text: """Base class for directed graphs."""
  #    Copyright (C) 2004-2015 by
  #    Aric Hagberg <hagberg@lanl.gov>
  #    Dan Schult <dschult@colgate.edu>
  #    Pieter Swart <swart@lanl.gov>
  #    All rights reserved.
  #    BSD license.
  from copy import deepcopy
  import networkx as nx
  from networkx.classes.graph import Graph
  from networkx.exception import NetworkXError
  import networkx.convert as convert
  __author__ = """\n""".join(['Aric Hagberg (hagberg@lanl.gov)',
                              'Pieter Swart (swart@lanl.gov)',
                              'Dan Schult(dschult@colgate.edu)'])
  
  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.
  
      Edges are represented as links between nodes with optional
      key/value attributes.
  
      Parameters
      ----------
      data : input graph
          Data to initialize graph.  If data=None (default) an empty
          graph is created.  The data can be an edge list, or any
          NetworkX graph object.  If the corresponding optional Python
          packages are installed the data can also be a NumPy matrix
          or 2d ndarray, a SciPy sparse matrix, or a 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.Graph()
      >>> H.add_path([0,1,2,3,4,5,6,7,8,9])
      >>> 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.node
  
      >>> G.add_node(1, time='5pm')
      >>> G.add_nodes_from([3], time='2pm')
      >>> G.node[1]
      {'time': '5pm'}
      >>> G.node[1]['room'] = 714
      >>> del G.node[1]['room'] # remove attribute
      >>> list(G.nodes(data=True))
      [(1, {'time': '5pm'}), (3, {'time': '2pm'})]
  
      Warning: adding a node to G.node does not add it to the graph.
  
      Add edge attributes using add_edge(), add_edges_from(), subscript
      notation, or G.edge.
  
      >>> 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.edge[1][2]['weight'] = 4
  
      **Shortcuts:**
  
      Many common graph features allow python syntax to speed reporting.
  
      >>> 1 in G     # check if node in graph
      True
      >>> [n for n in G if n<3]   # iterate through nodes
      [1, 2]
      >>> len(G)  # number of nodes in graph
      5
  
      The fastest way to traverse all edges of a graph is via
      adjacency(), but the edges() method is often more convenient.
  
      >>> for n,nbrsdict in G.adjacency():
      ...     for nbr,eattr in nbrsdict.items():
      ...        if 'weight' in eattr:
      ...            (n,nbr,eattr['weight'])
      (1, 2, 4)
      (2, 3, 8)
      >>> list(G.edges(data='weight'))
      [(1, 2, 4), (2, 3, 8), (3, 4, None), (4, 5, None)]
  
      **Reporting:**
  
      Simple graph information is obtained using methods.
      Reporting methods usually return iterators instead of containers
      to reduce memory usage.
      Methods exist for reporting nodes(), edges(), neighbors() and degree()
      as well as the number of nodes and edges.
  
      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, adjlist_dict_factory and edge_attr_dict_factory.
  
      node_dict_factory : function, optional (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_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 attrbute values keyed by attribute name.
          It should require no arguments and return a dict-like object.
  
      Examples
      --------
      Create a graph subclass that tracks the order nodes are added.
  
      >>> from collections import OrderedDict
      >>> class OrderedNodeGraph(nx.Graph):
      ...     node_dict_factory=OrderedDict
      >>> G=OrderedNodeGraph()
      >>> G.add_nodes_from( (2,1) )
      >>> list(G.nodes())
      [2, 1]
      >>> G.add_edges_from( ((2,2), (2,1), (1,1)) )
      >>> list(G.edges())
      [(2, 1), (2, 2), (1, 1)]
  
      Create a graph object that tracks the order nodes are added
      and for each node track the order that neighbors are added.
  
