u and v. If there are
+            multiple edges, removes the last edge added in terms of
+            insertion order.
+
+        Raises
+        ------
+        NetworkXError
+            If there is not an edge between u and v, or
+            if there is no edge with the specified key.
+
+        See Also
+        --------
+        remove_edges_from : remove a collection of edges
+
+        Examples
+        --------
+        >>> G = nx.MultiGraph()
+        >>> nx.add_path(G, [0, 1, 2, 3])
+        >>> G.remove_edge(0, 1)
+        >>> e = (1, 2)
+        >>> G.remove_edge(*e)  # unpacks e from an edge tuple
+
+        For multiple edges
+
+        >>> G = nx.MultiGraph()  # or MultiDiGraph, etc
+        >>> G.add_edges_from([(1, 2), (1, 2), (1, 2)])  # key_list returned
+        [0, 1, 2]
+
+        When ``key=None`` (the default), edges are removed in the opposite
+        order that they were added:
+
+        >>> G.remove_edge(1, 2)
+        >>> G.edges(keys=True)
+        MultiEdgeView([(1, 2, 0), (1, 2, 1)])
+        >>> G.remove_edge(2, 1)  # edges are not directed
+        >>> G.edges(keys=True)
+        MultiEdgeView([(1, 2, 0)])
+
+        For edges with keys
+
+        >>> G = nx.MultiGraph()
+        >>> G.add_edge(1, 2, key="first")
+        'first'
+        >>> G.add_edge(1, 2, key="second")
+        'second'
+        >>> G.remove_edge(1, 2, key="first")
+        >>> G.edges(keys=True)
+        MultiEdgeView([(1, 2, 'second')])
+
+        """
+        try:
+            d = self._adj[u][v]
+        except KeyError as err:
+            raise NetworkXError(f"The edge {u}-{v} is not in the graph.") from err
+        # remove the edge with specified data
+        if key is None:
+            d.popitem()
+        else:
+            try:
+                del d[key]
+            except KeyError as err:
+                msg = f"The edge {u}-{v} with key {key} is not in the graph."
+                raise NetworkXError(msg) from err
+        if len(d) == 0:
+            # remove the key entries if last edge
+            del self._adj[u][v]
+            if u != v:  # check for selfloop
+                del self._adj[v][u]
+        nx._clear_cache(self)
+
+    def remove_edges_from(self, ebunch):
+        """Remove all edges specified in ebunch.
+
+        Parameters
+        ----------
+        ebunch: list or container of edge tuples
+            Each edge given in the list or container will be removed
+            from the graph. The edges can be:
+
+                - 2-tuples (u, v) A single edge between u and v is removed.
+                - 3-tuples (u, v, key) The edge identified by key is removed.
+                - 4-tuples (u, v, key, data) where data is ignored.
+
+        See Also
+        --------
+        remove_edge : remove a single edge
+
+        Notes
+        -----
+        Will fail silently if an edge in ebunch is not in the graph.
+
+        Examples
+        --------
+        >>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> ebunch = [(1, 2), (2, 3)]
+        >>> G.remove_edges_from(ebunch)
+
+        Removing multiple copies of edges
+
+        >>> G = nx.MultiGraph()
+        >>> keys = G.add_edges_from([(1, 2), (1, 2), (1, 2)])
+        >>> G.remove_edges_from([(1, 2), (2, 1)])  # edges aren't directed
+        >>> list(G.edges())
+        [(1, 2)]
+        >>> G.remove_edges_from([(1, 2), (1, 2)])  # silently ignore extra copy
+        >>> list(G.edges)  # now empty graph
+        []
+
+        When the edge is a 2-tuple ``(u, v)`` but there are multiple edges between
+        u and v in the graph, the most recent edge (in terms of insertion
+        order) is removed.
