content: #    Copyright (C) 2004-2016 by
  #    Aric Hagberg <hagberg@lanl.gov>
  #    Dan Schult <dschult@colgate.edu>
  #    Pieter Swart <swart@lanl.gov>
  #    All rights reserved.
  #    BSD license.
  #
  # Author: Aric Hagberg (hagberg@lanl.gov)
  """
  **********
  Matplotlib
  **********
  
  Draw networks with matplotlib.
  
  See Also
  --------
  
  matplotlib:     http://matplotlib.org/
  
  pygraphviz:     http://pygraphviz.github.io/
  
  """
  import networkx as nx
  from networkx.drawing.layout import shell_layout,\
      circular_layout,spectral_layout,spring_layout,random_layout
  
  __all__ = ['draw',
             'draw_networkx',
             'draw_networkx_nodes',
             'draw_networkx_edges',
             'draw_networkx_labels',
             'draw_networkx_edge_labels',
             'draw_circular',
             'draw_random',
             'draw_spectral',
             'draw_spring',
             'draw_shell']
  
  
  def draw(G, pos=None, ax=None, **kwds):
      """Draw the graph G with Matplotlib.
  
      Draw the graph as a simple representation with no node
      labels or edge labels and using the full Matplotlib figure area
      and no axis labels by default.  See draw_networkx() for more
      full-featured drawing that allows title, axis labels etc.
  
      Parameters
      ----------
      G : graph
         A networkx graph
  
      pos : dictionary, optional
         A dictionary with nodes as keys and positions as values.
         If not specified a spring layout positioning will be computed.
         See :py:mod:`networkx.drawing.layout` for functions that
         compute node positions.
  
      ax : Matplotlib Axes object, optional
         Draw the graph in specified Matplotlib axes.
  
      kwds : optional keywords
         See networkx.draw_networkx() for a description of optional keywords.
  
      Examples
      --------
      >>> G=nx.dodecahedral_graph()
      >>> nx.draw(G)
      >>> nx.draw(G,pos=nx.spring_layout(G)) # use spring layout
  
      See Also
      --------
      draw_networkx()
      draw_networkx_nodes()
      draw_networkx_edges()
      draw_networkx_labels()
      draw_networkx_edge_labels()
  
      Notes
      -----
      This function has the same name as pylab.draw and pyplot.draw
      so beware when using
  
      >>> from networkx import *
  
      since you might overwrite the pylab.draw function.
  
      With pyplot use
  
      >>> import matplotlib.pyplot as plt
      >>> import networkx as nx
      >>> G=nx.dodecahedral_graph()
      >>> nx.draw(G)  # networkx draw()
      >>> plt.draw()  # pyplot draw()
  
      Also see the NetworkX drawing examples at
      http://networkx.readthedocs.io/en/latest/gallery.html
      """
      try:
          import matplotlib.pyplot as plt
      except ImportError:
          raise ImportError("Matplotlib required for draw()")
      except RuntimeError:
          print("Matplotlib unable to open display")
          raise
  
      if ax is None:
          cf = plt.gcf()
      else:
          cf = ax.get_figure()
      cf.set_facecolor('w')
      if ax is None:
          if cf._axstack() is None:
              ax = cf.add_axes((0, 0, 1, 1))
          else:
              ax = cf.gca()
  
      if 'with_labels' not in kwds:
          kwds['with_labels'] = 'labels' in kwds
  
      try:
          draw_networkx(G, pos=pos, ax=ax, **kwds)
          ax.set_axis_off()
          plt.draw_if_interactive()
      except:
          raise
      return
  
  
  def draw_networkx(G, pos=None, arrows=True, with_labels=True, **kwds):
      """Draw the graph G using Matplotlib.
  
      Draw the graph with Matplotlib with options for node positions,
      labeling, titles, and many other drawing features.
      See draw() for simple drawing without labels or axes.
  
