random_regular_graph#

random_regular_graph(d, n, seed=None)[source]#

Returns a random $$d$$-regular graph on $$n$$ nodes.

A regular graph is a graph where each node has the same number of neighbors.

The resulting graph has no self-loops or parallel edges.

Parameters:
dint

The degree of each node.

ninteger

The number of nodes. The value of $$n \times d$$ must be even.

seedinteger, random_state, or None (default)

Indicator of random number generation state. See Randomness.

Raises:
NetworkXError

If $$n \times d$$ is odd or $$d$$ is greater than or equal to $$n$$.

Notes

The nodes are numbered from $$0$$ to $$n - 1$$.

Kim and Vu’s paper [2] shows that this algorithm samples in an asymptotically uniform way from the space of random graphs when $$d = O(n^{1 / 3 - \epsilon})$$.

References

[1]

A. Steger and N. Wormald, Generating random regular graphs quickly, Probability and Computing 8 (1999), 377-396, 1999. https://doi.org/10.1017/S0963548399003867

[2]

Jeong Han Kim and Van H. Vu, Generating random regular graphs, Proceedings of the thirty-fifth ACM symposium on Theory of computing, San Diego, CA, USA, pp 213–222, 2003. http://portal.acm.org/citation.cfm?id=780542.780576