Skip to main content
`Ctrl`+`K`

# Source code for networkx.classes.digraph

    """Base class for directed graphs."""

    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.graph import Graph
    from networkx.classes.reportviews import (
        DiDegreeView,
        InDegreeView,
        InEdgeView,
        OutDegreeView,
        OutEdgeView,
    )
    from networkx.exception import NetworkXError

    __all__ = ["DiGraph"]

    class _CachedPropertyResetterAdjAndSucc:
        """Data Descriptor class that syncs and resets cached properties adj and succ

        The cached properties `adj` and `succ` are reset whenever `_adj` or `_succ`
        are set to new objects. In addition, the attributes `_succ` and `_adj`
        are synced so these two names point to the same object.

        Warning: most of the time, when ``G._adj`` is set, ``G._pred`` should also
        be set to maintain a valid data structure. They share datadicts.

        This object sits on a class and ensures that any instance of that
        class clears its cached properties "succ" and "adj" whenever the
        underlying instance attributes "_succ" or "_adj" are set to a new object.
        It only affects the set process of the obj._adj and obj._succ 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
            od["_succ"] = value
            # reset cached properties
            props = [
                "adj",
                "succ",
                "edges",
                "out_edges",
                "degree",
                "out_degree",
                "in_degree",
            ]
            for prop in props:
                if prop in od:
                    del od[prop]

    class _CachedPropertyResetterPred:
        """Data Descriptor class for _pred that resets ``pred`` cached_property when needed

        This assumes that the ``cached_property`` ``G.pred`` should be reset whenever
        ``G._pred`` is set to a new value.

        Warning: most of the time, when ``G._pred`` is set, ``G._adj`` should also
        be set to maintain a valid data structure. They share datadicts.

        This object sits on a class and ensures that any instance of that
        class clears its cached property "pred" whenever the underlying
        instance attribute "_pred" is set to a new object. It only affects
        the set process of the obj._pred 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["_pred"] = value
            # reset cached properties
            props = ["pred", "in_edges", "degree", "out_degree", "in_degree"]
            for prop in props:
                if prop in od:
                    del od[prop]

    class DiGraph(Graph):
        """
        Base class for directed graphs.

        A DiGraph stores nodes and edges with optional data, or attributes.

        DiGraphs hold directed edges.  Self loops are allowed but multiple
        (parallel) edges are not.

        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.

        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
        --------
        Graph
        MultiGraph
        MultiDiGraph

        Examples
        --------
        Create an empty graph structure (a "null graph") with no nodes and
        no edges.

        >>> G = nx.DiGraph()

        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.DiGraph(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.

        >>> 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[1, 2]` 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 reporting object 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 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]`, `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. The variable names are
        node_dict_factory, node_attr_dict_factory, adjlist_inner_dict_factory,
        adjlist_outer_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, optional (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, optional (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
        """

        _adj = _CachedPropertyResetterAdjAndSucc()  # type: ignore[assignment]
        _succ = _adj  # type: ignore[has-type]
        _pred = _CachedPropertyResetterPred()

        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()  # dictionary for node attr
            # We store two adjacency lists:
            # the predecessors of node n are stored in the dict self._pred
            # the successors of node n are stored in the dict self._succ=self._adj
            self._adj = self.adjlist_outer_dict_factory()  # empty adjacency dict successor
            self._pred = self.adjlist_outer_dict_factory()  # predecessor
            # Note: self._succ = self._adj  # successor

            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._succ)

        @cached_property
        def succ(self):
            """Graph adjacency object holding the successors 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.succ[3][2]['color'] = 'blue'` sets
            the color of the edge `(3, 2)` to `"blue"`.

            Iterating over G.succ behaves like a dict. Useful idioms include
            `for nbr, datadict in G.succ[n].items():`.  A data-view not provided
            by dicts also exists: `for nbr, foovalue in G.succ[node].data('foo'):`
            and a default can be set via a `default` argument to the `data` method.

