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+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)
+@nx._dispatchable(graphs=None, returns_graph=True)
+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 performs 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