Efficient and exact sampling of simple graphs with given arbitrary degree sequence

Charo I. Del Genio, Hyunju Kim, Zoltán Toroczkai, Kevin E. Bassler

Research output: Contribution to journalArticlepeer-review

115 Scopus citations


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 languageEnglish (US)
Article numbere10012
JournalPloS one
Issue number4
StatePublished - 2010
Externally publishedYes

ASJC Scopus subject areas

  • General Biochemistry, Genetics and Molecular Biology
  • General Agricultural and Biological Sciences
  • General


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