      >>> class OrderedGraph(nx.Graph):
      ...    node_dict_factory = OrderedDict
      ...    adjlist_dict_factory = OrderedDict
      >>> G = OrderedGraph()
      >>> G.add_nodes_from( (2,1) )
      >>> list(G.nodes())
      [2, 1]
      >>> G.add_edges_from( ((2,2), (2,1), (1,1)) )
      >>> list(G.edges())
      [(2, 2), (2, 1), (1, 1)]
  
      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)
      >>> list(G.edges(data= True))
      [(1, 2, {'weight': 1})]
      >>> G.add_edge(2,2)
      >>> G[2][1] is G[2][2]
      True
  
      """
      def __init__(self, data=None, **attr):
          """Initialize a graph with edges, name, graph attributes.
  
          Parameters
          ----------
          data : input graph
              Data to initialize graph.  If data=None (default) an empty
              graph is created.  The data can be an edge list, or any
              NetworkX graph object.  If the corresponding optional Python
              packages are installed the data can also be a NumPy matrix
              or 2d ndarray, a SciPy sparse matrix, or a PyGraphviz graph.
          name : string, optional (default='')
              An optional name for the 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.node_dict_factory = ndf = self.node_dict_factory
          self.adjlist_dict_factory = self.adjlist_dict_factory
          self.edge_attr_dict_factory = self.edge_attr_dict_factory
  
          self.graph = {} # dictionary for graph attributes
          self.node = ndf() # dictionary for node attributes
          # 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 = ndf()  # empty adjacency dictionary
          self.pred = ndf()  # predecessor
          self.succ = self.adj  # successor
  
          # attempt to load graph with data
          if data is not None:
              convert.to_networkx_graph(data,create_using=self)
          # load graph attributes (must be after convert)
          self.graph.update(attr)
          self.edge=self.adj
  
  
      def add_node(self, n, attr_dict=None, **attr):
          """Add a single node n and update node attributes.
  
          Parameters
          ----------
          n : node
              A node can be any hashable Python object except None.
          attr_dict : dictionary, optional (default= no attributes)
              Dictionary of node attributes.  Key/value pairs will
              update existing data associated with the node.
          attr : keyword arguments, optional
              Set or change 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.
          """
          # set up attribute dict
          if attr_dict is None:
              attr_dict=attr
          else:
              try:
                  attr_dict.update(attr)
              except AttributeError:
                  raise NetworkXError(\
                      "The attr_dict argument must be a dictionary.")
          if n not in self.succ:
              self.succ[n] = self.adjlist_dict_factory()
              self.pred[n] = self.adjlist_dict_factory()
              self.node[n] = attr_dict
          else: # update attr even if node already exists
              self.node[n].update(attr_dict)
  
  
      def add_nodes_from(self, nodes, **attr):
          """Add multiple nodes.
  
          Parameters
          ----------
          nodes : 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 generally.
  
          See Also
          --------
          add_node
  
          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.node[1]['size']
          11
          >>> H = nx.Graph()
          >>> H.add_nodes_from(G.nodes(data=True))
          >>> H.node[1]['size']
          11
  
          """
          for n in nodes:
              # keep all this inside try/except because
              # CPython throws TypeError on n not in self.succ,
              # while pre-2.7.5 ironpython throws on self.succ[n] 
              try:
                  if n not in self.succ:
                      self.succ[n] = self.adjlist_dict_factory()
                      self.pred[n] = self.adjlist_dict_factory()
                      self.node[n] = attr.copy()
                  else:
                      self.node[n].update(attr)
              except TypeError:
                  nn,ndict = n
                  if nn not in self.succ:
                      self.succ[nn] = self.adjlist_dict_factory()
                      self.pred[nn] = self.adjlist_dict_factory()
                      newdict = attr.copy()
                      newdict.update(ndict)
                      self.node[nn] = newdict
                  else:
                      olddict = self.node[nn]
                      olddict.update(attr)
                      olddict.update(ndict)
  
      def remove_node(self, n):
          """Remove node n.
  
          Removes the node n and all adjacent edges.
          Attempting to remove a non-existent 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.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2])
          >>> 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: # NetworkXError if n not in self
              raise NetworkXError("The node %s is not in the digraph."%(n,))
          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
  
  
      def remove_nodes_from(self, nbunch):
          """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
  
          Examples
          --------
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2])
          >>> e = list(G.nodes())
          >>> e
          [0, 1, 2]
          >>> G.remove_nodes_from(e)
          >>> list(G.nodes())
          []
  
          """
          for n in nbunch:
              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
  
  
      def add_edge(self, u, v, attr_dict=None, **attr):
          """Add an edge between u and v.
  