            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` is identical to `G.succ`.
            """
            return AdjacencyView(self._succ)

        @cached_property
        def pred(self):
            """Graph adjacency object holding the predecessors 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.pred[2][3]['color'] = 'blue'` sets
            the color of the edge `(3, 2)` to `"blue"`.

            Iterating over G.pred behaves like a dict. Useful idioms include
            `for nbr, datadict in G.pred[n].items():`.  A data-view not provided
            by dicts also exists: `for nbr, foovalue in G.pred[node].data('foo'):`
            A default can be set via a `default` argument to the `data` method.
            """
            return AdjacencyView(self._pred)

        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._succ:
                if node_for_adding is None:
                    raise ValueError("None cannot be a node")
                self._succ[node_for_adding] = self.adjlist_inner_dict_factory()
                self._pred[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.DiGraph([(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._succ[n] = self.adjlist_inner_dict_factory()
                    self._pred[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)
            []

            """
            try:
                nbrs = self._succ[n]
                del self._node[n]
            except KeyError as err:  # NetworkXError if n not in self
                raise NetworkXError(f"The node {n} is not in the digraph.") from err
            for u in nbrs:
                del self._pred[u][n]  # remove all edges n-u in digraph
            del self._succ[n]  # remove node from succ
            for u in self._pred[n]:
                del self._succ[u][n]  # remove all edges n-u in digraph
            del self._pred[n]  # remove node from pred
            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.DiGraph([(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))
            """
            for n in nodes:
                try:
                    succs = self._succ[n]
                    del self._node[n]
                    for u in succs:
                        del self._pred[u][n]  # remove all edges n-u in digraph
                    del self._succ[n]  # now remove node
                    for u in self._pred[n]:
                        del self._succ[u][n]  # remove all edges n-u in digraph
                    del self._pred[n]  # now remove node
                except KeyError:
                    pass  # silent failure on remove
            nx._clear_cache(self)

        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._succ:
                if u is None:
                    raise ValueError("None cannot be a node")
                self._succ[u] = self.adjlist_inner_dict_factory()
                self._pred[u] = self.adjlist_inner_dict_factory()
                self._node[u] = self.node_attr_dict_factory()
            if v not in self._succ:
                if v is None:
                    raise ValueError("None cannot be a node")
                self._succ[v] = self.adjlist_inner_dict_factory()
                self._pred[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._succ[u][v] = datadict
            self._pred[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.DiGraph([(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
            >>> 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 = {}
                else:
                    raise NetworkXError(f"Edge tuple {e} must be a 2-tuple or 3-tuple.")
                if u not in self._succ:
                    if u is None:
                        raise ValueError("None cannot be a node")
                    self._succ[u] = self.adjlist_inner_dict_factory()
                    self._pred[u] = self.adjlist_inner_dict_factory()
                    self._node[u] = self.node_attr_dict_factory()
                if v not in self._succ:
                    if v is None:
                        raise ValueError("None cannot be a node")
                    self._succ[v] = self.adjlist_inner_dict_factory()
                    self._pred[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._succ[u][v] = datadict
                self._pred[v][u] = datadict
            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.Graph()  # or DiGraph, etc
            >>> 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
            >>> e = (2, 3, {"weight": 7})  # an edge with attribute data
            >>> G.remove_edge(*e[:2])  # select first part of edge tuple
            """
            try:
                del self._succ[u][v]
                del self._pred[v][u]
            except KeyError as err:
                raise NetworkXError(f"The edge {u}-{v} not in 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)
            """
            for e in ebunch:
                u, v = e[:2]  # ignore edge data
                if u in self._succ and v in self._succ[u]:
                    del self._succ[u][v]
                    del self._pred[v][u]
            nx._clear_cache(self)

        def has_successor(self, u, v):
            """Returns True if node u has successor v.

