text: """Base class for undirected graphs.
  
  The Graph class allows any hashable object as a node
  and can associate key/value attribute pairs with each undirected edge.
  
  Self-loops are allowed but multiple edges are not (see MultiGraph).
  
  For directed graphs see DiGraph and MultiDiGraph.
  """
  #    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.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 Graph(object):
      """
      Base class for undirected graphs.
  
      A Graph stores nodes and edges with optional data, or attributes.
  
      Graphs hold undirected edges.  Self loops are allowed but multiple
      (parallel) edges are not.
  
      Nodes can be arbitrary (hashable) Python objects with optional
      key/value attributes.
  
      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
      --------
      DiGraph
      MultiGraph
      MultiDiGraph
  
      Examples
      --------
      Create an empty graph structure (a "null graph") with no nodes and
      no edges.
  
      >>> G = nx.Graph()
  
      G can be grown in several ways.
  
      **Nodes:**
  
      Add one node at a time:
  
      >>> G.add_node(1)
  
      Add the nodes from any container (a list, dict, set or
      even the lines from a file or the nodes from another graph).
  
      >>> G.add_nodes_from([2,3])
      >>> G.add_nodes_from(range(100,110))
      >>> H=nx.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.Graph(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
      >>> 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_iter(), but the edges() method is often more convenient.
  
      >>> for n,nbrsdict in G.adjacency_iter():
      ...     for nbr,eattr in nbrsdict.items():
      ...        if 'weight' in eattr:
      ...            (n,nbr,eattr['weight'])
      (1, 2, 4)
      (2, 1, 4)
      (2, 3, 8)
      (3, 2, 8)
      >>> G.edges(data='weight')
      [(1, 2, 4), (2, 3, 8), (3, 4, None), (4, 5, None)]
  
      **Reporting:**
  
      Simple graph information is obtained using methods.
      Iterator versions of many reporting methods exist for efficiency.
      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 lists keyed by node.
      The next dict (adjlist) represents the adjacency list and holds
      edge data keyed by neighbor.  The inner dict (edge_attr) represents
      the edge data and holds edge attribute values keyed by attribute names.
  
      Each of these three dicts can be replaced by a user defined
      dict-like object. In general, the dict-like features should be
      maintained but extra features can be added. To replace one of the
      dicts create a new graph class by changing the class(!) variable
      holding the factory for that dict-like structure. The variable names
      are node_dict_factory, adjlist_dict_factory and edge_attr_dict_factory.
  
      node_dict_factory : function, (default: dict)
          Factory function to be used to create the outer-most dict
          in the data structure that holds adjacency lists keyed by node.
          It should require no arguments and return a dict-like object.
  
      adjlist_dict_factory : function, (default: dict)
          Factory function to be used to create the adjacency list
          dict which holds edge data keyed by neighbor.
          It should require no arguments and return a dict-like object
  
      edge_attr_dict_factory : function, (default: dict)
          Factory function to be used to create the edge attribute
          dict which holds attrbute values keyed by attribute name.
          It should require no arguments and return a dict-like object.
  
      Examples
      --------
      Create a graph object 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) )
      >>> G.nodes()
      [2, 1]
      >>> G.add_edges_from( ((2,2), (2,1), (1,1)) )
      >>> 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) )
      >>> G.nodes()
      [2, 1]
      >>> G.add_edges_from( ((2,2), (2,1), (1,1)) )
      >>> 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)
      >>> G.edges(data= True)
      [(1, 2, {'weight': 1})]
      >>> G.add_edge(2,2)
      >>> G[2][1] is G[2][2]
      True
  
      """
      node_dict_factory = dict
      adjlist_dict_factory = dict
      edge_attr_dict_factory = dict
  
      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()  # empty node attribute dict
          self.adj = ndf()  # empty adjacency dict
          # 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
  
      @property
      def name(self):
          return self.graph.get('name', '')
  
      @name.setter
      def name(self, s):
          self.graph['name'] = s
  
      def __str__(self):
          """Return the graph name.
  
