Fuzzy Overlapping Community Quality Metrics

TL;DR

This paper reviews and generalizes overlapping community quality metrics, proposing a uniform framework and evaluating their effectiveness on real and synthetic networks to guide metric selection.

Contribution

It introduces a unified definition for overlapping modularity metrics and extends local metrics for overlapping communities, providing comprehensive comparison and practical recommendations.

Findings

Product of belonging coefficients yields best results

Unified framework enables flexible application of metrics

Guides researchers on metric selection for overlapping communities

Abstract

Modularity is widely used to effectively measure the strength of the disjoint community structure found by community detection algorithms. Several overlapping extensions of modularity were proposed to measure the quality of overlapping community structure. However, all these extensions differ just in the way they define the belonging coefficient and belonging function. Yet, there is lack of systematic comparison of different extensions. To fill this gap, we overview overlapping extensions of modularity and generalize them with a uniform definition enabling application of different belonging coefficients and belonging functions to select the best. In addition, we extend localized modularity, modularity density, and eight local community quality metrics to enable their usages for overlapping communities. The experimental results on a large number of real networks and synthetic networks using overlapping extensions of modularity, overlapping modularity density, and local metrics show that the best results are obtained when the product of the belonging coefficients of two nodes is used as the belonging function. Moreover, the results may be used to guide researchers on which metrics to adopt when measuring the quality of overlapping community structure.