      Parameters
      ----------
      G : graph
         A networkx graph
  
      pos : dictionary, optional
         A dictionary with nodes as keys and positions as values.
         If not specified a spring layout positioning will be computed.
         See :py:mod:`networkx.drawing.layout` for functions that
         compute node positions.
  
      arrows : bool, optional (default=True)
         For directed graphs, if True draw arrowheads.
  
      with_labels :  bool, optional (default=True)
         Set to True to draw labels on the nodes.
  
      ax : Matplotlib Axes object, optional
         Draw the graph in the specified Matplotlib axes.
  
      nodelist : list, optional (default G.nodes())
         Draw only specified nodes
  
      edgelist : list, optional (default=G.edges())
         Draw only specified edges
  
      node_size : scalar or array, optional (default=300)
         Size of nodes.  If an array is specified it must be the
         same length as nodelist.
  
      node_color : color string, or array of floats, (default='r')
         Node color. Can be a single color format string,
         or a  sequence of colors with the same length as nodelist.
         If numeric values are specified they will be mapped to
         colors using the cmap and vmin,vmax parameters.  See
         matplotlib.scatter for more details.
  
      node_shape :  string, optional (default='o')
         The shape of the node.  Specification is as matplotlib.scatter
         marker, one of 'so^>v<dph8'.
  
      alpha : float, optional (default=1.0)
         The node and edge transparency
  
      cmap : Matplotlib colormap, optional (default=None)
         Colormap for mapping intensities of nodes
  
      vmin,vmax : float, optional (default=None)
         Minimum and maximum for node colormap scaling
  
      linewidths : [None | scalar | sequence]
         Line width of symbol border (default =1.0)
  
      width : float, optional (default=1.0)
         Line width of edges
  
      edge_color : color string, or array of floats (default='r')
         Edge color. Can be a single color format string,
         or a sequence of colors with the same length as edgelist.
         If numeric values are specified they will be mapped to
         colors using the edge_cmap and edge_vmin,edge_vmax parameters.
  
      edge_cmap : Matplotlib colormap, optional (default=None)
         Colormap for mapping intensities of edges
  
      edge_vmin,edge_vmax : floats, optional (default=None)
         Minimum and maximum for edge colormap scaling
  
      style : string, optional (default='solid')
         Edge line style (solid|dashed|dotted,dashdot)
  
      labels : dictionary, optional (default=None)
         Node labels in a dictionary keyed by node of text labels
  
      font_size : int, optional (default=12)
         Font size for text labels
  
      font_color : string, optional (default='k' black)
         Font color string
  
      font_weight : string, optional (default='normal')
         Font weight
  
      font_family : string, optional (default='sans-serif')
         Font family
  
      label : string, optional
          Label for graph legend
  
      Notes
      -----
      For directed graphs, "arrows" (actually just thicker stubs) are drawn
      at the head end.  Arrows can be turned off with keyword arrows=False.
      Yes, it is ugly but drawing proper arrows with Matplotlib this
      way is tricky.
  
      Examples
      --------
      >>> G=nx.dodecahedral_graph()
      >>> nx.draw(G)
      >>> nx.draw(G,pos=nx.spring_layout(G)) # use spring layout
  
      >>> import matplotlib.pyplot as plt
      >>> limits=plt.axis('off') # turn of axis
  
      Also see the NetworkX drawing examples at
      http://networkx.readthedocs.io/en/latest/gallery.html
  
      See Also
      --------
      draw()
      draw_networkx_nodes()
      draw_networkx_edges()
      draw_networkx_labels()
      draw_networkx_edge_labels()
      """
      try:
          import matplotlib.pyplot as plt
      except ImportError:
          raise ImportError("Matplotlib required for draw()")
      except RuntimeError:
          print("Matplotlib unable to open display")
          raise
  
      if pos is None:
          pos = nx.drawing.spring_layout(G)  # default to spring layout
  
      node_collection = draw_networkx_nodes(G, pos, **kwds)
      edge_collection = draw_networkx_edges(G, pos, arrows=arrows, **kwds)
      if with_labels:
          draw_networkx_labels(G, pos, **kwds)
      plt.draw_if_interactive()
  
  
  def draw_networkx_nodes(G, pos,
                          nodelist=None,
                          node_size=300,
                          node_color='r',
                          node_shape='o',
                          alpha=1.0,
                          cmap=None,
                          vmin=None,
                          vmax=None,
                          ax=None,
                          linewidths=None,
                          label=None,
                          **kwds):
      """Draw the nodes of the graph G.
  
