Efficient and Exact Sampling of Simple Graphs with Given Arbitrary Degree Sequence

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 bas...

Descripción completa

Detalles Bibliográficos
Autores principales: Del Genio, Charo I., Kim, Hyunju, Toroczkai, Zoltán, Bassler, Kevin E.
Formato: Texto
Lenguaje:English
Publicado: Public Library of Science 2010
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2851615/
https://www.ncbi.nlm.nih.gov/pubmed/20386694
http://dx.doi.org/10.1371/journal.pone.0010012
_version_ 1782179884543508480
author Del Genio, Charo I.
Kim, Hyunju
Toroczkai, Zoltán
Bassler, Kevin E.
author_facet Del Genio, Charo I.
Kim, Hyunju
Toroczkai, Zoltán
Bassler, Kevin E.
author_sort Del Genio, Charo I.
collection PubMed
description 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 [Image: see text], 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.
format Text
id pubmed-2851615
institution National Center for Biotechnology Information
language English
publishDate 2010
publisher Public Library of Science
record_format MEDLINE/PubMed
spelling pubmed-28516152010-04-12 Efficient and Exact Sampling of Simple Graphs with Given Arbitrary Degree Sequence Del Genio, Charo I. Kim, Hyunju Toroczkai, Zoltán Bassler, Kevin E. PLoS One Research Article 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 [Image: see text], 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. Public Library of Science 2010-04-08 /pmc/articles/PMC2851615/ /pubmed/20386694 http://dx.doi.org/10.1371/journal.pone.0010012 Text en Del Genio et al. http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.
spellingShingle Research Article
Del Genio, Charo I.
Kim, Hyunju
Toroczkai, Zoltán
Bassler, Kevin E.
Efficient and Exact Sampling of Simple Graphs with Given Arbitrary Degree Sequence
title Efficient and Exact Sampling of Simple Graphs with Given Arbitrary Degree Sequence
title_full Efficient and Exact Sampling of Simple Graphs with Given Arbitrary Degree Sequence
title_fullStr Efficient and Exact Sampling of Simple Graphs with Given Arbitrary Degree Sequence
title_full_unstemmed Efficient and Exact Sampling of Simple Graphs with Given Arbitrary Degree Sequence
title_short Efficient and Exact Sampling of Simple Graphs with Given Arbitrary Degree Sequence
title_sort efficient and exact sampling of simple graphs with given arbitrary degree sequence
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2851615/
https://www.ncbi.nlm.nih.gov/pubmed/20386694
http://dx.doi.org/10.1371/journal.pone.0010012
work_keys_str_mv AT delgeniocharoi efficientandexactsamplingofsimplegraphswithgivenarbitrarydegreesequence
AT kimhyunju efficientandexactsamplingofsimplegraphswithgivenarbitrarydegreesequence
AT toroczkaizoltan efficientandexactsamplingofsimplegraphswithgivenarbitrarydegreesequence
AT basslerkevine efficientandexactsamplingofsimplegraphswithgivenarbitrarydegreesequence