Fast generation of random connected graphs with prescribed degrees

Fabien Viger (1, 2) , Matthieu Latapy (1)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
2 NPA - Networks and Performance Analysis

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 prove optimality conditions, and show how this optimality can be reached in practice. We then propose a different approach, specifically designed for typical real-world degree distributions, which outperforms the first one. Assuming a conjecture which we state and argue rigorously, we finally obtain an log-linear algorithm, which, in spite of being very simple, improves the best known complexity.

Mots clés: Connectivity; Generation; Model; Graphs; Random Graphs

Domaines: Réseaux et télécommunications [cs.NI]; Systèmes désordonnés et réseaux de neurones [cond-mat.dis-nn]; Mathématique discrète [cs.DM]

Fabien Viger, Matthieu Latapy. Fast generation of random connected graphs with prescribed degrees. 2005. ⟨hal-00004310⟩