      This draws only the nodes of the graph G.
  
      Parameters
      ----------
      G : graph
         A networkx graph
  
      pos : dictionary
         A dictionary with nodes as keys and positions as values.
         Positions should be sequences of length 2.
  
      ax : Matplotlib Axes object, optional
         Draw the graph in the specified Matplotlib axes.
  
      nodelist : list, optional
         Draw only specified nodes (default G.nodes())
  
      node_size : scalar or array
         Size of nodes (default=300).  If an array is specified it must be the
         same length as nodelist.
  
      node_color : color string, or array of floats
         Node color. Can be a single color format string (default='r'),
         or a  sequence of colors with the same length as nodelist.
         If numeric values are specified they will be mapped to
         colors using the cmap and vmin,vmax parameters.  See
         matplotlib.scatter for more details.
  
      node_shape :  string
         The shape of the node.  Specification is as matplotlib.scatter
         marker, one of 'so^>v<dph8' (default='o').
  
      alpha : float
         The node transparency (default=1.0)
  
      cmap : Matplotlib colormap
         Colormap for mapping intensities of nodes (default=None)
  
      vmin,vmax : floats
         Minimum and maximum for node colormap scaling (default=None)
  
      linewidths : [None | scalar | sequence]
         Line width of symbol border (default =1.0)
  
      label : [None| string]
         Label for legend
  
      Returns
      -------
      matplotlib.collections.PathCollection
          `PathCollection` of the nodes.
  
      Examples
      --------
      >>> G=nx.dodecahedral_graph()
      >>> nodes=nx.draw_networkx_nodes(G,pos=nx.spring_layout(G))
  
      Also see the NetworkX drawing examples at
      http://networkx.readthedocs.io/en/latest/gallery.html
  
      See Also
      --------
      draw()
      draw_networkx()
      draw_networkx_edges()
      draw_networkx_labels()
      draw_networkx_edge_labels()
      """
      import collections
      try:
          import matplotlib.pyplot as plt
          import numpy
      except ImportError:
          raise ImportError("Matplotlib required for draw()")
      except RuntimeError:
          print("Matplotlib unable to open display")
          raise
  
      if ax is None:
          ax = plt.gca()
  
      if nodelist is None:
          nodelist = list(G)
  
      if not nodelist or len(nodelist) == 0:  # empty nodelist, no drawing
          return None
  
      try:
          xy = numpy.asarray([pos[v] for v in nodelist])
      except KeyError as e:
          raise nx.NetworkXError('Node %s has no position.'%e)
      except ValueError:
          raise nx.NetworkXError('Bad value in node positions.')
  
      if isinstance(alpha, collections.Iterable):
          node_color = apply_alpha(node_color, alpha, nodelist, cmap, vmin, vmax)
          alpha = None
  
      node_collection = ax.scatter(xy[:, 0], xy[:, 1],
                                   s=node_size,
                                   c=node_color,
                                   marker=node_shape,
                                   cmap=cmap,
                                   vmin=vmin,
                                   vmax=vmax,
                                   alpha=alpha,
                                   linewidths=linewidths,
                                   label=label)
  
      node_collection.set_zorder(2)
      return node_collection
  
  
  def draw_networkx_edges(G, pos,
                          edgelist=None,
                          width=1.0,
                          edge_color='k',
                          style='solid',
                          alpha=1.0,
                          edge_cmap=None,
                          edge_vmin=None,
                          edge_vmax=None,
                          ax=None,
                          arrows=True,
                          label=None,
                          **kwds):
      """Draw the edges of the graph G.
  
