two version of R2R are hereHEADmaster

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diff --git a/.venv/lib/python3.12/site-packages/networkx/classes/graph.py b/.venv/lib/python3.12/site-packages/networkx/classes/graph.py
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+"""Base class for undirected graphs.
+
+The Graph class allows any hashable object as a node
+and can associate key/value attribute pairs with each undirected edge.
+
+Self-loops are allowed but multiple edges are not (see MultiGraph).
+
+For directed graphs see DiGraph and MultiDiGraph.
+"""
+
+from copy import deepcopy
+from functools import cached_property
+
+import networkx as nx
+from networkx import convert
+from networkx.classes.coreviews import AdjacencyView
+from networkx.classes.reportviews import DegreeView, EdgeView, NodeView
+from networkx.exception import NetworkXError
+
+__all__ = ["Graph"]
+
+
+class _CachedPropertyResetterAdj:
+    """Data Descriptor class for _adj that resets ``adj`` cached_property when needed
+
+    This assumes that the ``cached_property`` ``G.adj`` should be reset whenever
+    ``G._adj`` is set to a new value.
+
+    This object sits on a class and ensures that any instance of that
+    class clears its cached property "adj" whenever the underlying
+    instance attribute "_adj" is set to a new object. It only affects
+    the set process of the obj._adj attribute. All get/del operations
+    act as they normally would.
+
+    For info on Data Descriptors see: https://docs.python.org/3/howto/descriptor.html
+    """
+
+    def __set__(self, obj, value):
+        od = obj.__dict__
+        od["_adj"] = value
+        # reset cached properties
+        props = ["adj", "edges", "degree"]
+        for prop in props:
+            if prop in od:
+                del od[prop]
+
+
+class _CachedPropertyResetterNode:
+    """Data Descriptor class for _node that resets ``nodes`` cached_property when needed
+
+    This assumes that the ``cached_property`` ``G.node`` should be reset whenever
+    ``G._node`` is set to a new value.
+
+    This object sits on a class and ensures that any instance of that
+    class clears its cached property "nodes" whenever the underlying
+    instance attribute "_node" is set to a new object. It only affects
+    the set process of the obj._adj attribute. All get/del operations
+    act as they normally would.
+
+    For info on Data Descriptors see: https://docs.python.org/3/howto/descriptor.html
+    """
+
+    def __set__(self, obj, value):
+        od = obj.__dict__
+        od["_node"] = value
+        # reset cached properties
+        if "nodes" in od:
+            del od["nodes"]
+
+
+class Graph:
+    """
+    Base class for undirected graphs.
+
+    A Graph stores nodes and edges with optional data, or attributes.
+
+    Graphs hold undirected edges.  Self loops are allowed but multiple
+    (parallel) edges are not.
+
+    Nodes can be arbitrary (hashable) Python objects with optional
+    key/value attributes, except that `None` is not allowed as a node.
+
+    Edges are represented as links between nodes with optional
+    key/value attributes.
+
+    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 matrix, or PyGraphviz graph.
+
+    attr : keyword arguments, optional (default= no attributes)
+        Attributes to add to graph as key=value pairs.
+
+    See Also
+    --------
+    DiGraph
+    MultiGraph
+    MultiDiGraph
+
+    Examples
+    --------
+    Create an empty graph structure (a "null graph") with no nodes and
+    no edges.
+
+    >>> G = nx.Graph()
+
+    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,
+
+    >>> G.add_edge(1, 2)
+
+    a list of edges,
+
+    >>> G.add_edges_from([(1, 2), (1, 3)])
+
+    or a collection of edges,
+
+    >>> G.add_edges_from(H.edges)
+
+    If some edges connect nodes not yet in the graph, the nodes
+    are added automatically.  There are no errors when adding
+    nodes or edges that already exist.
+
+    **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.Graph(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  # node must exist already to use G.nodes
+    >>> 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.
+
+    >>> G.add_edge(1, 2, weight=4.7)
+    >>> G.add_edges_from([(3, 4), (4, 5)], color="red")
+    >>> G.add_edges_from([(1, 2, {"color": "blue"}), (2, 3, {"weight": 8})])
+    >>> G[1][2]["weight"] = 4.7
+    >>> G.edges[1, 2]["weight"] = 4
+
+    Warning: we protect the graph data structure by making `G.edges` a
+    read-only dict-like structure. However, you can assign to attributes
+    in e.g. `G.edges[1, 2]`. Thus, use 2 sets of brackets to add/change
+    data attributes: `G.edges[1, 2]['weight'] = 4`
+    (For multigraphs: `MG.edges[u, v, key][name] = value`).
+
+    **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
+
+    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, eattr in nbrsdict.items():
+    ...         if "weight" in eattr:
+    ...             # Do something useful with the edges
+    ...             pass
+
+    But the edges() method is often more convenient:
+
+    >>> for u, v, weight in G.edges.data("weight"):
+    ...     if weight is not None:
+    ...         # Do something useful with the edges
+    ...         pass
+
+    **Reporting:**
+
+    Simple graph information is obtained using object-attributes and methods.
+    Reporting typically 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]`, `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 Graph class uses a 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 data keyed by neighbor.  The inner dict (edge_attr_dict) represents
+    the edge data and holds edge attribute values keyed by attribute names.
+
+    Each of these three dicts can be replaced in a subclass 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.
+
+    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 edge data keyed by neighbor.
+        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 inherit 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
+    """
+
+    __networkx_backend__ = "networkx"
+
+    _adj = _CachedPropertyResetterAdj()
+    _node = _CachedPropertyResetterNode()
+
+    node_dict_factory = dict
+    node_attr_dict_factory = dict
+    adjlist_outer_dict_factory = dict
+    adjlist_inner_dict_factory = dict
+    edge_attr_dict_factory = dict
+    graph_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.DiGraph
+
+    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 Graph
+
+    def __init__(self, incoming_graph_data=None, **attr):
+        """Initialize a graph with edges, name, or graph attributes.
+
+        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 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.
+
+        attr : keyword arguments, optional (default= no attributes)
+            Attributes to add to graph as key=value pairs.
