67 lines
1.8 KiB
Python
67 lines
1.8 KiB
Python
|
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
|