A generalised significance test for individual communities in networks

TL;DR

This paper introduces a flexible statistical test for assessing the significance of individual communities in networks, accommodating various community detection algorithms and quality functions.

Contribution

It presents a novel method that evaluates community significance by estimating quality function distributions in randomized networks, compatible with multiple detection algorithms.

Findings

Effective in synthetic networks

Applicable to empirical networks

Compatible with different community detection methods

Abstract

Many empirical networks have community structure, in which nodes are densely interconnected within each community (i.e., a group of nodes) and sparsely across different communities. Like other local and meso-scale structure of networks, communities are generally heterogeneous in various aspects such as the size, density of edges, connectivity to other communities and significance. In the present study, we propose a method to statistically test the significance of individual communities in a given network. Compared to the previous methods, the present algorithm is unique in that it accepts different community-detection algorithms and the corresponding quality function for single communities. The present method requires that a quality of each community can be quantified and that community detection is performed as optimisation of such a quality function summed over the communities. Various community detection algorithms including modularity maximisation and graph partitioning meet this criterion. Our method estimates a distribution of the quality function for randomised networks to calculate a likelihood of each community in the given network. We illustrate our algorithm by synthetic and empirical networks.