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

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 $d = O (n^{1 / 3 - ϵ})$ .

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