Analysis of community structure in networks of correlated data

TL;DR

This paper introduces a generalized modularity measure for analyzing community structures in complex networks derived from correlated data, applicable to various network types including directed, weighted, signed, and self-looped networks.

Contribution

It reformulates modularity to handle the most general network conditions, maintaining probabilistic semantics for networks of correlated data.

Findings

Successfully applied to a real network of store correlations in Lyon.

Generalized modularity preserves probabilistic interpretation across diverse network types.

Enhances community detection in complex, real-world data networks.

Abstract

We present a reformulation of modularity that allows the analysis of the community structure in networks of correlated data. The new modularity preserves the probabilistic semantics of the original definition even when the network is directed, weighted, signed, and has self-loops. This is the most general condition one can find in the study of any network, in particular those defined from correlated data. We apply our results to a real network of correlated data between stores in the city of Lyon (France).