+
+        >>> G = nx.MultiGraph()
+        >>> for key in ("x", "y", "a"):
+        ...     k = G.add_edge(0, 1, key=key)
+        >>> G.edges(keys=True)
+        MultiEdgeView([(0, 1, 'x'), (0, 1, 'y'), (0, 1, 'a')])
+        >>> G.remove_edges_from([(0, 1)])
+        >>> G.edges(keys=True)
+        MultiEdgeView([(0, 1, 'x'), (0, 1, 'y')])
+
+        """
+        for e in ebunch:
+            try:
+                self.remove_edge(*e[:3])
+            except NetworkXError:
+                pass
+        nx._clear_cache(self)
+
+    def has_edge(self, u, v, key=None):
+        """Returns True if the graph has an edge between nodes u and v.
+
+        This is the same as `v in G[u] or key in G[u][v]`
+        without KeyError exceptions.
+
+        Parameters
+        ----------
+        u, v : nodes
+            Nodes can be, for example, strings or numbers.
+
+        key : hashable identifier, optional (default=None)
+            If specified return True only if the edge with
+            key is found.
+
+        Returns
+        -------
+        edge_ind : bool
+            True if edge is in the graph, False otherwise.
+
+        Examples
+        --------
+        Can be called either using two nodes u, v, an edge tuple (u, v),
+        or an edge tuple (u, v, key).
+
+        >>> G = nx.MultiGraph()  # or MultiDiGraph
+        >>> nx.add_path(G, [0, 1, 2, 3])
+        >>> G.has_edge(0, 1)  # using two nodes
+        True
+        >>> e = (0, 1)
+        >>> G.has_edge(*e)  #  e is a 2-tuple (u, v)
+        True
+        >>> G.add_edge(0, 1, key="a")
+        'a'
+        >>> G.has_edge(0, 1, key="a")  # specify key
+        True
+        >>> G.has_edge(1, 0, key="a")  # edges aren't directed
+        True
+        >>> e = (0, 1, "a")
+        >>> G.has_edge(*e)  # e is a 3-tuple (u, v, 'a')
+        True
+
+        The following syntax are equivalent:
+
+        >>> G.has_edge(0, 1)
+        True
+        >>> 1 in G[0]  # though this gives :exc:`KeyError` if 0 not in G
+        True
+        >>> 0 in G[1]  # other order; also gives :exc:`KeyError` if 0 not in G
+        True
+
+        """
+        try:
+            if key is None:
+                return v in self._adj[u]
+            else:
+                return key in self._adj[u][v]
+        except KeyError:
+            return False
+
+    @cached_property
+    def edges(self):
+        """Returns an iterator over the edges.
+
+        edges(self, nbunch=None, data=False, keys=False, default=None)
+
+        The MultiEdgeView provides set-like operations on the edge-tuples
+        as well as edge attribute lookup. When called, it also provides
+        an EdgeDataView object which allows control of access to edge
+        attributes (but does not provide set-like operations).
+        Hence, ``G.edges[u, v, k]['color']`` provides the value of the color
+        attribute for the edge from ``u`` to ``v`` with key ``k`` while
+        ``for (u, v, k, c) in G.edges(data='color', keys=True, default="red"):``
+        iterates through all the edges yielding the color attribute with
+        default `'red'` if no color attribute exists.
+
+        Edges are returned as tuples with optional data and keys
+        in the order (node, neighbor, key, data). If ``keys=True`` is not
+        provided, the tuples will just be (node, neighbor, data), but
+        multiple tuples with the same node and neighbor will be generated
+        when multiple edges exist between two nodes.
+
+        Parameters
+        ----------
+        nbunch : single node, container, or all nodes (default= all nodes)
+            The view will only report edges from these nodes.
+        data : string or bool, optional (default=False)
+            The edge attribute returned in 3-tuple (u, v, ddict[data]).
+            If True, return edge attribute dict in 3-tuple (u, v, ddict).
+            If False, return 2-tuple (u, v).
