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×d must be even.

seedinteger, random_state, or None (default)

Indicator of random number generation state. See Randomness.

Raises
NetworkXError

If n×d is odd or d is greater than or equal to n.

Notes

The nodes are numbered from 0 to n1.

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(n1/3ϵ).

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