Efficient and Exact Sampling of Simple Graphs with Given Arbitrary Degree Sequence
Abstract
Uniform sampling from graphical realizations of a given degree sequence is a fundamental component in simulationbased measurements of network observables, with applications ranging from epidemics, through social networks to Internet modeling. Existing graph sampling methods are either linkswap based (MarkovChain Monte Carlo algorithms) or stubmatching based (the Configuration Model). Both types are illcontrolled, with typically unknown mixing times for linkswap 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 theorembased 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 powerlaw distributions and from binomial distributions.
 Publication:

PLoS ONE
 Pub Date:
 April 2010
 DOI:
 10.1371/journal.pone.0010012
 arXiv:
 arXiv:1002.2975
 Bibcode:
 2010PLoSO...510012D
 Keywords:

 Physics  Physics and Society;
 Condensed Matter  Statistical Mechanics;
 Computer Science  Data Structures and Algorithms
 EPrint:
 8 pages, 3 figures