      This draws only the edges of the graph G.
  
      Parameters
      ----------
      G : graph
         A networkx graph
  
      pos : dictionary
         A dictionary with nodes as keys and positions as values.
         Positions should be sequences of length 2.
  
      edgelist : collection of edge tuples
         Draw only specified edges(default=G.edges())
  
      width : float, or array of floats
         Line width of edges (default=1.0)
  
      edge_color : color string, or array of floats
         Edge color. Can be a single color format string (default='r'),
         or a sequence of colors with the same length as edgelist.
         If numeric values are specified they will be mapped to
         colors using the edge_cmap and edge_vmin,edge_vmax parameters.
  
      style : string
         Edge line style (default='solid') (solid|dashed|dotted,dashdot)
  
      alpha : float
         The edge transparency (default=1.0)
  
      edge_ cmap : Matplotlib colormap
         Colormap for mapping intensities of edges (default=None)
  
      edge_vmin,edge_vmax : floats
         Minimum and maximum for edge colormap scaling (default=None)
  
      ax : Matplotlib Axes object, optional
         Draw the graph in the specified Matplotlib axes.
  
      arrows : bool, optional (default=True)
         For directed graphs, if True draw arrowheads.
  
      label : [None| string]
         Label for legend
  
      Returns
      -------
      matplotlib.collection.LineCollection
          `LineCollection` of the edges
  
      Notes
      -----
      For directed graphs, "arrows" (actually just thicker stubs) are drawn
      at the head end.  Arrows can be turned off with keyword arrows=False.
      Yes, it is ugly but drawing proper arrows with Matplotlib this
      way is tricky.
  
      Examples
      --------
      >>> G=nx.dodecahedral_graph()
      >>> edges=nx.draw_networkx_edges(G,pos=nx.spring_layout(G))
  
      Also see the NetworkX drawing examples at
      http://networkx.readthedocs.io/en/latest/gallery.html
  
      See Also
      --------
      draw()
      draw_networkx()
      draw_networkx_nodes()
      draw_networkx_labels()
      draw_networkx_edge_labels()
      """
      try:
          import matplotlib
          import matplotlib.pyplot as plt
          import matplotlib.cbook as cb
          from matplotlib.colors import colorConverter, Colormap
          from matplotlib.collections import LineCollection
          import numpy
      except ImportError:
          raise ImportError("Matplotlib required for draw()")
      except RuntimeError:
          print("Matplotlib unable to open display")
          raise
  
      if ax is None:
          ax = plt.gca()
  
      if edgelist is None:
          edgelist = list(G.edges())
  
      if not edgelist or len(edgelist) == 0:  # no edges!
          return None
  
      # set edge positions
      edge_pos = numpy.asarray([(pos[e[0]], pos[e[1]]) for e in edgelist])
  
      if not cb.iterable(width):
          lw = (width,)
      else:
          lw = width
  
      if not cb.is_string_like(edge_color) \
             and cb.iterable(edge_color) \
             and len(edge_color) == len(edge_pos):
          if numpy.alltrue([cb.is_string_like(c)
                           for c in edge_color]):
              # (should check ALL elements)
              # list of color letters such as ['k','r','k',...]
              edge_colors = tuple([colorConverter.to_rgba(c, alpha)
                                   for c in edge_color])
          elif numpy.alltrue([not cb.is_string_like(c)
                             for c in edge_color]):
              # If color specs are given as (rgb) or (rgba) tuples, we're OK
              if numpy.alltrue([cb.iterable(c) and len(c) in (3, 4)
                               for c in edge_color]):
                  edge_colors = tuple(edge_color)
              else:
                  # numbers (which are going to be mapped with a colormap)
                  edge_colors = None
          else:
              raise ValueError('edge_color must consist of either color names or numbers')
      else:
          if cb.is_string_like(edge_color) or len(edge_color) == 1:
              edge_colors = (colorConverter.to_rgba(edge_color, alpha), )
          else:
              raise ValueError('edge_color must be a single color or list of exactly m colors where m is the number or edges')
  
      edge_collection = LineCollection(edge_pos,
                                       colors=edge_colors,
                                       linewidths=lw,
                                       antialiaseds=(1,),
                                       linestyle=style,
                                       transOffset = ax.transData,
                                       )
  
      edge_collection.set_zorder(1)  # edges go behind nodes
      edge_collection.set_label(label)
      ax.add_collection(edge_collection)
  
