random_cograph

random_cograph(n, seed=None)

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:

nint

The order of the cograph.

seedinteger, random_state, or None (default)

Indicator of random number generation state. See Randomness.

Returns:

GA 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.