+
+        See Also
+        --------
+        convert
+
+        Examples
+        --------
+        >>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> G = nx.Graph(name="my graph")
+        >>> e = [(1, 2), (2, 3), (3, 4)]  # list of edges
+        >>> G = nx.Graph(e)
+
+        Arbitrary graph attribute pairs (key=value) may be assigned
+
+        >>> G = nx.Graph(e, day="Friday")
+        >>> G.graph
+        {'day': 'Friday'}
+
+        """
+        self.graph = self.graph_attr_dict_factory()  # dictionary for graph attributes
+        self._node = self.node_dict_factory()  # empty node attribute dict
+        self._adj = self.adjlist_outer_dict_factory()  # empty adjacency dict
+        self.__networkx_cache__ = {}
+        # attempt to load graph with data
+        if incoming_graph_data is not None:
+            convert.to_networkx_graph(incoming_graph_data, create_using=self)
+        # load graph attributes (must be after convert)
+        self.graph.update(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 edge-data-dict.  So `G.adj[3][2]['color'] = 'blue'` sets
+        the color of the edge `(3, 2)` to `"blue"`.
+
+        Iterating over G.adj behaves like a dict. Useful idioms include
+        `for nbr, datadict in G.adj[n].items():`.
+
+        The neighbor information is also provided by subscripting the graph.
+        So `for nbr, foovalue in G[node].data('foo', default=1):` works.
+
+        For directed graphs, `G.adj` holds outgoing (successor) info.
+        """
+        return AdjacencyView(self._adj)
+
+    @property
+    def name(self):
+        """String identifier of the graph.
+
+        This graph attribute appears in the attribute dict G.graph
+        keyed by the string `"name"`. as well as an attribute (technically
+        a property) `G.name`. This is entirely user controlled.
+        """
+        return self.graph.get("name", "")
+
+    @name.setter
+    def name(self, s):
+        self.graph["name"] = s
+        nx._clear_cache(self)
+
+    def __str__(self):
+        """Returns a short summary of the graph.
+
+        Returns
+        -------
+        info : string
+            Graph information including the graph name (if any), graph type, and the
+            number of nodes and edges.
+
+        Examples
+        --------
+        >>> G = nx.Graph(name="foo")
+        >>> str(G)
+        "Graph named 'foo' with 0 nodes and 0 edges"
+
+        >>> G = nx.path_graph(3)
+        >>> str(G)
+        'Graph with 3 nodes and 2 edges'
+
+        """
+        return "".join(
+            [
+                type(self).__name__,
+                f" named {self.name!r}" if self.name else "",
+                f" with {self.number_of_nodes()} nodes and {self.number_of_edges()} edges",
+            ]
+        )
+
+    def __iter__(self):
+        """Iterate over the nodes. Use: 'for n in G'.
+
+        Returns
+        -------
+        niter : iterator
+            An iterator over all nodes in the graph.
+
+        Examples
+        --------
+        >>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> [n for n in G]
+        [0, 1, 2, 3]
+        >>> list(G)
+        [0, 1, 2, 3]
+        """
+        return iter(self._node)
+
+    def __contains__(self, n):
+        """Returns True if n is a node, False otherwise. Use: 'n in G'.
+
+        Examples
+        --------
+        >>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> 1 in G
+        True
+        """
+        try:
+            return n in self._node
+        except TypeError:
+            return False
+
+    def __len__(self):
+        """Returns the number of nodes in the graph. Use: 'len(G)'.
+
+        Returns
+        -------
+        nnodes : int
+            The number of nodes in the graph.
+
+        See Also
+        --------
+        number_of_nodes: identical method
+        order: identical method
+
+        Examples
+        --------
+        >>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> len(G)
+        4
+
+        """
+        return len(self._node)
+
+    def __getitem__(self, n):
+        """Returns a dict of neighbors of node n.  Use: 'G[n]'.
+
+        Parameters
+        ----------
+        n : node
+           A node in the graph.
+
+        Returns
+        -------
+        adj_dict : dictionary
+           The adjacency dictionary for nodes connected to n.
+
+        Notes
+        -----
+        G[n] is the same as G.adj[n] and similar to G.neighbors(n)
+        (which is an iterator over G.adj[n])
+
+        Examples
+        --------
+        >>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> G[0]
+        AtlasView({1: {}})
+        """
+        return self.adj[n]
+
+    def add_node(self, node_for_adding, **attr):
+        """Add a single node `node_for_adding` and update node attributes.
+
+        Parameters
+        ----------
+        node_for_adding : node
+            A node can be any hashable Python object except None.
+        attr : keyword arguments, optional
+            Set or change node attributes using key=value.
+
+        See Also
+        --------
+        add_nodes_from
+
+        Examples
+        --------
+        >>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> G.add_node(1)
+        >>> G.add_node("Hello")
+        >>> K3 = nx.Graph([(0, 1), (1, 2), (2, 0)])
+        >>> G.add_node(K3)
+        >>> G.number_of_nodes()
+        3
+
+        Use keywords set/change node attributes:
+
+        >>> G.add_node(1, size=10)
+        >>> G.add_node(3, weight=0.4, UTM=("13S", 382871, 3972649))
+
+        Notes
+        -----
+        A hashable object is one that can be used as a key in a Python
+        dictionary. This includes strings, numbers, tuples of strings
+        and numbers, etc.
+
+        On many platforms hashable items also include mutables such as
+        NetworkX Graphs, though one should be careful that the hash
+        doesn't change on mutables.
+        """
+        if node_for_adding not in self._node:
+            if node_for_adding is None:
+                raise ValueError("None cannot be a node")
+            self._adj[node_for_adding] = self.adjlist_inner_dict_factory()
+            attr_dict = self._node[node_for_adding] = self.node_attr_dict_factory()
+            attr_dict.update(attr)
+        else:  # update attr even if node already exists
+            self._node[node_for_adding].update(attr)
+        nx._clear_cache(self)
+
+    def add_nodes_from(self, nodes_for_adding, **attr):
+        """Add multiple nodes.
+
+        Parameters
+        ----------
+        nodes_for_adding : iterable container
+            A container of nodes (list, dict, set, etc.).
+            OR
+            A container of (node, attribute dict) tuples.
+            Node attributes are updated using the attribute dict.