      # Note: there was a bug in mpl regarding the handling of alpha values for
      # each line in a LineCollection.  It was fixed in matplotlib in r7184 and
      # r7189 (June 6 2009).  We should then not set the alpha value globally,
      # since the user can instead provide per-edge alphas now.  Only set it
      # globally if provided as a scalar.
      if cb.is_numlike(alpha):
          edge_collection.set_alpha(alpha)
  
      if edge_colors is None:
          if edge_cmap is not None:
              assert(isinstance(edge_cmap, Colormap))
          edge_collection.set_array(numpy.asarray(edge_color))
          edge_collection.set_cmap(edge_cmap)
          if edge_vmin is not None or edge_vmax is not None:
              edge_collection.set_clim(edge_vmin, edge_vmax)
          else:
              edge_collection.autoscale()
  
      arrow_collection = None
  
      if G.is_directed() and arrows:
  
          # a directed graph hack
          # draw thick line segments at head end of edge
          # waiting for someone else to implement arrows that will work
          arrow_colors = edge_colors
          a_pos = []
          p = 1.0-0.25  # make head segment 25 percent of edge length
          for src, dst in edge_pos:
              x1, y1 = src
              x2, y2 = dst
              dx = x2-x1   # x offset
              dy = y2-y1   # y offset
              d = numpy.sqrt(float(dx**2 + dy**2))  # length of edge
              if d == 0:   # source and target at same position
                  continue
              if dx == 0:  # vertical edge
                  xa = x2
                  ya = dy*p+y1
              if dy == 0:  # horizontal edge
                  ya = y2
                  xa = dx*p+x1
              else:
                  theta = numpy.arctan2(dy, dx)
                  xa = p*d*numpy.cos(theta)+x1
                  ya = p*d*numpy.sin(theta)+y1
  
              a_pos.append(((xa, ya), (x2, y2)))
  
          arrow_collection = LineCollection(a_pos,
                                  colors=arrow_colors,
                                  linewidths=[4*ww for ww in lw],
                                  antialiaseds=(1,),
                                  transOffset = ax.transData,
                                  )
  
          arrow_collection.set_zorder(1)  # edges go behind nodes
          arrow_collection.set_label(label)
          ax.add_collection(arrow_collection)
  
      # update view
      minx = numpy.amin(numpy.ravel(edge_pos[:, :, 0]))
      maxx = numpy.amax(numpy.ravel(edge_pos[:, :, 0]))
      miny = numpy.amin(numpy.ravel(edge_pos[:, :, 1]))
      maxy = numpy.amax(numpy.ravel(edge_pos[:, :, 1]))
  
      w = maxx-minx
      h = maxy-miny
      padx,  pady = 0.05*w, 0.05*h
      corners = (minx-padx, miny-pady), (maxx+padx, maxy+pady)
      ax.update_datalim(corners)
      ax.autoscale_view()
  
  #    if arrow_collection:
  
      return edge_collection
  
  
  def draw_networkx_labels(G, pos,
                           labels=None,
                           font_size=12,
                           font_color='k',
                           font_family='sans-serif',
                           font_weight='normal',
                           alpha=1.0,
                           bbox=None,
                           ax=None,
                           **kwds):
      """Draw node labels on the graph G.
  
