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...
Autores principales: | , , , |
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Formato: | Texto |
Lenguaje: | English |
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Public Library of Science
2010
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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 |
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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 |
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