Open Access
September 2014 A testing based extraction algorithm for identifying significant communities in networks
James D. Wilson, Simi Wang, Peter J. Mucha, Shankar Bhamidi, Andrew B. Nobel
Ann. Appl. Stat. 8(3): 1853-1891 (September 2014). DOI: 10.1214/14-AOAS760


A common and important problem arising in the study of networks is how to divide the vertices of a given network into one or more groups, called communities, in such a way that vertices of the same community are more interconnected than vertices belonging to different ones. We propose and investigate a testing based community detection procedure called Extraction of Statistically Significant Communities (ESSC). The ESSC procedure is based on $p$-values for the strength of connection between a single vertex and a set of vertices under a reference distribution derived from a conditional configuration network model. The procedure automatically selects both the number of communities in the network and their size. Moreover, ESSC can handle overlapping communities and, unlike the majority of existing methods, identifies “background” vertices that do not belong to a well-defined community. The method has only one parameter, which controls the stringency of the hypothesis tests. We investigate the performance and potential use of ESSC and compare it with a number of existing methods, through a validation study using four real network data sets. In addition, we carry out a simulation study to assess the effectiveness of ESSC in networks with various types of community structure, including networks with overlapping communities and those with background vertices. These results suggest that ESSC is an effective exploratory tool for the discovery of relevant community structure in complex network systems. Data and software are available at


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James D. Wilson. Simi Wang. Peter J. Mucha. Shankar Bhamidi. Andrew B. Nobel. "A testing based extraction algorithm for identifying significant communities in networks." Ann. Appl. Stat. 8 (3) 1853 - 1891, September 2014.


Published: September 2014
First available in Project Euclid: 23 October 2014

zbMATH: 1304.62141
MathSciNet: MR3271356
Digital Object Identifier: 10.1214/14-AOAS760

Keywords: background , Community detection , extraction , multiple testing , networks

Rights: Copyright © 2014 Institute of Mathematical Statistics

Vol.8 • No. 3 • September 2014
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