      Parameters
      ----------
      G : graph
         A networkx graph
  
      pos : dictionary
         A dictionary with nodes as keys and positions as values.
         Positions should be sequences of length 2.
  
      labels : dictionary, optional (default=None)
         Node labels in a dictionary keyed by node of text labels
  
      font_size : int
         Font size for text labels (default=12)
  
      font_color : string
         Font color string (default='k' black)
  
      font_family : string
         Font family (default='sans-serif')
  
      font_weight : string
         Font weight (default='normal')
  
      alpha : float
         The text transparency (default=1.0)
  
      ax : Matplotlib Axes object, optional
         Draw the graph in the specified Matplotlib axes.
  
      Returns
      -------
      dict
          `dict` of labels keyed on the nodes
  
      Examples
      --------
      >>> G=nx.dodecahedral_graph()
      >>> labels=nx.draw_networkx_labels(G,pos=nx.spring_layout(G))
  
      Also see the NetworkX drawing examples at
      http://networkx.readthedocs.io/en/latest/gallery.html
  
  
      See Also
      --------
      draw()
      draw_networkx()
      draw_networkx_nodes()
      draw_networkx_edges()
      draw_networkx_edge_labels()
      """
      try:
          import matplotlib.pyplot as plt
          import matplotlib.cbook as cb
      except ImportError:
          raise ImportError("Matplotlib required for draw()")
      except RuntimeError:
          print("Matplotlib unable to open display")
          raise
  
      if ax is None:
          ax = plt.gca()
  
      if labels is None:
          labels = dict((n, n) for n in G.nodes())
  
      # set optional alignment
      horizontalalignment = kwds.get('horizontalalignment', 'center')
      verticalalignment = kwds.get('verticalalignment', 'center')
  
      text_items = {}  # there is no text collection so we'll fake one
      for n, label in labels.items():
          (x, y) = pos[n]
          if not cb.is_string_like(label):
              label = str(label)  # this will cause "1" and 1 to be labeled the same
          t = ax.text(x, y,
                    label,
                    size=font_size,
                    color=font_color,
                    family=font_family,
                    weight=font_weight,
                    alpha=alpha,
                    horizontalalignment=horizontalalignment,
                    verticalalignment=verticalalignment,
                    transform=ax.transData,
                    bbox=bbox,
                    clip_on=True,
                    )
          text_items[n] = t
  
      return text_items
  
  
  def draw_networkx_edge_labels(G, pos,
                                edge_labels=None,
                                label_pos=0.5,
                                font_size=10,
                                font_color='k',
                                font_family='sans-serif',
                                font_weight='normal',
                                alpha=1.0,
                                bbox=None,
                                ax=None,
                                rotate=True,
                                **kwds):
      """Draw edge labels.
  
      Parameters
      ----------
      G : graph
         A networkx graph
  
      pos : dictionary
         A dictionary with nodes as keys and positions as values.
         Positions should be sequences of length 2.
  
      ax : Matplotlib Axes object, optional
         Draw the graph in the specified Matplotlib axes.
  
      alpha : float
         The text transparency (default=1.0)
  
      edge_labels : dictionary
         Edge labels in a dictionary keyed by edge two-tuple of text
         labels (default=None). Only labels for the keys in the dictionary
         are drawn.
  
      label_pos : float
         Position of edge label along edge (0=head, 0.5=center, 1=tail)
  
      font_size : int
         Font size for text labels (default=12)
  
      font_color : string
         Font color string (default='k' black)
  
      font_weight : string
         Font weight (default='normal')
  
      font_family : string
         Font family (default='sans-serif')
  
      bbox : Matplotlib bbox
         Specify text box shape and colors.
  
      clip_on : bool
         Turn on clipping at axis boundaries (default=True)
  
      Returns
      -------
      dict
          `dict` of labels keyed on the edges
  
      Examples
      --------
      >>> G=nx.dodecahedral_graph()
      >>> edge_labels=nx.draw_networkx_edge_labels(G,pos=nx.spring_layout(G))
  
      Also see the NetworkX drawing examples at
      http://networkx.readthedocs.io/en/latest/gallery.html
  