          Returns
          -------
          name : string
              The name of the graph.
  
          Examples
          --------
          >>> G = nx.Graph(name='foo')
          >>> str(G)
          'foo'
          """
          return self.name
  
      def __iter__(self):
          """Iterate over the nodes. Use the expression 'for n in G'.
  
          Returns
          -------
          niter : iterator
              An iterator over all nodes in the graph.
  
          Examples
          --------
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2,3])
          """
          return iter(self.node)
  
      def __contains__(self, n):
          """Return True if n is a node, False otherwise. Use the expression
          'n in G'.
  
          Examples
          --------
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2,3])
          >>> 1 in G
          True
          """
          try:
              return n in self.node
          except TypeError:
              return False
  
      def __len__(self):
          """Return the number of nodes. Use the expression 'len(G)'.
  
          Returns
          -------
          nnodes : int
              The number of nodes in the graph.
  
          Examples
          --------
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2,3])
          >>> len(G)
          4
  
          """
          return len(self.node)
  
      def __getitem__(self, n):
          """Return a dict of neighbors of node n.  Use the expression 'G[n]'.
  
          Parameters
          ----------
          n : node
             A node in the graph.
  
          Returns
          -------
          adj_dict : dictionary
             The adjacency dictionary for nodes connected to n.
  
          Notes
          -----
          G[n] is similar to G.neighbors(n) but the internal data dictionary
          is returned instead of a list.
  
          Assigning G[n] will corrupt the internal graph data structure.
          Use G[n] for reading data only.
  
          Examples
          --------
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2,3])
          >>> G[0]
          {1: {}}
          """
          return self.adj[n]
  
      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.node:
              self.adj[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.node:
                      self.adj[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.node:
                      self.adj[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])
          >>> G.edges()
          [(0, 1), (1, 2)]
          >>> G.remove_node(1)
          >>> G.edges()
          []
  
          """
          adj = self.adj
          try:
              nbrs = list(adj[n].keys())  # keys handles self-loops (allow mutation later)
              del self.node[n]
          except KeyError:  # NetworkXError if n not in self
              raise NetworkXError("The node %s is not in the graph." % (n,))
          for u in nbrs:
              del adj[u][n]   # remove all edges n-u in graph
          del adj[n]          # now remove node
  
      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
  
          Examples
          --------
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2])
          >>> e = G.nodes()
          >>> e
          [0, 1, 2]
          >>> G.remove_nodes_from(e)
          >>> G.nodes()
          []
  
          """
          adj = self.adj
          for n in nodes:
              try:
                  del self.node[n]
                  for u in list(adj[n].keys()):   # keys() handles self-loops
                      del adj[u][n]  # (allows mutation of dict in loop)
                  del adj[n]
              except KeyError:
                  pass
  
      def nodes_iter(self, data=False):
          """Return an iterator over the nodes.
  
          Parameters
          ----------
          data : boolean, optional (default=False)
                 If False the iterator returns nodes.  If True
                 return a two-tuple of node and node data dictionary
  
          Returns
          -------
          niter : iterator
              An iterator over nodes.  If data=True the iterator gives
              two-tuples containing (node, node data, dictionary)
  
          Notes
          -----
          If the node data is not required it is simpler and equivalent
          to use the expression 'for n in G'.
  
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2])
  
          Examples
          --------
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2])
  
          >>> [d for n,d in G.nodes_iter(data=True)]
          [{}, {}, {}]
          """
          if data:
              return iter(self.node.items())
          return iter(self.node)
  
      def nodes(self, data=False):
          """Return a list of the nodes in the graph.
  
          Parameters
          ----------
          data : boolean, optional (default=False)
                 If False return a list of nodes.  If True return a
                 two-tuple of node and node data dictionary
  
          Returns
          -------
          nlist : list
              A list of nodes.  If data=True a list of two-tuples containing
              (node, node data dictionary).
  