+        attr : keyword arguments, optional (default= no attributes)
+            Update attributes for all nodes in nodes.
+            Node attributes specified in nodes as a tuple take
+            precedence over attributes specified via keyword arguments.
+
+        See Also
+        --------
+        add_node
+
+        Notes
+        -----
+        When adding nodes 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_nodes)`, and pass this
+        object to `G.add_nodes_from`.
+
+        Examples
+        --------
+        >>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> G.add_nodes_from("Hello")
+        >>> K3 = nx.Graph([(0, 1), (1, 2), (2, 0)])
+        >>> G.add_nodes_from(K3)
+        >>> sorted(G.nodes(), key=str)
+        [0, 1, 2, 'H', 'e', 'l', 'o']
+
+        Use keywords to update specific node attributes for every node.
+
+        >>> G.add_nodes_from([1, 2], size=10)
+        >>> G.add_nodes_from([3, 4], weight=0.4)
+
+        Use (node, attrdict) tuples to update attributes for specific nodes.
+
+        >>> G.add_nodes_from([(1, dict(size=11)), (2, {"color": "blue"})])
+        >>> G.nodes[1]["size"]
+        11
+        >>> H = nx.Graph()
+        >>> H.add_nodes_from(G.nodes(data=True))
+        >>> H.nodes[1]["size"]
+        11
+
+        Evaluate an iterator over a graph if using it to modify the same graph
+
+        >>> G = nx.Graph([(0, 1), (1, 2), (3, 4)])
+        >>> # wrong way - will raise RuntimeError
+        >>> # G.add_nodes_from(n + 1 for n in G.nodes)
+        >>> # correct way
+        >>> G.add_nodes_from(list(n + 1 for n in G.nodes))
+        """
+        for n in nodes_for_adding:
+            try:
+                newnode = n not in self._node
+                newdict = attr
+            except TypeError:
+                n, ndict = n
+                newnode = n not in self._node
+                newdict = attr.copy()
+                newdict.update(ndict)
+            if newnode:
+                if n is None:
+                    raise ValueError("None cannot be a node")
+                self._adj[n] = self.adjlist_inner_dict_factory()
+                self._node[n] = self.node_attr_dict_factory()
+            self._node[n].update(newdict)
+        nx._clear_cache(self)
+
+    def remove_node(self, n):
+        """Remove node n.
+
+        Removes the node n and all adjacent edges.
+        Attempting to remove a nonexistent node will raise an exception.
+
+        Parameters
+        ----------
+        n : node
+           A node in the graph
+
+        Raises
+        ------
+        NetworkXError
+           If n is not in the graph.
+
+        See Also
+        --------
+        remove_nodes_from
+
+        Examples
+        --------
+        >>> G = nx.path_graph(3)  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> list(G.edges)
+        [(0, 1), (1, 2)]
+        >>> G.remove_node(1)
+        >>> list(G.edges)
+        []
+
+        """
+        adj = self._adj
+        try:
+            nbrs = list(adj[n])  # list handles self-loops (allows mutation)
+            del self._node[n]
+        except KeyError as err:  # NetworkXError if n not in self
+            raise NetworkXError(f"The node {n} is not in the graph.") from err
+        for u in nbrs:
+            del adj[u][n]  # remove all edges n-u in graph
+        del adj[n]  # now remove node
+        nx._clear_cache(self)
+
+    def remove_nodes_from(self, nodes):
+        """Remove multiple nodes.
+
+        Parameters
+        ----------
+        nodes : iterable container
+            A container of nodes (list, dict, set, etc.).  If a node
+            in the container is not in the graph it is silently
+            ignored.
+
+        See Also
+        --------
+        remove_node
+
+        Notes
+        -----
+        When removing nodes from an iterator over the graph you are changing,
+        a `RuntimeError` will 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_nodes)`, and pass this
+        object to `G.remove_nodes_from`.
+
+        Examples
+        --------
+        >>> G = nx.path_graph(3)  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> e = list(G.nodes)
+        >>> e
+        [0, 1, 2]
+        >>> G.remove_nodes_from(e)
+        >>> list(G.nodes)
+        []
+
+        Evaluate an iterator over a graph if using it to modify the same graph
+
+        >>> G = nx.Graph([(0, 1), (1, 2), (3, 4)])
+        >>> # this command will fail, as the graph's dict is modified during iteration
+        >>> # G.remove_nodes_from(n for n in G.nodes if n < 2)
+        >>> # this command will work, since the dictionary underlying graph is not modified
+        >>> G.remove_nodes_from(list(n for n in G.nodes if n < 2))
+        """
+        adj = self._adj
+        for n in nodes:
+            try:
+                del self._node[n]
+                for u in list(adj[n]):  # list handles self-loops
+                    del adj[u][n]  # (allows mutation of dict in loop)
+                del adj[n]
+            except KeyError:
+                pass
+        nx._clear_cache(self)
+
+    @cached_property
+    def nodes(self):
+        """A NodeView of the Graph as G.nodes or G.nodes().
+
+        Can be used as `G.nodes` for data lookup and for set-like operations.
+        Can also be used as `G.nodes(data='color', default=None)` to return a
+        NodeDataView which reports specific node data but no set operations.
+        It presents a dict-like interface as well with `G.nodes.items()`
+        iterating over `(node, nodedata)` 2-tuples and `G.nodes[3]['foo']`
+        providing the value of the `foo` attribute for node `3`. In addition,
+        a view `G.nodes.data('foo')` provides a dict-like interface to the
+        `foo` attribute of each node. `G.nodes.data('foo', default=1)`
+        provides a default for nodes that do not have attribute `foo`.
+
+        Parameters
+        ----------
+        data : string or bool, optional (default=False)
+            The node attribute returned in 2-tuple (n, ddict[data]).
+            If True, return entire node attribute dict as (n, ddict).
+            If False, return just the nodes n.
+
+        default : value, optional (default=None)
+            Value used for nodes that don't have the requested attribute.
+            Only relevant if data is not True or False.
+
+        Returns
+        -------
+        NodeView
+            Allows set-like operations over the nodes as well as node
+            attribute dict lookup and calling to get a NodeDataView.
+            A NodeDataView iterates over `(n, data)` and has no set operations.
