A testing based extraction algorithm for identifying significant communities in networks

TL;DR

This paper introduces ESSC, a statistically grounded community detection algorithm that automatically determines community count and size, handles overlaps, and identifies background vertices, validated through real and simulated network data.

Contribution

The paper presents ESSC, a novel testing-based method for community detection that automatically identifies communities, overlaps, and background vertices in complex networks.

Findings

ESSC effectively detects communities in real networks.

It handles overlapping communities and background vertices.

Performance is validated through simulation studies.

Abstract

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 \urlhttp://www.unc.edu/~jameswd/research.html.