          Examples
          --------
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2])
          >>> G.nodes()
          [0, 1, 2]
          >>> G.add_node(1, time='5pm')
          >>> G.nodes(data=True)
          [(0, {}), (1, {'time': '5pm'}), (2, {})]
          """
          return list(self.nodes_iter(data=data))
  
      def number_of_nodes(self):
          """Return the number of nodes in the graph.
  
          Returns
          -------
          nnodes : int
              The number of nodes in the graph.
  
          See Also
          --------
          order, __len__  which are identical
  
          Examples
          --------
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2])
          >>> len(G)
          3
          """
          return len(self.node)
  
      def order(self):
          """Return the number of nodes in the graph.
  
          Returns
          -------
          nnodes : int
              The number of nodes in the graph.
  
          See Also
          --------
          number_of_nodes, __len__  which are identical
  
          """
          return len(self.node)
  
      def has_node(self, n):
          """Return True if the graph contains the node n.
  
          Parameters
          ----------
          n : node
  
          Examples
          --------
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2])
          >>> G.has_node(0)
          True
  
          It is more readable and simpler to use
  
          >>> 0 in G
          True
  
          """
          try:
              return n in self.node
          except TypeError:
              return False
  
      def add_edge(self, u, 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 dictionary
          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.node:
              self.adj[u] = self.adjlist_dict_factory()
              self.node[u] = {}
          if v not in self.node:
              self.adj[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.adj[u][v] = datadict
          self.adj[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 dictionary.")
          # process ebunch
          for e in ebunch:
              ne = len(e)
              if ne == 3:
                  u, v, dd = e
              elif ne == 2:
                  u, v = e
                  dd = {}  # doesnt need edge_attr_dict_factory
              else:
                  raise NetworkXError(
                      "Edge tuple %s must be a 2-tuple or 3-tuple." % (e,))
              if u not in self.node:
                  self.adj[u] = self.adjlist_dict_factory()
                  self.node[u] = {}
              if v not in self.node:
                  self.adj[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.adj[u][v] = datadict
              self.adj[v][u] = datadict
  
      def add_weighted_edges_from(self, ebunch, weight='weight', **attr):
          """Add all the edges in ebunch as weighted edges with specified
          weights.
  
          Parameters
          ----------
          ebunch : container of edges
              Each edge given in the list or container will be added
              to the graph. The edges must be given as 3-tuples (u,v,w)
              where w is a number.
          weight : string, optional (default= 'weight')
              The attribute name for the edge weights to be added.
          attr : keyword arguments, optional (default= no attributes)
              Edge attributes to add/update for all edges.
  
          See Also
          --------
          add_edge : add a single edge
          add_edges_from : add multiple edges
  
          Notes
          -----
          Adding the same edge twice for Graph/DiGraph simply updates
          the edge data.  For MultiGraph/MultiDiGraph, duplicate edges
          are stored.
  
          Examples
          --------
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_weighted_edges_from([(0,1,3.0),(1,2,7.5)])
          """
          self.add_edges_from(((u, v, {weight: d}) for u, v, d in ebunch), **attr)
  
      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.adj[u][v]
              if u != v:  # self-loop needs only one entry removed
                  del self.adj[v][u]
          except KeyError:
              raise NetworkXError("The edge %s-%s is not in the 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)
          """
          adj = self.adj
          for e in ebunch:
              u, v = e[:2]  # ignore edge data if present
              if u in adj and v in adj[u]:
                  del adj[u][v]
                  if u != v:  # self loop needs only one entry removed
                      del adj[v][u]
  
      def has_edge(self, u, v):
          """Return True if the edge (u,v) is in the graph.
  
          Parameters
          ----------
          u, v : nodes
              Nodes can be, for example, strings or numbers.
              Nodes must be hashable (and not None) Python objects.
  
          Returns
          -------
          edge_ind : bool
              True if edge is in the graph, False otherwise.
  
