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

Fabien Viger, Matthieu Latapy
2015 Journal of Complex Networks  
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,
more » ... ifferent approach, specifically designed for typical realworld degree distributions, which outperforms the first one. Assuming a conjecture, we finally obtain an O(n log n) algorithm, which, in spite of being very simple, improves the best known complexity. 1 LIP6, University Pierre and Marie Curie, 4 place Jussieu, 75005 Paris 2 LIAFA, University Denis Diderot, 2 place Jussieu, 75005 Paris 3 A simple graph has neither multiple edges, i.e. several edges binding the same pair of vertices, nor loops, i.e. edges binding a vertex to itself.
doi:10.1093/comnet/cnv013 fatcat:j74qoaqvsvb7te76zqib4f77ke