+            A NodeView iterates over `n` and includes set operations.
+
+            When called, if data is False, an iterator over nodes.
+            Otherwise an iterator of 2-tuples (node, attribute value)
+            where the attribute is specified in `data`.
+            If data is True then the attribute becomes the
+            entire data dictionary.
+
+        Notes
+        -----
+        If your node data is not needed, it is simpler and equivalent
+        to use the expression ``for n in G``, or ``list(G)``.
+
+        Examples
+        --------
+        There are two simple ways of getting a list of all nodes in the graph:
+
+        >>> G = nx.path_graph(3)
+        >>> list(G.nodes)
+        [0, 1, 2]
+        >>> list(G)
+        [0, 1, 2]
+
+        To get the node data along with the nodes:
+
+        >>> G.add_node(1, time="5pm")
+        >>> G.nodes[0]["foo"] = "bar"
+        >>> list(G.nodes(data=True))
+        [(0, {'foo': 'bar'}), (1, {'time': '5pm'}), (2, {})]
+        >>> list(G.nodes.data())
+        [(0, {'foo': 'bar'}), (1, {'time': '5pm'}), (2, {})]
+
+        >>> list(G.nodes(data="foo"))
+        [(0, 'bar'), (1, None), (2, None)]
+        >>> list(G.nodes.data("foo"))
+        [(0, 'bar'), (1, None), (2, None)]
+
+        >>> list(G.nodes(data="time"))
+        [(0, None), (1, '5pm'), (2, None)]
+        >>> list(G.nodes.data("time"))
+        [(0, None), (1, '5pm'), (2, None)]
+
+        >>> list(G.nodes(data="time", default="Not Available"))
+        [(0, 'Not Available'), (1, '5pm'), (2, 'Not Available')]
+        >>> list(G.nodes.data("time", default="Not Available"))
+        [(0, 'Not Available'), (1, '5pm'), (2, 'Not Available')]
+
+        If some of your nodes have an attribute and the rest are assumed
+        to have a default attribute value you can create a dictionary
+        from node/attribute pairs using the `default` keyword argument
+        to guarantee the value is never None::
+
+            >>> G = nx.Graph()
+            >>> G.add_node(0)
+            >>> G.add_node(1, weight=2)
+            >>> G.add_node(2, weight=3)
+            >>> dict(G.nodes(data="weight", default=1))
+            {0: 1, 1: 2, 2: 3}
+
+        """
+        return NodeView(self)
+
+    def number_of_nodes(self):
+        """Returns the number of nodes in the graph.
+
+        Returns
+        -------
+        nnodes : int
+            The number of nodes in the graph.
+
+        See Also
+        --------
+        order: identical method
+        __len__: identical method
+
+        Examples
+        --------
+        >>> G = nx.path_graph(3)  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> G.number_of_nodes()
+        3
+        """
+        return len(self._node)
+
+    def order(self):
+        """Returns the number of nodes in the graph.
+
+        Returns
+        -------
+        nnodes : int
+            The number of nodes in the graph.
+
+        See Also
+        --------
+        number_of_nodes: identical method
+        __len__: identical method
+
+        Examples
+        --------
+        >>> G = nx.path_graph(3)  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> G.order()
+        3
+        """
+        return len(self._node)
+
+    def has_node(self, n):
+        """Returns True if the graph contains the node n.
+
+        Identical to `n in G`
+
+        Parameters
+        ----------
+        n : node
+
+        Examples
+        --------
+        >>> G = nx.path_graph(3)  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> G.has_node(0)
+        True
+
+        It is more readable and simpler to use
+
+        >>> 0 in G
+        True
+
+        """
+        try:
+            return n in self._node
+        except TypeError:
+            return False
+
+    def add_edge(self, u_of_edge, v_of_edge, **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_of_edge, v_of_edge : nodes
+            Nodes can be, for example, strings or numbers.
+            Nodes must be hashable (and not None) Python objects.
+        attr : keyword arguments, optional
+            Edge data (or labels or objects) can be assigned using
+            keyword arguments.
+
+        See Also
+        --------
+        add_edges_from : add a collection of edges
+
+        Notes
+        -----
+        Adding an edge that already exists updates the edge data.
+
+        Many NetworkX algorithms designed for weighted graphs use
+        an edge attribute (by default `weight`) to hold a numerical value.
+
+        Examples
+        --------
+        The following all add the edge e=(1, 2) to graph G:
+
+        >>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> e = (1, 2)
+        >>> G.add_edge(1, 2)  # explicit two-node form
+        >>> G.add_edge(*e)  # single edge as tuple of two nodes
+        >>> G.add_edges_from([(1, 2)])  # add edges from iterable container
+
+        Associate data to edges using keywords:
+
+        >>> G.add_edge(1, 2, weight=3)
+        >>> G.add_edge(1, 3, weight=7, capacity=15, length=342.7)
+
+        For non-string attribute keys, use subscript notation.
+
+        >>> G.add_edge(1, 2)
+        >>> G[1][2].update({0: 5})
+        >>> G.edges[1, 2].update({0: 5})
+        """
+        u, v = u_of_edge, v_of_edge
+        # add nodes
+        if u not in self._node:
+            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._node:
+            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()
+        # add the edge
+        datadict = self._adj[u].get(v, self.edge_attr_dict_factory())
+        datadict.update(attr)
+        self._adj[u][v] = datadict
+        self._adj[v][u] = datadict
+        nx._clear_cache(self)
+
+    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 must be given as 2-tuples (u, v) or
+            3-tuples (u, v, d) where d is a dictionary containing edge data.
+        attr : keyword arguments, optional
+            Edge data (or labels or objects) can be assigned using
+            keyword arguments.
+
+        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.
+
+        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.Graph([(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))
+        >>> # correct way - note that there will be no self-edge for node 5
+        >>> G.add_edges_from(list((5, n) for n in G.nodes))
+        """
+        for e in ebunch_to_add:
+            ne = len(e)
+            if ne == 3:
+                u, v, dd = e
+            elif ne == 2:
+                u, v = e
+                dd = {}  # doesn't need edge_attr_dict_factory
+            else:
+                raise NetworkXError(f"Edge tuple {e} must be a 2-tuple or 3-tuple.")