          Examples
          --------
          Can be called either using two nodes u,v or edge tuple (u,v)
  
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2,3])
          >>> G.has_edge(0,1)  # using two nodes
          True
          >>> e = (0,1)
          >>> G.has_edge(*e)  #  e is a 2-tuple (u,v)
          True
          >>> e = (0,1,{'weight':7})
          >>> G.has_edge(*e[:2])  # e is a 3-tuple (u,v,data_dictionary)
          True
  
          The following syntax are all equivalent:
  
          >>> G.has_edge(0,1)
          True
          >>> 1 in G[0]  # though this gives KeyError if 0 not in G
          True
  
          """
          try:
              return v in self.adj[u]
          except KeyError:
              return False
  
      def neighbors(self, n):
          """Return a list of the nodes connected to the node n.
  
          Parameters
          ----------
          n : node
             A node in the graph
  
          Returns
          -------
          nlist : list
              A list of nodes that are adjacent to n.
  
          Raises
          ------
          NetworkXError
              If the node n is not in the graph.
  
          Notes
          -----
          It is usually more convenient (and faster) to access the
          adjacency dictionary as G[n]:
  
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_edge('a','b',weight=7)
          >>> G['a']
          {'b': {'weight': 7}}
  
          Examples
          --------
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2,3])
          >>> G.neighbors(0)
          [1]
  
          """
          try:
              return list(self.adj[n])
          except KeyError:
              raise NetworkXError("The node %s is not in the graph." % (n,))
  
      def neighbors_iter(self, n):
          """Return an iterator over all neighbors of node n.
  
          Examples
          --------
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2,3])
          >>> [n for n in G.neighbors_iter(0)]
          [1]
  
          Notes
          -----
          It is faster to use the idiom "in G[0]", e.g.
  
          >>> G = nx.path_graph(4)
          >>> [n for n in G[0]]
          [1]
          """
          try:
              return iter(self.adj[n])
          except KeyError:
              raise NetworkXError("The node %s is not in the graph." % (n,))
  
      def edges(self, nbunch=None, data=False, default=None):
          """Return a list of 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_list: list of edge tuples
              Edges that are adjacent to any node in nbunch, or a list
              of all edges if nbunch is not specified.
  
          See Also
          --------
          edges_iter : return an iterator over the 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.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2])
          >>> G.add_edge(2,3,weight=5)
          >>> G.edges()
          [(0, 1), (1, 2), (2, 3)]
          >>> G.edges(data=True) # default edge data is {} (empty dictionary)
          [(0, 1, {}), (1, 2, {}), (2, 3, {'weight': 5})]
          >>> list(G.edges_iter(data='weight', default=1))
          [(0, 1, 1), (1, 2, 1), (2, 3, 5)]
          >>> G.edges([0,3])
          [(0, 1), (3, 2)]
          >>> G.edges(0)
          [(0, 1)]
  
          """
          return list(self.edges_iter(nbunch, data, default))
  
      def edges_iter(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_iter : iterator
              An iterator of (u,v) or (u,v,d) tuples of edges.
  
          See Also
          --------
          edges : return a list of 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.Graph()   # or MultiGraph, etc
          >>> G.add_path([0,1,2])
          >>> G.add_edge(2,3,weight=5)
          >>> [e for e in G.edges_iter()]
          [(0, 1), (1, 2), (2, 3)]
          >>> list(G.edges_iter(data=True)) # default data is {} (empty dict)
          [(0, 1, {}), (1, 2, {}), (2, 3, {'weight': 5})]
          >>> list(G.edges_iter(data='weight', default=1))
          [(0, 1, 1), (1, 2, 1), (2, 3, 5)]
          >>> list(G.edges_iter([0,3]))
          [(0, 1), (3, 2)]
          >>> list(G.edges_iter(0))
          [(0, 1)]
  
          """
          seen = {}     # helper dict to keep track of multiply stored edges
          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():
                      if nbr not in seen:
                          yield (n, nbr, ddict)
                  seen[n] = 1
          elif data is not False:
              for n, nbrs in nodes_nbrs:
                  for nbr, ddict in nbrs.items():
                      if nbr not in seen:
                          d = ddict[data] if data in ddict else default
                          yield (n, nbr, d)
                  seen[n] = 1
          else:  # data is False
              for n, nbrs in nodes_nbrs:
                  for nbr in nbrs:
                      if nbr not in seen:
                          yield (n, nbr)
                  seen[n] = 1
          del seen
  
      def get_edge_data(self, u, v, default=None):
          """Return the attribute dictionary associated with edge (u,v).
  
