A New Metric for Quality of Network Community Structure

TL;DR

This paper introduces Modularity Density, a new metric for evaluating network community structures that addresses the limitations of traditional modularity, such as the resolution limit, and provides more consistent community quality assessments.

Contribution

The paper proposes Modularity Density, a modified modularity metric that resolves the resolution limit problem and improves community quality measurement.

Findings

Modularity Density effectively resolves the resolution limit issue.

It aligns better with various community quality metrics.

It outperforms traditional modularity in real network evaluations.

Abstract

Modularity is widely used to effectively measure the strength of the community structure found by community detection algorithms. However, modularity maximization suffers from two opposite yet coexisting problems: in some cases, it tends to favor small communities over large ones while in others, large communities over small ones. The latter tendency is known in the literature as the resolution limit problem. To address them, we propose to modify modularity by subtracting from it the fraction of edges connecting nodes of different communities and by including community density into modularity. We refer to the modified metric as Modularity Density and we demonstrate that it indeed resolves both problems mentioned above. We describe the motivation for introducing this metric by using intuitively clear and simple examples. We also prove that this new metric solves the resolution limit problem. Finally, we discuss the results of applying this metric, modularity, and several other popular community quality metrics to two real dynamic networks. The results imply that Modularity Density is consistent with all the community quality measurements but not modularity, which suggests that Modularity Density is an improved measurement of the community quality compared to modularity.