      See Also
      --------
      draw()
      draw_networkx()
      draw_networkx_nodes()
      draw_networkx_edges()
      draw_networkx_labels()
      """
      try:
          import matplotlib.pyplot as plt
          import matplotlib.cbook as cb
          import numpy
      except ImportError:
          raise ImportError("Matplotlib required for draw()")
      except RuntimeError:
          print("Matplotlib unable to open display")
          raise
  
      if ax is None:
          ax = plt.gca()
      if edge_labels is None:
          labels = dict(((u, v), d) for u, v, d in G.edges(data=True))
      else:
          labels = edge_labels
      text_items = {}
      for (n1, n2), label in labels.items():
          (x1, y1) = pos[n1]
          (x2, y2) = pos[n2]
          (x, y) = (x1 * label_pos + x2 * (1.0 - label_pos),
                    y1 * label_pos + y2 * (1.0 - label_pos))
  
          if rotate:
              angle = numpy.arctan2(y2-y1, x2-x1)/(2.0*numpy.pi)*360  # degrees
              # make label orientation "right-side-up"
              if angle > 90:
                  angle -= 180
              if angle < - 90:
                  angle += 180
              # transform data coordinate angle to screen coordinate angle
              xy = numpy.array((x, y))
              trans_angle = ax.transData.transform_angles(numpy.array((angle,)),
                                                          xy.reshape((1, 2)))[0]
          else:
              trans_angle = 0.0
          # use default box of white with white border
          if bbox is None:
              bbox = dict(boxstyle='round',
                          ec=(1.0, 1.0, 1.0),
                          fc=(1.0, 1.0, 1.0),
                          )
          if not cb.is_string_like(label):
              label = str(label)  # this will cause "1" and 1 to be labeled the same
  
          # set optional alignment
          horizontalalignment = kwds.get('horizontalalignment', 'center')
          verticalalignment = kwds.get('verticalalignment', 'center')
  
          t = ax.text(x, y,
                      label,
                      size=font_size,
                      color=font_color,
                      family=font_family,
                      weight=font_weight,
                      alpha=alpha,
                      horizontalalignment=horizontalalignment,
                      verticalalignment=verticalalignment,
                      rotation=trans_angle,
                      transform=ax.transData,
                      bbox=bbox,
                      zorder=1,
                      clip_on=True,
                      )
          text_items[(n1, n2)] = t
  
      return text_items
  
  
  def draw_circular(G, **kwargs):
      """Draw the graph G with a circular layout.
  
      Parameters
      ----------
      G : graph
         A networkx graph
  
      kwargs : optional keywords
         See networkx.draw_networkx() for a description of optional keywords,
         with the exception of the pos parameter which is not used by this
         function.
      """
      draw(G, circular_layout(G), **kwargs)
  
  
  def draw_random(G, **kwargs):
      """Draw the graph G with a random layout.
  
      Parameters
      ----------
      G : graph
         A networkx graph
  
      kwargs : optional keywords
         See networkx.draw_networkx() for a description of optional keywords,
         with the exception of the pos parameter which is not used by this
         function.
      """
      draw(G, random_layout(G), **kwargs)
  
  
  def draw_spectral(G, **kwargs):
      """Draw the graph G with a spectral layout.
  
      Parameters
      ----------
      G : graph
         A networkx graph
  
      kwargs : optional keywords
         See networkx.draw_networkx() for a description of optional keywords,
         with the exception of the pos parameter which is not used by this
         function.
      """
      draw(G, spectral_layout(G), **kwargs)
  
  
  def draw_spring(G, **kwargs):
      """Draw the graph G with a spring layout.
  
      Parameters
      ----------
      G : graph
         A networkx graph
  
      kwargs : optional keywords
         See networkx.draw_networkx() for a description of optional keywords,
         with the exception of the pos parameter which is not used by this
         function.
      """
      draw(G, spring_layout(G), **kwargs)
  
  
  def draw_shell(G, **kwargs):
      """Draw networkx graph with shell layout.
  
