Scalable detection of statistically significant communities and hierarchies, using message passing for modularity

Modularity is a popular measure of community structure. However, maximizing the modularity can lead to many competing partitions, with almost the same modularity, that are poorly correlated with each other. It can also produce illusory ''communities'' in random graphs where none...

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Veröffentlicht in:Proceedings of the National Academy of Sciences - PNAS Jg. 111; H. 51; S. 18144
Hauptverfasser: Zhang, Pan, Moore, Cristopher
Format: Journal Article
Sprache:Englisch
Veröffentlicht: United States 23.12.2014
Schlagworte:
Algorithms
Cluster Analysis
Models, Theoretical
Stochastic Processes
phase transitions
statistical significance
networks
community detection
message-passing algorithms
ISSN:1091-6490, 1091-6490
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Zusammenfassung:Modularity is a popular measure of community structure. However, maximizing the modularity can lead to many competing partitions, with almost the same modularity, that are poorly correlated with each other. It can also produce illusory ''communities'' in random graphs where none exist. We address this problem by using the modularity as a Hamiltonian at finite temperature and using an efficient belief propagation algorithm to obtain the consensus of many partitions with high modularity, rather than looking for a single partition that maximizes it. We show analytically and numerically that the proposed algorithm works all of the way down to the detectability transition in networks generated by the stochastic block model. It also performs well on real-world networks, revealing large communities in some networks where previous work has claimed no communities exist. Finally we show that by applying our algorithm recursively, subdividing communities until no statistically significant subcommunities can be found, we can detect hierarchical structure in real-world networks more efficiently than previous methods.
Bibliographie:ObjectType-Article-1
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ISSN:1091-6490
1091-6490
DOI:10.1073/pnas.1409770111