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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.

  • d (int) – The degree of each node.
  • n (integer) – The number of nodes. The value of \(n \times d\) must be even.
  • seed (integer, random_state, or None (default)) – Indicator of random number generation state. See Randomness.


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 \(n \times d\) is odd or \(d\) is greater than or equal to \(n\).


[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