Spaces:
Running
Running
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"] | |
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 | |