Random generation of large connected simple graphs with prescribed degree distribution

By Fabien Viger and Matthieu Latapy

Submitted. Extended abstract published in LNCS, proceedings of the 11-th international conference on Computing and Combinatorics COCOON'05, 2005, Kunming, Yunnan, Chine

Abstract

We address here the problem of generating random graphs uniformly from the set of simple connected graphs having a prescribed degree sequence. Our goal is to provide an algorithm suitable for practical use both because of its ability to generate very large graphs (efficiency) and because it is easy to implement (simplicity). We focus on a family of heuristics for which we introduce optimality conditions, and show how this optimality can be reached in practice. We then propose a different approach, specifically designed for real-world degree distributions, which outperforms the first one. Based on a conjecture which we discuss rigorously and study empirically, we finally reduce the best asymptotic complexity bound known so far.

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