We present a practical algorithm for generating random regular graphs. For all d growing as a small power of n , the d -regular graphs on n vertices are generated approximately uniformly at random, in the sense that all d -regular graphs on n vertices have in the limit the same probability as n → ∞. The expected runtime for these d s is [Oscr ]( nd 2 ).
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Steger et al. (1999) studied this question.
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