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

Return a random regular graph of n nodes each with degree d.

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

Parameters :

d : int


n : integer

Number of nodes. The value of n*d must be even.

seed : hashable object

The seed for random number generator.


The nodes are numbered form 0 to n-1.

Kim and Vu’s paper [R312] shows that this algorithm samples in an asymptotically uniform way from the space of random graphs when d = O(n**(1/3-epsilon)).


[R311]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
[R312](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