          The nodes u and v will be automatically added if they are
          not already in the graph.
  
          Edge attributes can be specified with keywords or by providing
          a dictionary with key/value pairs.  See examples below.
  
          Parameters
          ----------
          u, v : nodes
              Nodes can be, for example, strings or numbers.
              Nodes must be hashable (and not None) Python objects.
          attr_dict : dictionary, optional (default= no attributes)
              Dictionary of edge attributes.  Key/value pairs will
              update existing data associated with the edge.
          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 as
          the edge weight a numerical value assigned to a keyword
          which by default is 'weight'.
  
          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)
          """
          # set up attribute dict
          if attr_dict is None:
              attr_dict=attr
          else:
              try:
                  attr_dict.update(attr)
              except AttributeError:
                  raise NetworkXError(\
                      "The attr_dict argument must be a dictionary.")
          # add nodes
          if u not in self.succ:
              self.succ[u]= self.adjlist_dict_factory()
              self.pred[u]= self.adjlist_dict_factory()
              self.node[u] = {}
          if v not in self.succ:
              self.succ[v]= self.adjlist_dict_factory()
              self.pred[v]= self.adjlist_dict_factory()
              self.node[v] = {}
          # add the edge
          datadict=self.adj[u].get(v,self.edge_attr_dict_factory())
          datadict.update(attr_dict)
          self.succ[u][v]=datadict
          self.pred[v][u]=datadict
  
      def add_edges_from(self, ebunch, attr_dict=None, **attr):
          """Add all the edges in ebunch.
  
          Parameters
          ----------
          ebunch : container of edges
              Each edge given in the container will be added to the
              graph. The edges must be given as as 2-tuples (u,v) or
              3-tuples (u,v,d) where d is a dictionary containing edge
              data.
          attr_dict : dictionary, optional (default= no attributes)
              Dictionary of edge attributes.  Key/value pairs will
              update existing data associated with each edge.
          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 edges take precedence
          over attributes specified generally.
  
          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')
          """
          # set up attribute dict
          if attr_dict is None:
              attr_dict=attr
          else:
              try:
                  attr_dict.update(attr)
              except AttributeError:
                  raise NetworkXError(\
                      "The attr_dict argument must be a dict.")
          # process ebunch
          for e in ebunch:
              ne = len(e)
              if ne==3:
                  u,v,dd = e
                  assert hasattr(dd,"update")
              elif ne==2:
                  u,v = e
                  dd = {}
              else:
                  raise NetworkXError(\
                      "Edge tuple %s must be a 2-tuple or 3-tuple."%(e,))
              if u not in self.succ:
                  self.succ[u] = self.adjlist_dict_factory()
                  self.pred[u] = self.adjlist_dict_factory()
                  self.node[u] = {}
              if v not in self.succ:
                  self.succ[v] = self.adjlist_dict_factory()
                  self.pred[v] = self.adjlist_dict_factory()
                  self.node[v] = {}
              datadict=self.adj[u].get(v,self.edge_attr_dict_factory())
              datadict.update(attr_dict)
              datadict.update(dd)
              self.succ[u][v] = datadict
              self.pred[v][u] = datadict
  
  
      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
          >>> G.add_path([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:
              raise NetworkXError("The edge %s-%s not in graph."%(u,v))
  
  
      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.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2,3])
          >>> 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]
  
  
      def has_successor(self, u, v):
          """Return 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):
          """Return 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):
          """Return an iterator over successor nodes of n.
  
          neighbors() and successors() are the same.
          """
          try:
              return iter(self.succ[n])
          except KeyError:
              raise NetworkXError("The node %s is not in the digraph."%(n,))
  
      def predecessors(self,n):
          """Return an iterator over predecessor nodes of n."""
          try:
              return iter(self.pred[n])
          except KeyError:
              raise NetworkXError("The node %s is not in the digraph."%(n,))
  
      # digraph definitions
      neighbors = successors
  
      def edges(self, nbunch=None, data=False, default=None):
          """Return an iterator over the edges.
  
