Fast generation of random connected graphs with prescribed degrees
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 realworld degree distributions, which outperforms the first one. Assuming a conjecture which we state and argue rigorously, we finally obtain an loglinear algorithm, which, in spite of being very simple, improves the best known complexity.
 Publication:

arXiv eprints
 Pub Date:
 February 2005
 arXiv:
 arXiv:cs/0502085
 Bibcode:
 2005cs........2085V
 Keywords:

 Computer Science  Networking and Internet Architecture;
 Computer Science  Discrete Mathematics;
 Condensed Matter  Disordered Systems and Neural Networks;
 G.2.2