Community characterization of heterogeneous complex systems

TL;DR

This paper presents a statistical method using hypergeometric distribution to characterize communities in heterogeneous complex systems, effectively identifying over-expressed properties within communities.

Contribution

The paper introduces a novel analytical approach for community characterization that works across different community sizes and types in complex networks.

Findings

Method effectively characterizes communities in diverse networks.

It identifies over-expressed properties with high statistical significance.

Works well for both large and small communities.

Abstract

We introduce an analytical statistical method to characterize the communities detected in heterogeneous complex systems. By posing a suitable null hypothesis, our method makes use of the hypergeometric distribution to assess the probability that a given property is over-expressed in the elements of a community with respect to all the elements of the investigated set. We apply our method to two specific complex networks, namely a network of world movies and a network of physics preprints. The characterization of the elements and of the communities is done in terms of languages and countries for the movie network and of journals and subject categories for papers. We find that our method is able to characterize clearly the identified communities. Moreover our method works well both for large and for small communities.