          Parameters
          ----------
          u, v : nodes
          default:  any Python object (default=None)
              Value to return if the edge (u,v) is not found.
  
          Returns
          -------
          edge_dict : dictionary
              The edge attribute dictionary.
  
          Notes
          -----
          It is faster to use G[u][v].
  
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2,3])
          >>> G[0][1]
          {}
  
          Warning: Assigning G[u][v] corrupts the graph data structure.
          But it is safe to assign attributes to that dictionary,
  
          >>> G[0][1]['weight'] = 7
          >>> G[0][1]['weight']
          7
          >>> G[1][0]['weight']
          7
  
          Examples
          --------
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2,3])
          >>> G.get_edge_data(0,1) # default edge data is {}
          {}
          >>> e = (0,1)
          >>> G.get_edge_data(*e) # tuple form
          {}
          >>> G.get_edge_data('a','b',default=0) # edge not in graph, return 0
          0
          """
          try:
              return self.adj[u][v]
          except KeyError:
              return default
  
      def adjacency_list(self):
          """Return an adjacency list representation of the graph.
  
          The output adjacency list is in the order of G.nodes().
          For directed graphs, only outgoing adjacencies are included.
  
          Returns
          -------
          adj_list : lists of lists
              The adjacency structure of the graph as a list of lists.
  
          See Also
          --------
          adjacency_iter
  
          Examples
          --------
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2,3])
          >>> G.adjacency_list() # in order given by G.nodes()
          [[1], [0, 2], [1, 3], [2]]
  
          """
          return list(map(list, iter(self.adj.values())))
  
      def adjacency_iter(self):
          """Return an iterator of (node, adjacency dict) tuples for all nodes.
  
          This is the fastest way to look at every edge.
          For directed graphs, only outgoing adjacencies are included.
  
          Returns
          -------
          adj_iter : iterator
             An iterator of (node, adjacency dictionary) for all nodes in
             the graph.
  
          See Also
          --------
          adjacency_list
  
          Examples
          --------
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2,3])
          >>> [(n,nbrdict) for n,nbrdict in G.adjacency_iter()]
          [(0, {1: {}}), (1, {0: {}, 2: {}}), (2, {1: {}, 3: {}}), (3, {2: {}})]
  
          """
          return iter(self.adj.items())
  
      def degree(self, nbunch=None, weight=None):
          """Return the degree of a node or nodes.
  
          The node degree is the number of edges adjacent to that node.
  
          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
          -------
          nd : dictionary, or number
              A dictionary with nodes as keys and degree as values or
              a number if a single node is specified.
  
          Examples
          --------
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2,3])
          >>> G.degree(0)
          1
          >>> G.degree([0,1])
          {0: 1, 1: 2}
          >>> list(G.degree([0,1]).values())
          [1, 2]
  
          """
          if nbunch in self:      # return a single node
              return next(self.degree_iter(nbunch, weight))[1]
          else:           # return a dict
              return dict(self.degree_iter(nbunch, weight))
  
      def degree_iter(self, nbunch=None, weight=None):
          """Return an iterator for (node, degree).
  
          The node degree is the number of edges adjacent to the node.
  
          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
          -------
          nd_iter : an iterator
              The iterator returns two-tuples of (node, degree).
  