+        keys : bool, optional (default=False)
+            If True, return edge keys with each edge, creating (u, v, k)
+            tuples or (u, v, k, d) tuples if data is also requested.
+        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
+        -------
+        edges : MultiEdgeView
+            A view of edge attributes, usually it iterates over (u, v)
+            (u, v, k) or (u, v, k, d) tuples of edges, but can also be
+            used for attribute lookup as ``edges[u, v, k]['foo']``.
+
+        Notes
+        -----
+        Nodes in nbunch that are not in the graph will be (quietly) ignored.
+        For directed graphs this returns the out-edges.
+
+        Examples
+        --------
+        >>> G = nx.MultiGraph()
+        >>> nx.add_path(G, [0, 1, 2])
+        >>> key = G.add_edge(2, 3, weight=5)
+        >>> key2 = G.add_edge(2, 1, weight=2)  # multi-edge
+        >>> [e for e in G.edges()]
+        [(0, 1), (1, 2), (1, 2), (2, 3)]
+        >>> G.edges.data()  # default data is {} (empty dict)
+        MultiEdgeDataView([(0, 1, {}), (1, 2, {}), (1, 2, {'weight': 2}), (2, 3, {'weight': 5})])
+        >>> G.edges.data("weight", default=1)
+        MultiEdgeDataView([(0, 1, 1), (1, 2, 1), (1, 2, 2), (2, 3, 5)])
+        >>> G.edges(keys=True)  # default keys are integers
+        MultiEdgeView([(0, 1, 0), (1, 2, 0), (1, 2, 1), (2, 3, 0)])
+        >>> G.edges.data(keys=True)
+        MultiEdgeDataView([(0, 1, 0, {}), (1, 2, 0, {}), (1, 2, 1, {'weight': 2}), (2, 3, 0, {'weight': 5})])
+        >>> G.edges.data("weight", default=1, keys=True)
+        MultiEdgeDataView([(0, 1, 0, 1), (1, 2, 0, 1), (1, 2, 1, 2), (2, 3, 0, 5)])
+        >>> G.edges([0, 3])  # Note ordering of tuples from listed sources
+        MultiEdgeDataView([(0, 1), (3, 2)])
+        >>> G.edges([0, 3, 2, 1])  # Note ordering of tuples
+        MultiEdgeDataView([(0, 1), (3, 2), (2, 1), (2, 1)])
+        >>> G.edges(0)
+        MultiEdgeDataView([(0, 1)])
+        """
+        return MultiEdgeView(self)
+
+    def get_edge_data(self, u, v, key=None, default=None):
+        """Returns the attribute dictionary associated with edge (u, v,
+        key).
+
+        If a key is not provided, returns a dictionary mapping edge keys
+        to attribute dictionaries for each edge between u and v.
+
+        This is identical to `G[u][v][key]` except the default is returned
+        instead of an exception is the edge doesn't exist.
+
+        Parameters
+        ----------
+        u, v : nodes
+
+        default :  any Python object (default=None)
+            Value to return if the specific edge (u, v, key) is not
+            found, OR if there are no edges between u and v and no key
+            is specified.
+
+        key : hashable identifier, optional (default=None)
+            Return data only for the edge with specified key, as an
+            attribute dictionary (rather than a dictionary mapping keys
+            to attribute dictionaries).
+
+        Returns
+        -------
+        edge_dict : dictionary
+            The edge attribute dictionary, OR a dictionary mapping edge
+            keys to attribute dictionaries for each of those edges if no
+            specific key is provided (even if there's only one edge
+            between u and v).
+
+        Examples
+        --------
+        >>> G = nx.MultiGraph()  # or MultiDiGraph
+        >>> key = G.add_edge(0, 1, key="a", weight=7)
+        >>> G[0][1]["a"]  # key='a'
+        {'weight': 7}
+        >>> G.edges[0, 1, "a"]  # key='a'
+        {'weight': 7}
+
+        Warning: we protect the graph data structure by making
+        `G.edges` and `G[1][2]` read-only dict-like structures.