            This is true if graph has the edge u->v.
            """
            return u in self._succ and v in self._succ[u]

        def has_predecessor(self, u, v):
            """Returns True if node u has predecessor v.

            This is true if graph has the edge u<-v.
            """
            return u in self._pred and v in self._pred[u]

        def successors(self, n):
            """Returns an iterator over successor nodes of n.

            A successor of n is a node m such that there exists a directed
            edge from n to m.

            Parameters
            ----------
            n : node
               A node in the graph

            Raises
            ------
            NetworkXError
               If n is not in the graph.

            See Also
            --------
            predecessors

            Notes
            -----
            neighbors() and successors() are the same.
            """
            try:
                return iter(self._succ[n])
            except KeyError as err:
                raise NetworkXError(f"The node {n} is not in the digraph.") from err

        # digraph definitions
        neighbors = successors

        def predecessors(self, n):
            """Returns an iterator over predecessor nodes of n.

            A predecessor of n is a node m such that there exists a directed
            edge from m to n.

            Parameters
            ----------
            n : node
               A node in the graph

            Raises
            ------
            NetworkXError
               If n is not in the graph.

            See Also
            --------
            successors
            """
            try:
                return iter(self._pred[n])
            except KeyError as err:
                raise NetworkXError(f"The node {n} is not in the digraph.") from err

        @cached_property
        def edges(self):
            """An OutEdgeView of the DiGraph as G.edges or G.edges().

            edges(self, nbunch=None, data=False, default=None)

            The OutEdgeView 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 : OutEdgeView
                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']`.

            See Also
            --------
            in_edges, out_edges

            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.DiGraph()  # or MultiDiGraph, etc
            >>> nx.add_path(G, [0, 1, 2])
            >>> 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)
            OutEdgeDataView([(0, 1, {}), (1, 2, {}), (2, 3, {'weight': 5})])
            >>> G.edges.data("weight", default=1)
            OutEdgeDataView([(0, 1, 1), (1, 2, 1), (2, 3, 5)])
            >>> G.edges([0, 2])  # only edges originating from these nodes
            OutEdgeDataView([(0, 1), (2, 3)])
            >>> G.edges(0)  # only edges from node 0
            OutEdgeDataView([(0, 1)])

            """
            return OutEdgeView(self)

        # alias out_edges to edges

        @cached_property
        def out_edges(self):
            return OutEdgeView(self)

        out_edges.__doc__ = edges.__doc__

        @cached_property
        def in_edges(self):
            """A view of the in edges of the graph as G.in_edges or G.in_edges().

            in_edges(self, nbunch=None, data=False, default=None):

            Parameters
            ----------
            nbunch : single node, container, or all nodes (default= all nodes)
                The view will only report edges incident to 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
            -------
            in_edges : InEdgeView or InEdgeDataView
                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']`.

            Examples
            --------
            >>> G = nx.DiGraph()
            >>> G.add_edge(1, 2, color="blue")
            >>> G.in_edges()
            InEdgeView([(1, 2)])
            >>> G.in_edges(nbunch=2)
            InEdgeDataView([(1, 2)])

            See Also
            --------
            edges
            """
            return InEdgeView(self)

        @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
            -------
            DiDegreeView or int
                If multiple nodes are requested (the default), returns a `DiDegreeView`
                mapping nodes to their degree.
                If a single node is requested, returns the degree of the node as an integer.

            See Also
            --------
            in_degree, out_degree

            Examples
            --------
            >>> G = nx.DiGraph()  # or MultiDiGraph
            >>> nx.add_path(G, [0, 1, 2, 3])
            >>> G.degree(0)  # node 0 with degree 1
            1
            >>> list(G.degree([0, 1, 2]))
            [(0, 1), (1, 2), (2, 2)]

            """
            return DiDegreeView(self)

        @cached_property
        def in_degree(self):
            """An InDegreeView for (node, in_degree) or in_degree for single node.

