TY - JOUR
T1 - Efficient and Exact Sampling of Simple Graphs with Given Arbitrary Degree Sequence
A1 - Del Genio, Charo I.
A1 - Kim, Hyunju
A1 - Toroczkai, Zoltán
A1 - Bassler, Kevin E.
Y1 - 2010/04/08
N2 - 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 back-tracking or rejections. Using a central limit theorem-based reasoning, we argue, that for large , 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.
JF - PLOS ONE
JA - PLOS ONE
VL - 5
IS - 4
UR - https://doi.org/10.1371/journal.pone.0010012
SP - e10012
EP -
PB - Public Library of Science
M3 - doi:10.1371/journal.pone.0010012
ER -