+        However, you can assign values to attributes in e.g.
+        `G.edges[1, 2, 'a']` or `G[1][2]['a']` using an additional
+        bracket as shown next. You need to specify all edge info
+        to assign to the edge data associated with an edge.
+
+        >>> G[0][1]["a"]["weight"] = 10
+        >>> G.edges[0, 1, "a"]["weight"] = 10
+        >>> G[0][1]["a"]["weight"]
+        10
+        >>> G.edges[1, 0, "a"]["weight"]
+        10
+
+        >>> G = nx.MultiGraph()  # or MultiDiGraph
+        >>> nx.add_path(G, [0, 1, 2, 3])
+        >>> G.edges[0, 1, 0]["weight"] = 5
+        >>> G.get_edge_data(0, 1)
+        {0: {'weight': 5}}
+        >>> e = (0, 1)
+        >>> G.get_edge_data(*e)  # tuple form
+        {0: {'weight': 5}}
+        >>> G.get_edge_data(3, 0)  # edge not in graph, returns None
+        >>> G.get_edge_data(3, 0, default=0)  # edge not in graph, return default
+        0
+        >>> G.get_edge_data(1, 0, 0)  # specific key gives back
+        {'weight': 5}
+        """
+        try:
+            if key is None:
+                return self._adj[u][v]
+            else:
+                return self._adj[u][v][key]
+        except KeyError:
+            return default
+
+    @cached_property
+    def degree(self):
+        """A DegreeView for the Graph as G.degree or G.degree().
+
+        The node degree is the number of edges adjacent to the node.
+        The weighted node degree is the sum of the edge weights for
+        edges incident to that node.
+
+        This object provides an iterator for (node, degree) as well as
+        lookup for the degree for a single node.
+
+        Parameters
+        ----------
+        nbunch : single node, container, or all nodes (default= all nodes)
+            The view will only report edges incident to these nodes.
+
+        weight : string or None, optional (default=None)
+           The name of an edge attribute that holds the numerical value used
+           as a weight.  If None, then each edge has weight 1.
+           The degree is the sum of the edge weights adjacent to the node.
+
+        Returns
+        -------
+        MultiDegreeView or int
+            If multiple nodes are requested (the default), returns a `MultiDegreeView`
+            mapping nodes to their degree.
+            If a single node is requested, returns the degree of the node as an integer.
+
+        Examples
+        --------
+        >>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> nx.add_path(G, [0, 1, 2, 3])
+        >>> G.degree(0)  # node 0 with degree 1
+        1
+        >>> list(G.degree([0, 1]))
+        [(0, 1), (1, 2)]
+
+        """
+        return MultiDegreeView(self)
+
+    def is_multigraph(self):
+        """Returns True if graph is a multigraph, False otherwise."""
+        return True
+
+    def is_directed(self):
+        """Returns True if graph is directed, False otherwise."""
+        return False
+
+    def copy(self, as_view=False):
+        """Returns a copy of the graph.
+
+        The copy method by default returns an independent shallow copy
+        of the graph and attributes. That is, if an attribute is a
+        container, that container is shared by the original an the copy.
+        Use Python's `copy.deepcopy` for new containers.
+
+        If `as_view` is True then a view is returned instead of a copy.
+
+        Notes
+        -----
+        All copies reproduce the graph structure, but data attributes
+        may be handled in different ways. There are four types of copies
+        of a graph that people might want.
+
+        Deepcopy -- A "deepcopy" copies the graph structure as well as
+        all data attributes and any objects they might contain.
+        The entire graph object is new so that changes in the copy
+        do not affect the original object. (see Python's copy.deepcopy)
+
+        Data Reference (Shallow) -- For a shallow copy the graph structure
+        is copied but the edge, node and graph attribute dicts are
+        references to those in the original graph. This saves
+        time and memory but could cause confusion if you change an attribute
+        in one graph and it changes the attribute in the other.
