Significant communities in large sparse networks

TL;DR

This paper introduces a new method to assess the significance of communities in large sparse networks by perturbing the network with added links and analyzing the stability of detected communities.

Contribution

The authors propose a simple perturbation approach using added links and aggregation to identify significant communities in sparse networks, demonstrated on benchmark and legal networks.

Findings

Method effectively identifies significant communities.

Applied to ECJ case law network to map legal areas.

Robustness of communities correlates with their significance.

Abstract

Researchers use community-detection algorithms to reveal large-scale organization in biological and social networks, but community detection is useful only if the communities are significant and not a result of noisy data. To assess the statistical significance of the network communities, or the robustness of the detected structure, one approach is to perturb the network structure by removing links and measure how much the communities change. However, perturbing sparse networks is challenging because they are inherently sensitive; they shatter easily if links are removed. Here we propose a simple method to perturb sparse networks and assess the significance of their communities. We generate resampled networks by adding extra links based on local information, then we aggregate the information from multiple resampled networks to find a coarse-grained description of significant clusters. In addition to testing our method on benchmark networks, we use our method on the sparse network of the European Court of Justice (ECJ) case law, to detect significant and insignificant areas of law. We use our significance analysis to draw a map of the ECJ case law network that reveals the relations between the areas of law.