### Abstract

Uniform sampling from graphical realizations of a given degree sequence is a fundamental component in simulation-based measurements of network observables, with applications ranging from epidemics, through social networks to Internet modeling. Existing graph sampling methods are either link-swap based (Markov-Chain Monte Carlo algorithms) or stubmatching based (the Configuration Model). Both types are ill-controlled, with typically unknown mixing times for link-swap methods and uncontrolled rejections for the Configuration Model. Here we propose an efficient, polynomial time algorithm that generates statistically independent graph samples with a given, arbitrary, degree sequence. The algorithm provides a weight associated with each sample, allowing the observable to be measured either uniformly over the graph ensemble, or, alternatively, with a desired distribution. Unlike other algorithms, this method always produces a sample, without backtracking or rejections. Using a central limit theorem-based reasoning, we argue, that for large N, and for degree sequences admitting many realizations, the sample weights are expected to have a lognormal distribution. As examples, we apply our algorithm to generate networks with degree sequences drawn from power-law distributions and from binomial distributions.

Original language | English (US) |
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Article number | e10012 |

Journal | PloS one |

Volume | 5 |

Issue number | 4 |

DOIs | |

State | Published - Sep 10 2010 |

Externally published | Yes |

### ASJC Scopus subject areas

- Biochemistry, Genetics and Molecular Biology(all)
- Agricultural and Biological Sciences(all)
- General

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## Cite this

*PloS one*,

*5*(4), [e10012]. https://doi.org/10.1371/journal.pone.0010012