+            if u not in self._node:
+                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._node:
+                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()
+            datadict = self._adj[u].get(v, self.edge_attr_dict_factory())
+            datadict.update(attr)
+            datadict.update(dd)
+            self._adj[u][v] = datadict
+            self._adj[v][u] = datadict
+        nx._clear_cache(self)
+
+    def add_weighted_edges_from(self, ebunch_to_add, weight="weight", **attr):
+        """Add weighted edges in `ebunch_to_add` with specified weight attr
+
+        Parameters
+        ----------
+        ebunch_to_add : container of edges
+            Each edge given in the list or container will be added
+            to the graph. The edges must be given as 3-tuples (u, v, w)
+            where w is a number.
+        weight : string, optional (default= 'weight')
+            The attribute name for the edge weights to be added.
+        attr : keyword arguments, optional (default= no attributes)
+            Edge attributes to add/update for all edges.
+
+        See Also
+        --------
+        add_edge : add a single edge
+        add_edges_from : add multiple edges
+
+        Notes
+        -----
+        Adding the same edge twice for Graph/DiGraph simply updates
+        the edge data. For MultiGraph/MultiDiGraph, duplicate edges
+        are stored.
+
+        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_weighted_edges_from`.
+
+        Examples
+        --------
+        >>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> G.add_weighted_edges_from([(0, 1, 3.0), (1, 2, 7.5)])
+
+        Evaluate an iterator over edges before passing it
+
+        >>> G = nx.Graph([(1, 2), (2, 3), (3, 4)])
+        >>> weight = 0.1
+        >>> # Grow graph by one new node, adding edges to all existing nodes.
+        >>> # wrong way - will raise RuntimeError
+        >>> # G.add_weighted_edges_from(((5, n, weight) for n in G.nodes))
+        >>> # correct way - note that there will be no self-edge for node 5
+        >>> G.add_weighted_edges_from(list((5, n, weight) for n in G.nodes))
+        """
+        self.add_edges_from(((u, v, {weight: d}) for u, v, d in ebunch_to_add), **attr)
+        nx._clear_cache(self)
+
+    def remove_edge(self, u, v):
+        """Remove the edge between u and v.
+
+        Parameters
+        ----------
+        u, v : nodes
+            Remove the edge between nodes u and v.
+
+        Raises
+        ------
+        NetworkXError
+            If there is not an edge between u and v.
+
+        See Also
+        --------
+        remove_edges_from : remove a collection of edges
+
+        Examples
+        --------
+        >>> G = nx.path_graph(4)  # or DiGraph, etc
+        >>> G.remove_edge(0, 1)
+        >>> e = (1, 2)
+        >>> G.remove_edge(*e)  # unpacks e from an edge tuple
+        >>> e = (2, 3, {"weight": 7})  # an edge with attribute data
+        >>> G.remove_edge(*e[:2])  # select first part of edge tuple
+        """
+        try:
+            del self._adj[u][v]
+            if u != v:  # self-loop needs only one entry removed
+                del self._adj[v][u]
+        except KeyError as err:
+            raise NetworkXError(f"The edge {u}-{v} is not in the graph") from err
+        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) edge between u and v.
+                - 3-tuples (u, v, k) where k 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)
+        """
+        adj = self._adj
+        for e in ebunch:
+            u, v = e[:2]  # ignore edge data if present
+            if u in adj and v in adj[u]:
+                del adj[u][v]
+                if u != v:  # self loop needs only one entry removed
+                    del adj[v][u]
+        nx._clear_cache(self)
+
+    def update(self, edges=None, nodes=None):
+        """Update the graph using nodes/edges/graphs as input.
+
+        Like dict.update, this method takes a graph as input, adding the
+        graph's nodes and edges to this graph. It can also take two inputs:
+        edges and nodes. Finally it can take either edges or nodes.
+        To specify only nodes the keyword `nodes` must be used.
+
+        The collections of edges and nodes are treated similarly to
+        the add_edges_from/add_nodes_from methods. When iterated, they
+        should yield 2-tuples (u, v) or 3-tuples (u, v, datadict).
+
+        Parameters
+        ----------
+        edges : Graph object, collection of edges, or None
+            The first parameter can be a graph or some edges. If it has
+            attributes `nodes` and `edges`, then it is taken to be a
+            Graph-like object and those attributes are used as collections
+            of nodes and edges to be added to the graph.
+            If the first parameter does not have those attributes, it is
+            treated as a collection of edges and added to the graph.
+            If the first argument is None, no edges are added.
+        nodes : collection of nodes, or None
+            The second parameter is treated as a collection of nodes
+            to be added to the graph unless it is None.
+            If `edges is None` and `nodes is None` an exception is raised.
+            If the first parameter is a Graph, then `nodes` is ignored.
+
+        Examples
+        --------
+        >>> G = nx.path_graph(5)
+        >>> G.update(nx.complete_graph(range(4, 10)))
+        >>> from itertools import combinations
+        >>> edges = (
+        ...     (u, v, {"power": u * v})
+        ...     for u, v in combinations(range(10, 20), 2)
+        ...     if u * v < 225
+        ... )
+        >>> nodes = [1000]  # for singleton, use a container
+        >>> G.update(edges, nodes)
+
+        Notes
+        -----
+        It you want to update the graph using an adjacency structure
+        it is straightforward to obtain the edges/nodes from adjacency.
