On community structure validation in real networks

TL;DR

This paper introduces new statistical indices for validating community structures in real networks, enabling comparison of partitions, assessment of similarity between networks, and evaluation of clustering algorithms.

Contribution

It proposes a set of hypothesis testing-based indices for community validation, addressing a less-explored aspect of community detection in real networks.

Findings

Indices effectively compare community partitions.

Indices assess similarity between different networks.

Indices evaluate clustering algorithm performance.

Abstract

Community structure is a commonly observed feature of real networks. The term refers to the presence in a network of groups of nodes (communities) that feature high internal connectivity, but are poorly connected between each other. Whereas the issue of community detection has been addressed in several works, the problem of validating a partition of nodes as a good community structure for a real network has received considerably less attention and remains an open issue. We propose a set of indices for community structure validation of network partitions that are based on an hypothesis testing procedure that assesses the distribution of links between and within communities. Using both simulations and real data, we illustrate how the proposed indices can be employed to compare the adequacy of different partitions of nodes as community structures in a given network, to assess whether two networks share the same or similar community structures, and to evaluate the performance of different network clustering algorithms.