      Parameters
      ----------
      G : graph
         A networkx graph
  
      kwargs : optional keywords
         See networkx.draw_networkx() for a description of optional keywords,
         with the exception of the pos parameter which is not used by this
         function.
      """
      nlist = kwargs.get('nlist', None)
      if nlist is not None:
          del(kwargs['nlist'])
      draw(G, shell_layout(G, nlist=nlist), **kwargs)
  
  
  def draw_nx(G, pos, **kwds):
      """For backward compatibility; use draw or draw_networkx."""
      draw(G, pos, **kwds)
  
  
  def apply_alpha(colors, alpha, elem_list, cmap=None, vmin=None, vmax=None):
      """Apply an alpha (or list of alphas) to the colors provided.
  
      Parameters
      ----------
  
      color : color string, or array of floats
         Color of element. Can be a single color format string (default='r'),
         or a  sequence of colors with the same length as nodelist.
         If numeric values are specified they will be mapped to
         colors using the cmap and vmin,vmax parameters.  See
         matplotlib.scatter for more details.
  
      alpha : float or array of floats
         Alpha values for elements. This can be a single alpha value, in
         which case it will be applied to all the elements of color. Otherwise,
         if it is an array, the elements of alpha will be applied to the colors
         in order (cycling through alpha multiple times if necessary).
  
      elem_list : array of networkx objects
         The list of elements which are being colored. These could be nodes, edges
         or labels.
  
      cmap : matplotlib colormap
         Color map for use if colors is a list of floats corresponding to points on
         a color mapping.
  
      vmin, vmax : float
         Minimum and maximum values for normalizing colors if a color mapping is used.
  
      Returns
      -------
  
      rgba_colors : numpy ndarray
          Array containing RGBA format values for each of the node colours.
  
      """
      import numbers
      import itertools
  
      try:
          import numpy
          from matplotlib.colors import colorConverter
          import matplotlib.cm as cm
      except ImportError:
          raise ImportError("Matplotlib required for draw()")
  
      # If we have been provided with a list of numbers as long as elem_list, apply the color mapping.
      if len(colors) == len(elem_list) and isinstance(colors[0], numbers.Number):
          mapper = cm.ScalarMappable(cmap=cmap)
          mapper.set_clim(vmin, vmax)
          rgba_colors = mapper.to_rgba(colors)
      # Otherwise, convert colors to matplotlib's RGB using the colorConverter object.
      # These are converted to numpy ndarrays to be consistent with the to_rgba method of ScalarMappable.
      else:
          try:
              rgba_colors = numpy.array([colorConverter.to_rgba(colors)])
          except ValueError:
              rgba_colors = numpy.array([colorConverter.to_rgba(color) for color in colors])
      # Set the final column of the rgba_colors to have the relevant alpha values.
      try:
          # If alpha is longer than the number of colors, resize to the number of elements.
          # Also, if rgba_colors.size (the number of elements of rgba_colors) is the same as the number of
          # elements, resize the array, to avoid it being interpreted as a colormap by scatter()
          if len(alpha) > len(rgba_colors) or rgba_colors.size == len(elem_list):
              rgba_colors.resize((len(elem_list), 4))
              rgba_colors[1:, 0] = rgba_colors[0, 0]
              rgba_colors[1:, 1] = rgba_colors[0, 1]
              rgba_colors[1:, 2] = rgba_colors[0, 2]
          rgba_colors[:,  3] = list(itertools.islice(itertools.cycle(alpha), len(rgba_colors)))
      except TypeError:
          rgba_colors[:, -1] = alpha
      return rgba_colors
  
  # fixture for nose tests
  def setup_module(module):
      from nose import SkipTest
      try:
          import matplotlib as mpl
          mpl.use('PS', warn=False)
          import matplotlib.pyplot as plt
      except:
          raise SkipTest("matplotlib not available")
  