+        The following examples provide common cases, your adjacency may
+        be slightly different and require tweaks of these examples::
+
+        >>> # dict-of-set/list/tuple
+        >>> adj = {1: {2, 3}, 2: {1, 3}, 3: {1, 2}}
+        >>> e = [(u, v) for u, nbrs in adj.items() for v in nbrs]
+        >>> G.update(edges=e, nodes=adj)
+
+        >>> DG = nx.DiGraph()
+        >>> # dict-of-dict-of-attribute
+        >>> adj = {1: {2: 1.3, 3: 0.7}, 2: {1: 1.4}, 3: {1: 0.7}}
+        >>> e = [
+        ...     (u, v, {"weight": d})
+        ...     for u, nbrs in adj.items()
+        ...     for v, d in nbrs.items()
+        ... ]
+        >>> DG.update(edges=e, nodes=adj)
+
+        >>> # dict-of-dict-of-dict
+        >>> adj = {1: {2: {"weight": 1.3}, 3: {"color": 0.7, "weight": 1.2}}}
+        >>> e = [
+        ...     (u, v, {"weight": d})
+        ...     for u, nbrs in adj.items()
+        ...     for v, d in nbrs.items()
+        ... ]
+        >>> DG.update(edges=e, nodes=adj)
+
+        >>> # predecessor adjacency (dict-of-set)
+        >>> pred = {1: {2, 3}, 2: {3}, 3: {3}}
+        >>> e = [(v, u) for u, nbrs in pred.items() for v in nbrs]
+
+        >>> # MultiGraph dict-of-dict-of-dict-of-attribute
+        >>> MDG = nx.MultiDiGraph()
+        >>> adj = {
+        ...     1: {2: {0: {"weight": 1.3}, 1: {"weight": 1.2}}},
+        ...     3: {2: {0: {"weight": 0.7}}},
+        ... }
+        >>> e = [
+        ...     (u, v, ekey, d)
+        ...     for u, nbrs in adj.items()
+        ...     for v, keydict in nbrs.items()
+        ...     for ekey, d in keydict.items()
+        ... ]
+        >>> MDG.update(edges=e)
+
+        See Also
+        --------
+        add_edges_from: add multiple edges to a graph
+        add_nodes_from: add multiple nodes to a graph
+        """
+        if edges is not None:
+            if nodes is not None:
+                self.add_nodes_from(nodes)
+                self.add_edges_from(edges)
+            else:
+                # check if edges is a Graph object
+                try:
+                    graph_nodes = edges.nodes
+                    graph_edges = edges.edges
+                except AttributeError:
+                    # edge not Graph-like
+                    self.add_edges_from(edges)
+                else:  # edges is Graph-like
+                    self.add_nodes_from(graph_nodes.data())
+                    self.add_edges_from(graph_edges.data())
+                    self.graph.update(edges.graph)
+        elif nodes is not None:
+            self.add_nodes_from(nodes)
+        else:
+            raise NetworkXError("update needs nodes or edges input")
+
+    def has_edge(self, u, v):
+        """Returns True if the edge (u, v) is in the graph.
+
+        This is the same as `v in G[u]` without KeyError exceptions.
+
+        Parameters
+        ----------
+        u, v : nodes
+            Nodes can be, for example, strings or numbers.
+            Nodes must be hashable (and not None) Python objects.
+
+        Returns
+        -------
+        edge_ind : bool
+            True if edge is in the graph, False otherwise.
+
+        Examples
+        --------
+        >>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> G.has_edge(0, 1)  # using two nodes
+        True
+        >>> e = (0, 1)
+        >>> G.has_edge(*e)  #  e is a 2-tuple (u, v)
+        True
+        >>> e = (0, 1, {"weight": 7})
+        >>> G.has_edge(*e[:2])  # e is a 3-tuple (u, v, data_dictionary)
+        True
+
+        The following syntax are equivalent:
+
+        >>> G.has_edge(0, 1)
+        True
+        >>> 1 in G[0]  # though this gives KeyError if 0 not in G
+        True
+
+        """
+        try:
+            return v in self._adj[u]
+        except KeyError:
+            return False
+
+    def neighbors(self, n):
+        """Returns an iterator over all neighbors of node n.
+
+        This is identical to `iter(G[n])`
+
+        Parameters
+        ----------
+        n : node
+           A node in the graph
+
+        Returns
+        -------
+        neighbors : iterator
+            An iterator over all neighbors of node n
+
+        Raises
+        ------
+        NetworkXError
+            If the node n is not in the graph.
+
+        Examples
+        --------
+        >>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> [n for n in G.neighbors(0)]
+        [1]
+
+        Notes
+        -----
+        Alternate ways to access the neighbors are ``G.adj[n]`` or ``G[n]``:
+
+        >>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> G.add_edge("a", "b", weight=7)
+        >>> G["a"]
+        AtlasView({'b': {'weight': 7}})
+        >>> G = nx.path_graph(4)
+        >>> [n for n in G[0]]
+        [1]
+        """
+        try:
+            return iter(self._adj[n])
+        except KeyError as err:
+            raise NetworkXError(f"The node {n} is not in the graph.") from err
+
+    @cached_property
+    def edges(self):
+        """An EdgeView of the Graph as G.edges or G.edges().
+
+        edges(self, nbunch=None, data=False, default=None)
+
+        The EdgeView 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]['color']` provides the value of the color
+        attribute for edge `(u, v)` while
+        `for (u, v, c) in G.edges.data('color', default='red'):`
+        iterates through all the edges yielding the color attribute
+        with default `'red'` if no color attribute exists.
+
+        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).
+        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 : EdgeView
+            A view of edge attributes, usually it iterates over (u, v)
+            or (u, v, d) tuples of edges, but can also be used for
+            attribute lookup as `edges[u, v]['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.path_graph(3)  # or MultiGraph, etc
+        >>> G.add_edge(2, 3, weight=5)
+        >>> [e for e in G.edges]
+        [(0, 1), (1, 2), (2, 3)]
+        >>> G.edges.data()  # default data is {} (empty dict)
+        EdgeDataView([(0, 1, {}), (1, 2, {}), (2, 3, {'weight': 5})])
+        >>> G.edges.data("weight", default=1)
+        EdgeDataView([(0, 1, 1), (1, 2, 1), (2, 3, 5)])
+        >>> G.edges([0, 3])  # only edges from these nodes
+        EdgeDataView([(0, 1), (3, 2)])
+        >>> G.edges(0)  # only edges from node 0
+        EdgeDataView([(0, 1)])
+        """
+        return EdgeView(self)
+
+    def get_edge_data(self, u, v, default=None):
+        """Returns the attribute dictionary associated with edge (u, v).
+
+        This is identical to `G[u][v]` except the default is returned
+        instead of an exception if the edge doesn't exist.
+
+        Parameters
+        ----------
+        u, v : nodes
+        default:  any Python object (default=None)
+            Value to return if the edge (u, v) is not found.
+
+        Returns
+        -------
+        edge_dict : dictionary
+            The edge attribute dictionary.