            The node in_degree is the number of edges pointing to the node.
            The weighted node degree is the sum of the edge weights for
            edges incident to that node.

            This object provides an iteration over (node, in_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
            -------
            If a single node is requested
            deg : int
                In-degree of the node

            OR if multiple nodes are requested
            nd_iter : iterator
                The iterator returns two-tuples of (node, in-degree).

            See Also
            --------
            degree, out_degree

            Examples
            --------
            >>> G = nx.DiGraph()
            >>> nx.add_path(G, [0, 1, 2, 3])
            >>> G.in_degree(0)  # node 0 with degree 0
            0
            >>> list(G.in_degree([0, 1, 2]))
            [(0, 0), (1, 1), (2, 1)]

            """
            return InDegreeView(self)

        @cached_property
        def out_degree(self):
            """An OutDegreeView for (node, out_degree)

            The node out_degree is the number of edges pointing out of the node.
            The weighted node degree is the sum of the edge weights for
            edges incident to that node.

            This object provides an iterator over (node, out_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
            -------
            If a single node is requested
            deg : int
                Out-degree of the node

            OR if multiple nodes are requested
            nd_iter : iterator
                The iterator returns two-tuples of (node, out-degree).

            See Also
            --------
            degree, in_degree

            Examples
            --------
            >>> G = nx.DiGraph()
            >>> nx.add_path(G, [0, 1, 2, 3])
            >>> G.out_degree(0)  # node 0 with degree 1
            1
            >>> list(G.out_degree([0, 1, 2]))
            [(0, 1), (1, 1), (2, 1)]

            """
            return OutDegreeView(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._succ.clear()
            self._pred.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 predecessor_dict in self._pred.values():
                predecessor_dict.clear()
            for successor_dict in self._succ.values():
                successor_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 True

        def to_undirected(self, reciprocal=False, as_view=False):
            """Returns an undirected representation of the digraph.

            Parameters
            ----------
            reciprocal : bool (optional)
              If True only keep edges that appear in both directions
              in the original digraph.
            as_view : bool (optional, default=False)
              If True return an undirected view of the original directed graph.

            Returns
            -------
            G : Graph
                An undirected graph with the same name and nodes and
                with edge (u, v, data) if either (u, v, data) or (v, u, data)
                is in the digraph.  If both edges exist in digraph and
                their edge data is different, only one edge is created
                with an arbitrary choice of which edge data to use.
                You must check and correct for this manually if desired.

            See Also
            --------
            Graph, copy, add_edge, add_edges_from

            Notes
            -----
            If edges in both directions (u, v) and (v, u) exist in the
            graph, attributes for the new undirected edge will be a combination of
            the attributes of the directed edges.  The edge data is updated
            in the (arbitrary) order that the edges are encountered.  For
            more customized control of the edge attributes use add_edge().

            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=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())
            if reciprocal is True:
                G.add_edges_from(
                    (u, v, deepcopy(d))
                    for u, nbrs in self._adj.items()
                    for v, d in nbrs.items()
                    if v in self._pred[u]
                )
            else:
                G.add_edges_from(
                    (u, v, deepcopy(d))
                    for u, nbrs in self._adj.items()
                    for v, d in nbrs.items()
                )
            return G

        def reverse(self, copy=True):
            """Returns the reverse of the graph.

            The reverse is a graph with the same nodes and edges
            but with the directions of the edges reversed.

            Parameters
            ----------
            copy : bool optional (default=True)
                If True, return a new DiGraph holding the reversed edges.
                If False, the reverse graph is created using a view of
                the original graph.
            """
            if copy:
                H = self.__class__()
                H.graph.update(deepcopy(self.graph))
                H.add_nodes_from((n, deepcopy(d)) for n, d in self.nodes.items())
                H.add_edges_from((v, u, deepcopy(d)) for u, v, d in self.edges(data=True))
                return H
            return nx.reverse_view(self)