Z-score-based modularity for community detection in networks

TL;DR

This paper introduces Z-modularity, a new community detection quality function based on Z-scores, which addresses the resolution limit of traditional modularity in network analysis.

Contribution

It proposes Z-modularity, a novel measure that improves community detection by overcoming limitations of existing modularity functions.

Findings

Z-modularity mitigates the resolution limit in certain cases

The new measure performs well on artificial and real-world networks

Computational experiments validate the effectiveness of Z-modularity

Abstract

Identifying community structure in networks is an issue of particular interest in network science. The modularity introduced by Newman and Girvan [Phys. Rev. E 69, 026113 (2004)] is the most popular quality function for community detection in networks. In this study, we identify a problem in the concept of modularity and suggest a solution to overcome this problem. Specifically, we obtain a new quality function for community detection. We refer to the function as Z-modularity because it measures the Z-score of a given division with respect to the fraction of the number of edges within communities. Our theoretical analysis shows that Z-modularity mitigates the resolution limit of the original modularity in certain cases. Computational experiments using both artificial networks and well-known real-world networks demonstrate the validity and reliability of the proposed quality function.