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"]
[docs]@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