Finding Statistically Significant Communities in Networks

TLDR

Community structure reveals a network’s internal organization and unit similarity, yet existing methods lack a versatile, multi‑purpose approach. We introduce OSLOM, the first algorithm that detects clusters while handling edge direction, weight, overlap, hierarchy, and dynamics. OSLOM optimizes a fitness function that quantifies cluster significance against random fluctuations using extreme and order statistics, and can be applied alone or as a refinement step, with sequential hybrids enabling analysis of very large networks. OSLOM matches the best existing algorithms on benchmark graphs, performs well on real networks, and is freely available at http://www.oslom.org.

Abstract

Community structure is one of the main structural features of networks, revealing both their internal organization and the similarity of their elementary units. Despite the large variety of methods proposed to detect communities in graphs, there is a big need for multi-purpose techniques, able to handle different types of datasets and the subtleties of community structure. In this paper we present OSLOM (Order Statistics Local Optimization Method), the first method capable to detect clusters in networks accounting for edge directions, edge weights, overlapping communities, hierarchies and community dynamics. It is based on the local optimization of a fitness function expressing the statistical significance of clusters with respect to random fluctuations, which is estimated with tools of Extreme and Order Statistics. OSLOM can be used alone or as a refinement procedure of partitions/covers delivered by other techniques. We have also implemented sequential algorithms combining OSLOM with other fast techniques, so that the community structure of very large networks can be uncovered. Our method has a comparable performance as the best existing algorithms on artificial benchmark graphs. Several applications on real networks are shown as well. OSLOM is implemented in a freely available software (http://www.oslom.org), and we believe it will be a valuable tool in the analysis of networks.