Limited resolution in complex network community detection with Potts model approach

TL;DR

This paper investigates the resolution limitations of the q-state Potts model in community detection, revealing a tunable threshold and challenges in detecting communities with broad size distributions.

Contribution

It generalizes previous work on modularity resolution limits to the Potts model, highlighting the existence of a tunable resolution threshold and limitations of global optimization.

Findings

The Potts model has a tunable resolution threshold.

Global optimization struggles with broad community size distributions.

Resolution issues are similar to those in modularity-based methods.

Abstract

According to Fortunato and Barthelemy, modularity-based community detection algorithms have a resolution threshold such that small communities in a large network are invisible. Here we generalize their work and show that the q-state Potts community detection method introduced by Reichardt and Bornholdt also has a resolution threshold. The model contains a parameter by which this threshold can be tuned, but no a priori principle is known to select the proper value. Single global optimization criteria do not seem capable for detecting all communities if their size distribution is broad.