+        NetworkX does not provide this level of shallow copy.
+
+        Independent Shallow -- This copy creates new independent attribute
+        dicts and then does a shallow copy of the attributes. That is, any
+        attributes that are containers are shared between the new graph
+        and the original. This is exactly what `dict.copy()` provides.
+        You can obtain this style copy using:
+
+            >>> G = nx.path_graph(5)
+            >>> H = G.copy()
+            >>> H = G.copy(as_view=False)
+            >>> H = nx.Graph(G)
+            >>> H = G.__class__(G)
+
+        Fresh Data -- For fresh data, the graph structure is copied while
+        new empty data attribute dicts are created. The resulting graph
+        is independent of the original and it has no edge, node or graph
+        attributes. Fresh copies are not enabled. Instead use:
+
+            >>> H = G.__class__()
+            >>> H.add_nodes_from(G)
+            >>> H.add_edges_from(G.edges)
+
+        View -- Inspired by dict-views, graph-views act like read-only
+        versions of the original graph, providing a copy of the original
+        structure without requiring any memory for copying the information.
+
+        See the Python copy module for more information on shallow
+        and deep copies, https://docs.python.org/3/library/copy.html.
+
+        Parameters
+        ----------
+        as_view : bool, optional (default=False)
+            If True, the returned graph-view provides a read-only view
+            of the original graph without actually copying any data.
+
+        Returns
+        -------
+        G : Graph
+            A copy of the graph.
+
+        See Also
+        --------
+        to_directed: return a directed copy of the graph.
+
+        Examples
+        --------
+        >>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> H = G.copy()
+
+        """
+        if as_view is True:
+            return nx.graphviews.generic_graph_view(self)
+        G = self.__class__()
+        G.graph.update(self.graph)
+        G.add_nodes_from((n, d.copy()) for n, d in self._node.items())
+        G.add_edges_from(
+            (u, v, key, datadict.copy())
+            for u, nbrs in self._adj.items()
+            for v, keydict in nbrs.items()
+            for key, datadict in keydict.items()
+        )
+        return G
+
+    def to_directed(self, as_view=False):
+        """Returns a directed representation of the graph.
+
+        Returns
+        -------
+        G : MultiDiGraph
+            A directed graph with the same name, same nodes, and with
+            each edge (u, v, k, data) replaced by two directed edges
+            (u, v, k, data) and (v, u, k, data).
+
+        Notes
+        -----
+        This returns a "deepcopy" of the edge, node, and
+        graph attributes which attempts to completely copy
+        all of the data and references.
+
+        This is in contrast to the similar D=MultiDiGraph(G) which
+        returns a shallow copy of the data.
+
+        See the Python copy module for more information on shallow
+        and deep copies, https://docs.python.org/3/library/copy.html.
+
+        Warning: If you have subclassed MultiGraph to use dict-like objects
+        in the data structure, those changes do not transfer to the
+        MultiDiGraph created by this method.
+
+        Examples
+        --------
+        >>> G = nx.MultiGraph()
+        >>> G.add_edge(0, 1)
+        0
+        >>> G.add_edge(0, 1)
+        1
+        >>> H = G.to_directed()
+        >>> list(H.edges)
+        [(0, 1, 0), (0, 1, 1), (1, 0, 0), (1, 0, 1)]
+
+        If already directed, return a (deep) copy
+
+        >>> G = nx.MultiDiGraph()
+        >>> G.add_edge(0, 1)
+        0
+        >>> H = G.to_directed()
+        >>> list(H.edges)
+        [(0, 1, 0)]
+        """
+        graph_class = self.to_directed_class()
+        if as_view is True:
+            return nx.graphviews.generic_graph_view(self, graph_class)
+        # deepcopy when not a view
+        G = graph_class()
+        G.graph.update(deepcopy(self.graph))
+        G.add_nodes_from((n, deepcopy(d)) for n, d in self._node.items())
+        G.add_edges_from(
+            (u, v, key, deepcopy(datadict))
+            for u, nbrs in self.adj.items()
+            for v, keydict in nbrs.items()
+            for key, datadict in keydict.items()
+        )
+        return G
+
+    def to_undirected(self, as_view=False):
+        """Returns an undirected copy of the graph.