          Edges are returned as tuples with optional data
          in the order (node, neighbor, data).
  
          Parameters
          ----------
          nbunch : iterable container, optional (default= all nodes)
              A container of nodes.  The container will be iterated
              through once.
          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 dont have the requested attribute.
              Only relevant if data is not True or False.
  
          Returns
          -------
          edge : iterator
              An iterator over (u,v) or (u,v,d) tuples of edges.
  
          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
          >>> G.add_path([0,1,2])
          >>> G.add_edge(2,3,weight=5)
          >>> [e for e in G.edges()]
          [(0, 1), (1, 2), (2, 3)]
          >>> list(G.edges(data=True)) # default data is {} (empty dict)
          [(0, 1, {}), (1, 2, {}), (2, 3, {'weight': 5})]
          >>> list(G.edges(data='weight', default=1)) 
          [(0, 1, 1), (1, 2, 1), (2, 3, 5)]
          >>> list(G.edges([0,2]))
          [(0, 1), (2, 3)]
          >>> list(G.edges(0))
          [(0, 1)]
  
          """
          if nbunch is None:
              nodes_nbrs=self.adj.items()
          else:
              nodes_nbrs=((n,self.adj[n]) for n in self.nbunch_iter(nbunch))
          if data is True:
              for n,nbrs in nodes_nbrs:
                  for nbr,ddict in nbrs.items():
                      yield (n,nbr,ddict)
          elif data is not False:
              for n,nbrs in nodes_nbrs:
                  for nbr,ddict in nbrs.items():
                      d=ddict[data] if data in ddict else default
                      yield (n,nbr,d)
          else:
              for n,nbrs in nodes_nbrs:
                  for nbr in nbrs:
                      yield (n,nbr)
  
      # alias out_edges to edges
      out_edges = edges
  
      def in_edges(self, nbunch=None, data=False):
          """Return an iterator over the incoming edges.
  
          Parameters
          ----------
          nbunch : iterable container, optional (default= all nodes)
              A container of nodes.  The container will be iterated
              through once.
          data : bool, optional (default=False)
              If True, return edge attribute dict in 3-tuple (u,v,data).
  
          Returns
          -------
          in_edge : iterator
              An iterator over (u,v) or (u,v,d) tuples of incoming edges.
  
          See Also
          --------
          edges : return an iterator over edges
          """
          if nbunch is None:
              nodes_nbrs=self.pred.items()
          else:
              nodes_nbrs=((n,self.pred[n]) for n in self.nbunch_iter(nbunch))
          if data:
              for n,nbrs in nodes_nbrs:
                  for nbr,data in nbrs.items():
                      yield (nbr,n,data)
          else:
              for n,nbrs in nodes_nbrs:
                  for nbr in nbrs:
                      yield (nbr,n)
  
  
      def degree(self, nbunch=None, weight=None):
          """Return an iterator for (node, degree) or degree for single node.
  
          The node degree is the number of edges adjacent to the node.
          This function returns the degree for a single node or an iterator
          for a bunch of nodes or if nothing is passed as argument.
  
          Parameters
          ----------
          nbunch : iterable container, optional (default=all nodes)
              A container of nodes.  The container will be iterated
              through once.
  
          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.
             The degree is the sum of the edge weights adjacent to the node.
  
          Returns
          -------
          If a single node is requested
          deg : int
              Degree of the node
  
          OR if multiple nodes are requested
          nd_iter : iterator
              The iterator returns two-tuples of (node, degree).
  
