Fast generation of random connected graphs with prescribed degrees
arXiv:cs/0502085
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 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.
References in corpus (8)
- Statistical mechanics of complex networks
- The structure and function of complex networks
- Random graphs with arbitrary degree distributions and their applications
- Evolution of networks
- Search in Power-Law Networks
- Accuracy and Scaling Phenomena in Internet Mapping
- Traceroute sampling makes random graphs appear to have power law degree distributions
- Scalable Percolation Search in Power Law Networks