+
+        Returns
+        -------
+        G : Graph/MultiGraph
+            A deepcopy of the graph.
+
+        See Also
+        --------
+        copy, add_edge, add_edges_from
+
+        Notes
+        -----
+        This returns a "deepcopy" of the edge, node, and
+        graph attributes which attempts to completely copy
+        all of the data and references.
+
+        This is in contrast to the similar `G = nx.MultiGraph(D)`
+        which returns a shallow copy of the data.
+
+        See the Python copy module for more information on shallow
+        and deep copies, https://docs.python.org/3/library/copy.html.
+
+        Warning: If you have subclassed MultiGraph to use dict-like
+        objects in the data structure, those changes do not transfer
+        to the MultiGraph created by this method.
+
+        Examples
+        --------
+        >>> G = nx.MultiGraph([(0, 1), (0, 1), (1, 2)])
+        >>> H = G.to_directed()
+        >>> list(H.edges)
+        [(0, 1, 0), (0, 1, 1), (1, 0, 0), (1, 0, 1), (1, 2, 0), (2, 1, 0)]
+        >>> G2 = H.to_undirected()
+        >>> list(G2.edges)
+        [(0, 1, 0), (0, 1, 1), (1, 2, 0)]
+        """
+        graph_class = self.to_undirected_class()
+        if as_view is True:
+            return nx.graphviews.generic_graph_view(self, graph_class)
+        # deepcopy when not a view
+        G = graph_class()
+        G.graph.update(deepcopy(self.graph))
+        G.add_nodes_from((n, deepcopy(d)) for n, d in self._node.items())
+        G.add_edges_from(
+            (u, v, key, deepcopy(datadict))
+            for u, nbrs in self._adj.items()
+            for v, keydict in nbrs.items()
+            for key, datadict in keydict.items()
+        )
+        return G
+
+    def number_of_edges(self, u=None, v=None):
+        """Returns the number of edges between two nodes.
+
+        Parameters
+        ----------
+        u, v : nodes, optional (Default=all edges)
+            If u and v are specified, return the number of edges between
+            u and v. Otherwise return the total number of all edges.
+
+        Returns
+        -------
+        nedges : int
+            The number of edges in the graph.  If nodes `u` and `v` are
+            specified return the number of edges between those nodes. If
+            the graph is directed, this only returns the number of edges
+            from `u` to `v`.
+
+        See Also
+        --------
+        size
+
+        Examples
+        --------
+        For undirected multigraphs, this method counts the total number
+        of edges in the graph::
+
+            >>> G = nx.MultiGraph()
+            >>> G.add_edges_from([(0, 1), (0, 1), (1, 2)])
+            [0, 1, 0]
+            >>> G.number_of_edges()
+            3
+
+        If you specify two nodes, this counts the total number of edges
+        joining the two nodes::
+
+            >>> G.number_of_edges(0, 1)
+            2
+
+        For directed multigraphs, this method can count the total number
+        of directed edges from `u` to `v`::
+
+            >>> G = nx.MultiDiGraph()
+            >>> G.add_edges_from([(0, 1), (0, 1), (1, 0)])
+            [0, 1, 0]
+            >>> G.number_of_edges(0, 1)
+            2
+            >>> G.number_of_edges(1, 0)
+            1
+
+        """
+        if u is None:
+            return self.size()
+        try:
+            edgedata = self._adj[u][v]
+        except KeyError:
+            return 0  # no such edge
+        return len(edgedata)