random_regular_graph¶

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

Returns a random d-regular graph on n nodes.

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

Parameters:	d (int) – The degree of each node. n (integer) – The number of nodes. The value of `n * d` must be even. seed (hashable object) – The seed for random number generator.

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 \(d = O(n^{1 / 3 - \epsilon})\).

Raises:	`NetworkXError` – If `n * d` is odd or `d` is greater than or equal to `n`.

References

[1]	A. Steger and N. Wormald, Generating random regular graphs quickly, Probability and Computing 8 (1999), 377-396, 1999. http://citeseer.ist.psu.edu/steger99generating.html

[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