+
+        Examples
+        --------
+        >>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> G[0][1]
+        {}
+
+        Warning: Assigning to `G[u][v]` is not permitted.
+        But it is safe to assign attributes `G[u][v]['foo']`
+
+        >>> G[0][1]["weight"] = 7
+        >>> G[0][1]["weight"]
+        7
+        >>> G[1][0]["weight"]
+        7
+
+        >>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> G.get_edge_data(0, 1)  # default edge data is {}
+        {}
+        >>> e = (0, 1)
+        >>> G.get_edge_data(*e)  # tuple form
+        {}
+        >>> G.get_edge_data("a", "b", default=0)  # edge not in graph, return 0
+        0
+        """
+        try:
+            return self._adj[u][v]
+        except KeyError:
+            return default
+
+    def adjacency(self):
+        """Returns an iterator over (node, adjacency dict) tuples for all nodes.
+
+        For directed graphs, only outgoing neighbors/adjacencies are included.
+
+        Returns
+        -------
+        adj_iter : iterator
+           An iterator over (node, adjacency dictionary) for all nodes in
+           the graph.
+
+        Examples
+        --------
+        >>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> [(n, nbrdict) for n, nbrdict in G.adjacency()]
+        [(0, {1: {}}), (1, {0: {}, 2: {}}), (2, {1: {}, 3: {}}), (3, {2: {}})]
+
+        """
+        return iter(self._adj.items())
+
+    @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
+        -------
+        DegreeView or int
+            If multiple nodes are requested (the default), returns a `DegreeView`
+            mapping nodes to their degree.
+            If a single node is requested, returns the degree of the node as an integer.
+
+        Examples
+        --------
+        >>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> G.degree[0]  # node 0 has degree 1
+        1
+        >>> list(G.degree([0, 1, 2]))
+        [(0, 1), (1, 2), (2, 2)]
+        """
+        return DegreeView(self)
+
+    def clear(self):
+        """Remove all nodes and edges from the graph.
+
+        This also removes the name, and all graph, node, and edge attributes.
+
+        Examples
+        --------
+        >>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> G.clear()
+        >>> list(G.nodes)
+        []
+        >>> list(G.edges)
+        []
+
+        """
+        self._adj.clear()
+        self._node.clear()
+        self.graph.clear()
+        nx._clear_cache(self)
+
+    def clear_edges(self):
+        """Remove all edges from the graph without altering nodes.
+
+        Examples
+        --------
+        >>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> G.clear_edges()
+        >>> list(G.nodes)
+        [0, 1, 2, 3]
+        >>> list(G.edges)
+        []
+        """
+        for nbr_dict in self._adj.values():
+            nbr_dict.clear()
+        nx._clear_cache(self)
+
+    def is_multigraph(self):
+        """Returns True if graph is a multigraph, False otherwise."""
+        return False
+
+    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, datadict.copy())
+            for u, nbrs in self._adj.items()
+            for v, datadict in nbrs.items()
+        )
+        return G
+
+    def to_directed(self, as_view=False):
+        """Returns a directed representation of the graph.
+
+        Returns
+        -------
+        G : DiGraph
+            A directed graph with the same name, same nodes, and with
+            each edge (u, v, data) replaced by two directed edges
+            (u, v, data) and (v, u, 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=DiGraph(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 Graph to use dict-like objects
+        in the data structure, those changes do not transfer to the
+        DiGraph created by this method.
+
+        Examples
+        --------
+        >>> G = nx.Graph()  # or MultiGraph, etc
+        >>> G.add_edge(0, 1)
+        >>> H = G.to_directed()
+        >>> list(H.edges)
+        [(0, 1), (1, 0)]
+
+        If already directed, return a (deep) copy
+
+        >>> G = nx.DiGraph()  # or MultiDiGraph, etc
+        >>> G.add_edge(0, 1)
+        >>> H = G.to_directed()
+        >>> list(H.edges)
+        [(0, 1)]
+        """
+        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, deepcopy(data))
+            for u, nbrs in self._adj.items()
+            for v, data in nbrs.items()
+        )
+        return G
+
+    def to_undirected(self, as_view=False):
+        """Returns an undirected copy of the graph.
+
+        Parameters
+        ----------
+        as_view : bool (optional, default=False)
+          If True return a view of the original undirected graph.
+
+        Returns
+        -------
+        G : Graph/MultiGraph
+            A deepcopy of the graph.
+
+        See Also
+        --------
+        Graph, 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.DiGraph(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 DiGraph to use dict-like objects
+        in the data structure, those changes do not transfer to the
+        Graph created by this method.
+
+        Examples
+        --------
+        >>> G = nx.path_graph(2)  # or MultiGraph, etc
+        >>> H = G.to_directed()
+        >>> list(H.edges)
+        [(0, 1), (1, 0)]
+        >>> G2 = H.to_undirected()
+        >>> list(G2.edges)
+        [(0, 1)]
+        """
+        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, deepcopy(d))
+            for u, nbrs in self._adj.items()
+            for v, d in nbrs.items()
+        )
+        return G
+
+    def subgraph(self, nodes):
+        """Returns a SubGraph view of the subgraph induced on `nodes`.
+
+        The induced subgraph of the graph contains the nodes in `nodes`
+        and the edges between those nodes.
+
+        Parameters
+        ----------
+        nodes : list, iterable
+            A container of nodes which will be iterated through once.
+
+        Returns
+        -------
+        G : SubGraph View
+            A subgraph view of the graph. The graph structure cannot be
+            changed but node/edge attributes can and are shared with the
+            original graph.
+
+        Notes
+        -----
+        The graph, edge and node attributes are shared with the original graph.
+        Changes to the graph structure is ruled out by the view, but changes
+        to attributes are reflected in the original graph.
