Community Detection via Maximization of Modularity and Its Variants

TL;DR

This paper reviews modularity-based community detection methods, discusses the resolution limit problem, introduces two new algorithms (Fine-tuned Q and Qds), and demonstrates that Fine-tuned Qds outperforms existing methods in various networks.

Contribution

It introduces two novel community detection algorithms based on modularity and modularity density, improving community quality and addressing the resolution limit problem.

Findings

Fine-tuned Qds outperforms other algorithms in tests.

Fine-tuned Qds improves community detection results when applied to other algorithms.

The study provides a comprehensive comparison of modularity-based methods.

Abstract

In this paper, we first discuss the definition of modularity (Q) used as a metric for community quality and then we review the modularity maximization approaches which were used for community detection in the last decade. Then, we discuss two opposite yet coexisting problems of modularity optimization: in some cases, it tends to favor small communities over large ones while in others, large communities over small ones (so called the resolution limit problem). Next, we overview several community quality metrics proposed to solve the resolution limit problem and discuss Modularity Density (Qds) which simultaneously avoids the two problems of modularity. Finally, we introduce two novel fine-tuned community detection algorithms that iteratively attempt to improve the community quality measurements by splitting and merging the given network community structure. The first of them, referred to as Fine-tuned Q, is based on modularity (Q) while the second one is based on Modularity Density (Qds) and denoted as Fine-tuned Qds. Then, we compare the greedy algorithm of modularity maximization (denoted as Greedy Q), Fine-tuned Q, and Fine-tuned Qds on four real networks, and also on the classical clique network and the LFR benchmark networks, each of which is instantiated by a wide range of parameters. The results indicate that Fine-tuned Qds is the most effective among the three algorithms discussed. Moreover, we show that Fine-tuned Qds can be applied to the communities detected by other algorithms to significantly improve their results.