          See Also
          --------
          in_degree, out_degree
  
          Examples
          --------
          >>> G = nx.DiGraph()   # or MultiDiGraph
          >>> G.add_path([0,1,2,3])
          >>> G.degree(0) # node 0 with degree 1
          1
          >>> list(G.degree([0,1]))
          [(0, 1), (1, 2)]
  
          """
          # Test to see if nbunch is a single node, an iterator of nodes or
          # None(indicating all nodes). (nbunch in self) is True when nbunch
          # is a single node.
          if nbunch in self:
              succ = self.succ[nbunch]
              pred = self.pred[nbunch]
              if weight is None:
                  return len(succ) + len(pred)
              return sum(data.get(weight, 1) for data in succ.values()) + \
                     sum(data.get(weight, 1) for data in pred.values())
  
          if nbunch is None:
              nodes_nbrs=( (n,succs,self.pred[n]) for n,succs in self.succ.items())
          else:
              nodes_nbrs=( (n,self.succ[n],self.pred[n]) for n in self.nbunch_iter(nbunch))
          if weight is None:
              def d_iter():
                  for n,succ,pred in nodes_nbrs:
                      yield (n,len(succ)+len(pred))
          else:
              def d_iter():
                  for n,succ,pred in nodes_nbrs:
                      yield (n,
                        sum((data.get(weight,1) for data in succ.values()))+
                        sum((data.get(weight,1) for data in pred.values())))
          return d_iter()
  
  
      def in_degree(self, nbunch=None, weight=None):
          """Return an iterator for (node, in-degree) or in-degree for single node.
  
          The node in-degree is the number of edges pointing in to the node.
          This function returns the in-degree for a single node or an iterator
          for a bunch of nodes or if nothing is passed as argument.
  
          Parameters
          ----------
          nbunch : iterable container, optional (default=all nodes)
              A container of nodes.  The container will be iterated
              through once.
  
          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.
             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()
          >>> G.add_path([0,1,2,3])
          >>> G.in_degree(0) # node 0 with degree 0
          0
          >>> list(G.in_degree([0,1]))
          [(0, 0), (1, 1)]
  
          """
          # Test to see if nbunch is a single node, an iterator of nodes or
          # None(indicating all nodes). (nbunch in self) is True when nbunch
          # is a single node.
          if nbunch in self:
              pred = self.pred[nbunch]
              if weight is None:
                  return len(pred)
              return sum(data.get(weight, 1) for data in pred.values())
  
          if nbunch is None:
              nodes_nbrs=self.pred.items()
          else:
              nodes_nbrs=((n,self.pred[n]) for n in self.nbunch_iter(nbunch))
  
          if weight is None:
              def d_iter():
                  for n,nbrs in nodes_nbrs:
                      yield (n,len(nbrs))
          else:
          # edge weighted graph - degree is sum of edge weights
              def d_iter():
                  for n,nbrs in nodes_nbrs:
                      yield (n, sum(data.get(weight,1) for data in nbrs.values()))
          return d_iter()
  
  
      def out_degree(self, nbunch=None, weight=None):
          """Return an iterator for (node, out-degree) or out-degree for single node.
  
          The node out-degree is the number of edges pointing out of the node.
          This function returns the out-degree for a single node or an iterator
          for a bunch of nodes or if nothing is passed as argument.
  
          Parameters
          ----------
          nbunch : iterable container, optional (default=all nodes)
              A container of nodes.  The container will be iterated
              through once.
  
          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.
             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()
          >>> G.add_path([0,1,2,3])
          >>> G.out_degree(0) # node 0 with degree 1
          1
          >>> list(G.out_degree([0,1]))
          [(0, 1), (1, 1)]
  
          """
          # Test to see if nbunch is a single node, an iterator of nodes or
          # None(indicating all nodes). (nbunch in self) is True when nbunch
          # is a single node.
          if nbunch in self:
              succ = self.succ[nbunch]
              if weight is None:
                  return len(succ)
              return sum(data.get(weight, 1) for data in succ.values())
  
          if nbunch is None:
              nodes_nbrs=self.succ.items()
          else:
              nodes_nbrs=((n,self.succ[n]) for n in self.nbunch_iter(nbunch))
  
          if weight is None:
              def d_iter():
                  for n,nbrs in nodes_nbrs:
                      yield (n,len(nbrs))
          else:
          # edge weighted graph - degree is sum of edge weights
              def d_iter():
                  for n,nbrs in nodes_nbrs:
                      yield (n, sum(data.get(weight,1) for data in nbrs.values()))
          return d_iter()
  
      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.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2,3])
          >>> G.clear()
          >>> list(G.nodes())
          []
          >>> list(G.edges())
          []
  
          """
          self.succ.clear()
          self.pred.clear()
          self.node.clear()
          self.graph.clear()
  
  
      def is_multigraph(self):
          """Return True if graph is a multigraph, False otherwise."""
          return False
  
  
      def is_directed(self):
          """Return True if graph is directed, False otherwise."""
          return True
  
      def to_directed(self):
          """Return a directed copy of the graph.
  
