Efficient and Simple Generation of Random Simple Connected Graphs with Prescribed Degree Sequence

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 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, we finally obtain an O(n log n) algorithm, which, in spite of being very simple, improves the best known complexity.