Finding network communities using modularity density

TL;DR

This paper analyzes modularity density as a community detection metric, demonstrating its advantages over traditional modularity, its analytical properties, and introducing an efficient algorithm validated on benchmarks.

Contribution

It provides a detailed analysis of modularity density, highlighting its benefits, limitations, and introduces a new quadratic algorithm for community detection.

Findings

Modularity density avoids drawbacks of traditional modularity.

It can identify communities without ground-truth labels.

The proposed algorithm is efficient and accurate on benchmarks.

Abstract

Many real-world complex networks exhibit a community structure, in which the modules correspond to actual functional units. Identifying these communities is a key challenge for scientists. A common approach is to search for the network partition that maximizes a quality function. Here, we present a detailed analysis of a recently proposed function, namely modularity density. We show that it does not incur in the drawbacks suffered by traditional modularity, and that it can identify networks without ground-truth community structure, deriving its analytical dependence on link density in generic random graphs. In addition, we show that modularity density allows an easy comparison between networks of different sizes, and we also present some limitations that methods based on modularity density may suffer from. Finally, we introduce an efficient, quadratic community detection algorithm based on modularity density maximization, validating its accuracy against theoretical predictions and on a set of benchmark networks.