          See Also
          --------
          degree
  
          Examples
          --------
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2,3])
          >>> list(G.degree_iter(0)) # node 0 with degree 1
          [(0, 1)]
          >>> list(G.degree_iter([0,1]))
          [(0, 1), (1, 2)]
  
          """
          if nbunch is None:
              nodes_nbrs = self.adj.items()
          else:
              nodes_nbrs = ((n, self.adj[n]) for n in self.nbunch_iter(nbunch))
  
          if weight is None:
              for n, nbrs in nodes_nbrs:
                  yield (n, len(nbrs) + (n in nbrs))  # return tuple (n,degree)
          else:
              # edge weighted graph - degree is sum of nbr edge weights
              for n, nbrs in nodes_nbrs:
                  yield (n, sum((nbrs[nbr].get(weight, 1) for nbr in nbrs)) +
                      (n in nbrs and nbrs[n].get(weight, 1)))
  
      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()
          >>> G.nodes()
          []
          >>> G.edges()
          []
  
          """
          self.name = ''
          self.adj.clear()
          self.node.clear()
          self.graph.clear()
  
      def copy(self):
          """Return a copy of the graph.
  
          Returns
          -------
          G : Graph
              A copy of the graph.
  
          See Also
          --------
          to_directed: return a directed copy of the graph.
  
          Notes
          -----
          This makes a complete copy of the graph including all of the
          node or edge attributes.
  
          Examples
          --------
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2,3])
          >>> H = G.copy()
  
          """
          return deepcopy(self)
  
      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 False
  
      def to_directed(self):
          """Return a directed representation of the graph.
  
          Returns
          -------
          G : DiGraph
              A directed graph with the same name, same nodes, and with
              each edge (u,v,data) replaced by two directed edges
              (u,v,data) and (v,u,data).
  
          Notes
          -----
          This returns a "deepcopy" of the edge, node, and
          graph attributes which attempts to completely copy
          all of the data and references.
  
          This is in contrast to the similar D=DiGraph(G) which returns a
          shallow copy of the data.
  
          See the Python copy module for more information on shallow
          and deep copies, http://docs.python.org/library/copy.html.
  
          Warning: If you have subclassed Graph to use dict-like objects in the
          data structure, those changes do not transfer to the DiGraph
          created by this method.
  
          Examples
          --------
          >>> G = nx.Graph()   # or MultiGraph, etc
          >>> G.add_path([0,1])
          >>> H = G.to_directed()
          >>> 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()
          >>> H.edges()
          [(0, 1)]
          """
          from networkx import DiGraph
          G = DiGraph()
          G.name = self.name
          G.add_nodes_from(self)
          G.add_edges_from(((u, v, deepcopy(data))
              for u, nbrs in self.adjacency_iter()
              for v, data in nbrs.items()))
          G.graph = deepcopy(self.graph)
          G.node = deepcopy(self.node)
          return G
  
      def to_undirected(self):
          """Return an undirected copy of the graph.
  
          Returns
          -------
          G : Graph/MultiGraph
              A deepcopy of the graph.
  
          See Also
          --------
          copy, add_edge, add_edges_from
  
          Notes
          -----
          This returns a "deepcopy" of the edge, node, and
          graph attributes which attempts to completely copy
          all of the data and references.
  
          This is in contrast to the similar G=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.
  
          Examples
          --------
          >>> G = nx.Graph()   # or MultiGraph, etc
          >>> G.add_path([0,1])
          >>> H = G.to_directed()
          >>> H.edges()
          [(0, 1), (1, 0)]
          >>> G2 = H.to_undirected()
          >>> G2.edges()
          [(0, 1)]
          """
          return deepcopy(self)
  
      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])
          >>> 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_adj = H.adj
          self_adj = self.adj
          # add nodes and edges (undirected method)
          for n in H.node:
              Hnbrs = H.adjlist_dict_factory()
              H_adj[n] = Hnbrs
              for nbr, d in self_adj[n].items():
                  if nbr in H_adj:
                      # add both representations of edge: n-nbr and nbr-n
                      Hnbrs[nbr] = d
                      H_adj[nbr][n] = d
          H.graph = self.graph
          return H
  
      def nodes_with_selfloops(self):
          """Return a list of nodes with self loops.
  
