networkx.random_regular_graph¶

networkx.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.
Raises:	NetworkXError If \(n * d\) 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 [R1234] shows that this algorithm samples in an asymptotically uniform way from the space of random graphs when d = O(n^{1 / 3 - epsilon}).

References

[R1233]

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

[R1234]

(1, 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