期刊
PLOS ONE
卷 5, 期 4, 页码 -出版社
PUBLIC LIBRARY SCIENCE
DOI: 10.1371/journal.pone.0010012
关键词
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资金
- National Science Foundation (NSF) [DMR-0908286]
- Norman Hackerman Advanced Research Program [95921]
- NSF [BCS-0826958]
- Defense Threat Reduction Agency (DTRA) [HDTRA 201473-35045]
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 stub-matching 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.
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