Narrow scope for resolution-limit-free community detection

TL;DR

This paper rigorously defines resolution-limit-free community detection, characterizes which methods are resolution-limit-free, and demonstrates that only a limited class of methods possess this property, providing a natural, effective formulation.

Contribution

It offers a formal definition of resolution-limit-free methods, characterizes their properties, and identifies the limited scope of such methods in community detection.

Findings

Identifies the class of resolution-limit-free community detection methods.

Proves that only a limited scope of methods are resolution-limit-free.

Provides a natural formulation that performs well.

Abstract

Detecting communities in large networks has drawn much attention over the years. While modularity remains one of the more popular methods of community detection, the so-called resolution limit remains a significant drawback. To overcome this issue, it was recently suggested that instead of comparing the network to a random null model, as is done in modularity, it should be compared to a constant factor. However, it is unclear what is meant exactly by "resolution-limit-free", that is, not suffering from the resolution limit. Furthermore, the question remains what other methods could be classified as resolution-limit-free. In this paper we suggest a rigorous definition and derive some basic properties of resolution-limit-free methods. More importantly, we are able to prove exactly which class of community detection methods are resolution-limit-free. Furthermore, we analyze which methods are not resolution-limit-free, suggesting there is only a limited scope for resolution-limit-free community detection methods. Finally, we provide such a natural formulation, and show it performs superbly.