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dense_gnm_random_graph(n, m, seed=None)[source]

Returns a \(G_{n,m}\) random graph.

In the \(G_{n,m}\) model, a graph is chosen uniformly at random from the set of all graphs with \(n\) nodes and \(m\) edges.

This algorithm should be faster than gnm_random_graph() for dense graphs.

  • n (int) – The number of nodes.
  • m (int) – The number of edges.
  • seed (integer, random_state, or None (default)) – Indicator of random number generation state. See Randomness.


Algorithm by Keith M. Briggs Mar 31, 2006. Inspired by Knuth’s Algorithm S (Selection sampling technique), in section 3.4.2 of [1].


[1]Donald E. Knuth, The Art of Computer Programming, Volume 2/Seminumerical algorithms, Third Edition, Addison-Wesley, 1997.