          A node with a self loop has an edge with both ends adjacent
          to that node.
  
          Returns
          -------
          nodelist : list
              A list of nodes with self loops.
  
          See Also
          --------
          selfloop_edges, number_of_selfloops
  
          Examples
          --------
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_edge(1,1)
          >>> G.add_edge(1,2)
          >>> G.nodes_with_selfloops()
          [1]
          """
          return [n for n, nbrs in self.adj.items() if n in nbrs]
  
      def selfloop_edges(self, data=False, default=None):
          """Return a list of selfloop edges.
  
          A selfloop edge has the same node at both ends.
  
          Parameters
          ----------
          data : string or bool, optional (default=False)
              Return selfloop edges as two tuples (u,v) (data=False)
              or three-tuples (u,v,datadict) (data=True)
              or three-tuples (u,v,datavalue) (data='attrname')
          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
          -------
          edgelist : list of edge tuples
              A list of all selfloop edges.
  
          See Also
          --------
          nodes_with_selfloops, number_of_selfloops
  
          Examples
          --------
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_edge(1,1)
          >>> G.add_edge(1,2)
          >>> G.selfloop_edges()
          [(1, 1)]
          >>> G.selfloop_edges(data=True)
          [(1, 1, {})]
          """
          if data is True:
              return [(n, n, nbrs[n])
                      for n, nbrs in self.adj.items() if n in nbrs]
          elif data is not False:
              return [(n, n, nbrs[n].get(data, default))
                      for n, nbrs in self.adj.items() if n in nbrs]
          else:
              return [(n, n)
                      for n, nbrs in self.adj.items() if n in nbrs]
  
      def number_of_selfloops(self):
          """Return the number of selfloop edges.
  
          A selfloop edge has the same node at both ends.
  
          Returns
          -------
          nloops : int
              The number of selfloops.
  
          See Also
          --------
          nodes_with_selfloops, selfloop_edges
  
          Examples
          --------
          >>> G=nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_edge(1,1)
          >>> G.add_edge(1,2)
          >>> G.number_of_selfloops()
          1
          """
          return len(self.selfloop_edges())
  
      def size(self, weight=None):
          """Return the number of edges.
  
          Parameters
          ----------
          weight : string or None, optional (default=None)
             The edge attribute that holds the numerical value used
             as a weight.  If None, then each edge has weight 1.
  
          Returns
          -------
          nedges : int
              The number of edges or sum of edge weights in the graph.
  
          See Also
          --------
          number_of_edges
  
          Examples
          --------
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2,3])
          >>> G.size()
          3
  
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_edge('a','b',weight=2)
          >>> G.add_edge('b','c',weight=4)
          >>> G.size()
          2
          >>> G.size(weight='weight')
          6.0
          """
          s = sum(self.degree(weight=weight).values()) / 2
          if weight is None:
              return int(s)
          else:
              return float(s)
  
      def number_of_edges(self, u=None, v=None):
          """Return the number of edges between two nodes.
  
          Parameters
          ----------
          u, v : nodes, optional (default=all edges)
              If u and v are specified, return the number of edges between
              u and v. Otherwise return the total number of all edges.
  
          Returns
          -------
          nedges : int
              The number of edges in the graph.  If nodes u and v are specified
              return the number of edges between those nodes.
  
          See Also
          --------
          size
  
          Examples
          --------
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2,3])
          >>> G.number_of_edges()
          3
          >>> G.number_of_edges(0,1)
          1
          >>> e = (0,1)
          >>> G.number_of_edges(*e)
          1
          """
          if u is None: return int(self.size())
          if v in self.adj[u]:
              return 1
          else:
              return 0
  
      def add_star(self, nodes, **attr):
          """Add a star.
  
