random_regular_graph#
- random_regular_graph(d, n, seed=None)[source]#
Returns a random \(d\)-regular graph on \(n\) nodes.
A regular graph is a graph where each node has the same number of neighbors.
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 \(d = O(n^{1 / 3 - \epsilon})\).
References
[1]A. Steger and N. Wormald, Generating random regular graphs quickly, Probability and Computing 8 (1999), 377-396, 1999. https://doi.org/10.1017/S0963548399003867
[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