+
+        To create a subgraph with its own copy of the edge/node attributes use:
+        G.subgraph(nodes).copy()
+
+        For an inplace reduction of a graph to a subgraph you can remove nodes:
+        G.remove_nodes_from([n for n in G if n not in set(nodes)])
+
+        Subgraph views are sometimes NOT what you want. In most cases where
+        you want to do more than simply look at the induced edges, it makes
+        more sense to just create the subgraph as its own graph with code like:
+
+        ::
+
+            # Create a subgraph SG based on a (possibly multigraph) G
+            SG = G.__class__()
+            SG.add_nodes_from((n, G.nodes[n]) for n in largest_wcc)
+            if SG.is_multigraph():
+                SG.add_edges_from(
+                    (n, nbr, key, d)
+                    for n, nbrs in G.adj.items()
+                    if n in largest_wcc
+                    for nbr, keydict in nbrs.items()
+                    if nbr in largest_wcc
+                    for key, d in keydict.items()
+                )
+            else:
+                SG.add_edges_from(
+                    (n, nbr, d)
+                    for n, nbrs in G.adj.items()
+                    if n in largest_wcc
+                    for nbr, d in nbrs.items()
+                    if nbr in largest_wcc
+                )
+            SG.graph.update(G.graph)
+
+        Examples
+        --------
+        >>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> H = G.subgraph([0, 1, 2])
+        >>> list(H.edges)
+        [(0, 1), (1, 2)]
+        """
+        induced_nodes = nx.filters.show_nodes(self.nbunch_iter(nodes))
+        # if already a subgraph, don't make a chain
+        subgraph = nx.subgraph_view
+        if hasattr(self, "_NODE_OK"):
+            return subgraph(
+                self._graph, filter_node=induced_nodes, filter_edge=self._EDGE_OK
+            )
+        return subgraph(self, filter_node=induced_nodes)
+
+    def edge_subgraph(self, edges):
+        """Returns the subgraph induced by the specified edges.
+
+        The induced subgraph contains each edge in `edges` and each
+        node incident to any one of those edges.
+
+        Parameters
+        ----------
+        edges : iterable
+            An iterable of edges in this graph.
+
+        Returns
+        -------
+        G : Graph
+            An edge-induced subgraph of this graph with the same edge
+            attributes.
+
+        Notes
+        -----
+        The graph, edge, and node attributes in the returned subgraph
+        view are references to the corresponding attributes in the original
+        graph. The view is read-only.
+
+        To create a full graph version of the subgraph with its own copy
+        of the edge or node attributes, use::
+
+            G.edge_subgraph(edges).copy()
+
+        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)]
+
+        """
+        return nx.edge_subgraph(self, edges)
+
+    def size(self, weight=None):
+        """Returns the number of edges or total of all edge weights.
+
+        Parameters
+        ----------
+        weight : string or None, optional (default=None)
+            The edge attribute that holds the numerical value used
+            as a weight. If None, then each edge has weight 1.
+
+        Returns
+        -------
+        size : numeric
+            The number of edges or
+            (if weight keyword is provided) the total weight sum.
+
+            If weight is None, returns an int. Otherwise a float
+            (or more general numeric if the weights are more general).
+
+        See Also
+        --------
+        number_of_edges
+
+        Examples
+        --------
+        >>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> G.size()
+        3
+
+        >>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
+        >>> G.add_edge("a", "b", weight=2)
+        >>> G.add_edge("b", "c", weight=4)
+        >>> G.size()
+        2
+        >>> G.size(weight="weight")
+        6.0
+        """
+        s = sum(d for v, d in self.degree(weight=weight))
+        # If `weight` is None, the sum of the degrees is guaranteed to be
+        # even, so we can perform integer division and hence return an
+        # integer. Otherwise, the sum of the weighted degrees is not
+        # guaranteed to be an integer, so we perform "real" division.
+        return s // 2 if weight is None else s / 2
+
+    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 graphs, this method counts the total number of
+        edges in the graph:
+
+        >>> G = nx.path_graph(4)
+        >>> 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)
+        1
+
+        For directed graphs, this method can count the total number of
+        directed edges from `u` to `v`:
+
+        >>> G = nx.DiGraph()
+        >>> G.add_edge(0, 1)
+        >>> G.add_edge(1, 0)
+        >>> G.number_of_edges(0, 1)
+        1
+
+        """
+        if u is None:
+            return int(self.size())
+        if v in self._adj[u]:
+            return 1
+        return 0
+
+    def nbunch_iter(self, nbunch=None):
+        """Returns an iterator over nodes contained in nbunch that are
+        also in the graph.
+
+        The nodes in nbunch are checked for membership in the graph
+        and if not are silently ignored.
+
+        Parameters
+        ----------
+        nbunch : single node, container, or all nodes (default= all nodes)
+            The view will only report edges incident to these nodes.
+
+        Returns
+        -------
+        niter : iterator
+            An iterator over nodes in nbunch that are also in the graph.
+            If nbunch is None, iterate over all nodes in the graph.
+
+        Raises
+        ------
+        NetworkXError
+            If nbunch is not a node or sequence of nodes.
+            If a node in nbunch is not hashable.
+
+        See Also
+        --------
+        Graph.__iter__
+
+        Notes
+        -----
+        When nbunch is an iterator, the returned iterator yields values
+        directly from nbunch, becoming exhausted when nbunch is exhausted.
+
+        To test whether nbunch is a single node, one can use
+        "if nbunch in self:", even after processing with this routine.
+
+        If nbunch is not a node or a (possibly empty) sequence/iterator
+        or None, a :exc:`NetworkXError` is raised.  Also, if any object in
+        nbunch is not hashable, a :exc:`NetworkXError` is raised.
+        """
+        if nbunch is None:  # include all nodes via iterator
+            bunch = iter(self._adj)
+        elif nbunch in self:  # if nbunch is a single node
+            bunch = iter([nbunch])
+        else:  # if nbunch is a sequence of nodes
+
+            def bunch_iter(nlist, adj):
+                try:
+                    for n in nlist:
+                        if n in adj:
+                            yield n
+                except TypeError as err:
+                    exc, message = err, err.args[0]
+                    # capture error for non-sequence/iterator nbunch.
+                    if "iter" in message:
+                        exc = NetworkXError(
+                            "nbunch is not a node or a sequence of nodes."
+                        )
+                    # capture error for unhashable node.
+                    if "hashable" in message:
+                        exc = NetworkXError(
+                            f"Node {n} in sequence nbunch is not a valid node."
+                        )
+                    raise exc
+
+            bunch = bunch_iter(nbunch, self._adj)
+        return bunch