Quality functions in community detection

TL;DR

This paper critically examines the use of quality functions, especially modularity, in community detection, highlighting their limitations in comparing partitions with different numbers of communities and discussing their applicability.

Contribution

It provides a critical analysis of quality functions in community detection, emphasizing their limitations and the challenges in comparing partitions with varying numbers of communities.

Findings

Quality functions are useful for comparing partitions with the same number of modules.

Comparing partitions with different numbers of modules using quality functions can lead to ambiguities.

Modularity has a resolution limit that affects its effectiveness in community detection.

Abstract

Community structure represents the local organization of complex networks and the single most important feature to extract functional relationships between nodes. In the last years, the problem of community detection has been reformulated in terms of the optimization of a function, the Newman-Girvan modularity, that is supposed to express the quality of the partitions of a network into communities. Starting from a recent critical survey on modularity optimization, pointing out the existence of a resolution limit that poses severe limits to its applicability, we discuss the general issue of the use of quality functions in community detection. Our main conclusion is that quality functions are useful to compare partitions with the same number of modules, whereas the comparison of partitions with different numbers of modules is not straightforward and may lead to ambiguities.