          Returns
          -------
          G : DiGraph
              A deepcopy of the graph.
  
          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, http://docs.python.org/library/copy.html.
  
          Examples
          --------
          >>> G = nx.Graph()   # or MultiGraph, etc
          >>> G.add_path([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_path([0,1])
          >>> H = G.to_directed()
          >>> list(H.edges())
          [(0, 1)]
          """
          return deepcopy(self)
  
      def to_undirected(self, reciprocal=False):
          """Return an undirected representation of the digraph.
  
          Parameters
          ----------
          reciprocal : bool (optional)
            If True only keep edges that appear in both directions
            in the original digraph.
  
          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.
  
          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, http://docs.python.org/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.
          """
          H=Graph()
          H.name=self.name
          H.add_nodes_from(self)
          if reciprocal is True:
              H.add_edges_from( (u,v,deepcopy(d))
                                for u,nbrs in self.adjacency()
                                for v,d in nbrs.items()
                                if v in self.pred[u])
          else:
              H.add_edges_from( (u,v,deepcopy(d))
                                for u,nbrs in self.adjacency()
                                for v,d in nbrs.items() )
          H.graph=deepcopy(self.graph)
          H.node=deepcopy(self.node)
          return H
  
  
      def reverse(self, copy=True):
          """Return 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, reverse the reverse graph is created using
              the original graph (this changes the original graph).
          """
          if copy:
              H = self.__class__(name="Reverse of (%s)"%self.name)
              H.add_nodes_from(self)
              H.add_edges_from( (v,u,deepcopy(d)) for u,v,d
                                in self.edges(data=True) )
              H.graph=deepcopy(self.graph)
              H.node=deepcopy(self.node)
          else:
              self.pred,self.succ=self.succ,self.pred
              self.adj=self.succ
              H=self
          return H
  
  
      def subgraph(self, nbunch):
          """Return the subgraph induced on nodes in nbunch.
  
          The induced subgraph of the graph contains the nodes in nbunch
          and the edges between those nodes.
  
          Parameters
          ----------
          nbunch : list, iterable
              A container of nodes which will be iterated through once.
  
          Returns
          -------
          G : Graph
              A subgraph of the graph with the same edge attributes.
  
          Notes
          -----
          The graph, edge or node attributes just point to the original graph.
          So changes to the node or edge structure will not be reflected in
          the original graph while changes to the attributes will.
  
          To create a subgraph with its own copy of the edge/node attributes use:
          nx.Graph(G.subgraph(nbunch))
  
          If edge attributes are containers, a deep copy can be obtained using:
          G.subgraph(nbunch).copy()
  
          For an inplace reduction of a graph to a subgraph you can remove nodes:
          G.remove_nodes_from([ n in G if n not in set(nbunch)])
  
          Examples
          --------
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2,3])
          >>> H = G.subgraph([0,1,2])
          >>> list(H.edges())
          [(0, 1), (1, 2)]
          """
          bunch = self.nbunch_iter(nbunch)
          # create new graph and copy subgraph into it
          H = self.__class__()
          # copy node and attribute dictionaries
          for n in bunch:
              H.node[n]=self.node[n]
          # namespace shortcuts for speed
          H_succ=H.succ
          H_pred=H.pred
          self_succ=self.succ
          # add nodes
          for n in H:
              H_succ[n]=H.adjlist_dict_factory()
              H_pred[n]=H.adjlist_dict_factory()
          # add edges
          for u in H_succ:
              Hnbrs=H_succ[u]
              for v,datadict in self_succ[u].items():
                  if v in H_succ:
                      # add both representations of edge: u-v and v-u
                      Hnbrs[v]=datadict
                      H_pred[v][u]=datadict
          H.graph=self.graph
          return H
  