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Efficient and simple generation of random simple connected graphs with prescribed degree sequence

Fabien Viger 1 Matthieu Latapy 1
1 ComplexNetworks
LIP6 - Laboratoire d'Informatique de Paris 6
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 designed 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 argue rigorously and which was confirmed by strong empirical evidence, we finally reduce the best asymptotic complexity bond known so far.
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https://hal.archives-ouvertes.fr/hal-01468081
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Submitted on : Wednesday, February 15, 2017 - 10:49:41 AM
Last modification on : Tuesday, April 7, 2020 - 4:34:03 PM
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Fabien Viger, Matthieu Latapy. Efficient and simple generation of random simple connected graphs with prescribed degree sequence. Journal of Complex Networks, Oxford University Press, 2016, 4 (1), pp.15 - 37. ⟨10.1093/comnet/cnv013⟩. ⟨hal-01468081⟩

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