text: # -*- coding: utf-8 -*-
  #    Copyright (C) 2004-2019 by
  #    Aric Hagberg <hagberg@lanl.gov>
  #    Dan Schult <dschult@colgate.edu>
  #    Pieter Swart <swart@lanl.gov>
  #    All rights reserved.
  #    BSD license.
  #
  # Authors: Efraim Rodrigues (efraimnaassom@gmail.com)
  r"""Generators for cographs
  
  A cograph is a graph containing no path on four vertices.
  Cographs or $P_4$-free graphs can be obtained from a single vertex
  by disjoint union and complementation operations.
  
  References
  ----------
  .. [0] D.G. Corneil, H. Lerchs, L.Stewart Burlingham,
      "Complement reducible graphs",
      Discrete Applied Mathematics, Volume 3, Issue 3, 1981, Pages 163-174,
      ISSN 0166-218X.
  """
  import networkx as nx
  from networkx.utils import py_random_state
  
  __all__ = ['random_cograph']
  
  
  @py_random_state(1)
  def random_cograph(n, seed=None):
      r"""Returns a random cograph with $2 ^ n$ nodes.
  
      A cograph is a graph containing no path on four vertices.
      Cographs or $P_4$-free graphs can be obtained from a single vertex
      by disjoint union and complementation operations.
  
      This generator starts off from a single vertex and performes disjoint
      union and full join operations on itself.
      The decision on which operation will take place is random.
  
      Parameters
      ----------
      n : int
              The order of the cograph.
      seed : integer, random_state, or None (default)
          Indicator of random number generation state.
          See :ref:`Randomness<randomness>`.
  
      Returns
      -------
      G : A random graph containing no path on four vertices.
  
      See Also
      --------
      full_join
      union
  
      References
      ----------
      .. [1] D.G. Corneil, H. Lerchs, L.Stewart Burlingham,
         "Complement reducible graphs",
         Discrete Applied Mathematics, Volume 3, Issue 3, 1981, Pages 163-174,
         ISSN 0166-218X.
      """
      R = nx.empty_graph(1)
  
      for i in range(n):
          RR = nx.relabel_nodes(R.copy(), lambda x: x + len(R))
  
          if seed.randint(0, 1) == 0:
              R = nx.full_join(R, RR)
          else:
              R = nx.disjoint_union(R, RR)
  
      return R
  