          The first node in nodes is the middle of the star.  It is connected
          to all other nodes.
  
          Parameters
          ----------
          nodes : iterable container
              A container of nodes.
          attr : keyword arguments, optional (default= no attributes)
              Attributes to add to every edge in star.
  
          See Also
          --------
          add_path, add_cycle
  
          Examples
          --------
          >>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_star([0,1,2,3])
          >>> G.add_star([10,11,12],weight=2)
  
          """
          nlist = list(nodes)
          v = nlist[0]
          edges = ((v, n) for n in nlist[1:])
          self.add_edges_from(edges, **attr)
  
      def add_path(self, nodes, **attr):
          """Add a path.
  
          Parameters
          ----------
          nodes : iterable container
              A container of nodes.  A path will be constructed from
              the nodes (in order) and added to the graph.
          attr : keyword arguments, optional (default= no attributes)
              Attributes to add to every edge in path.
  
          See Also
          --------
          add_star, add_cycle
  
          Examples
          --------
          >>> G=nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_path([0,1,2,3])
          >>> G.add_path([10,11,12],weight=7)
  
          """
          nlist = list(nodes)
          edges = zip(nlist[:-1], nlist[1:])
          self.add_edges_from(edges, **attr)
  
      def add_cycle(self, nodes, **attr):
          """Add a cycle.
  
          Parameters
          ----------
          nodes: iterable container
              A container of nodes.  A cycle will be constructed from
              the nodes (in order) and added to the graph.
          attr : keyword arguments, optional (default= no attributes)
              Attributes to add to every edge in cycle.
  
          See Also
          --------
          add_path, add_star
  
          Examples
          --------
          >>> G=nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
          >>> G.add_cycle([0,1,2,3])
          >>> G.add_cycle([10,11,12],weight=7)
  
          """
          nlist = list(nodes)
          edges = zip(nlist, nlist[1:] + [nlist[0]])
          self.add_edges_from(edges, **attr)
  
      def nbunch_iter(self, nbunch=None):
          """Return an iterator of nodes contained in nbunch that are
          also in the graph.
  
          The nodes in nbunch are checked for membership in the graph
          and if not are silently ignored.
  
          Parameters
          ----------
          nbunch : iterable container, optional (default=all nodes)
              A container of nodes.  The container will be iterated
              through once.
  
          Returns
          -------
          niter : iterator
              An iterator over nodes in nbunch that are also in the graph.
              If nbunch is None, iterate over all nodes in the graph.
  
          Raises
          ------
          NetworkXError
              If nbunch is not a node or or sequence of nodes.
              If a node in nbunch is not hashable.
  
          See Also
          --------
          Graph.__iter__
  
          Notes
          -----
          When nbunch is an iterator, the returned iterator yields values
          directly from nbunch, becoming exhausted when nbunch is exhausted.
  
          To test whether nbunch is a single node, one can use
          "if nbunch in self:", even after processing with this routine.
  
          If nbunch is not a node or a (possibly empty) sequence/iterator
          or None, a NetworkXError is raised.  Also, if any object in
          nbunch is not hashable, a NetworkXError is raised.
          """
          if nbunch is None:   # include all nodes via iterator
              bunch = iter(self.adj.keys())
          elif nbunch in self:  # if nbunch is a single node
              bunch = iter([nbunch])
          else:                # if nbunch is a sequence of nodes
              def bunch_iter(nlist, adj):
                  try:
                      for n in nlist:
                          if n in adj:
                              yield n
                  except TypeError as e:
                      message = e.args[0]
                      # capture error for non-sequence/iterator nbunch.
                      if 'iter' in message:
                          raise NetworkXError(
                              "nbunch is not a node or a sequence of nodes.")
                      # capture error for unhashable node.
                      elif 'hashable' in message:
                          raise NetworkXError(
                              "Node %s in the sequence nbunch is not a valid node."%n)
                      else:
                          raise
              bunch = bunch_iter(nbunch, self.adj)
          return bunch
  