Detecting fuzzy community structures in complex networks with a Potts model

TL;DR

This paper introduces a fast community detection algorithm using a q-state Potts model that identifies fuzzy communities in complex networks without prior knowledge of the number of communities.

Contribution

It presents a novel method that detects overlapping and fuzzy communities by analyzing minima of a modified Potts spin glass Hamiltonian, without needing pre-specified community counts.

Findings

Effective detection of overlapping communities

Quantification of node-community associations

No prior knowledge of community number required

Abstract

A fast community detection algorithm based on a q-state Potts model is presented. Communities in networks (groups of densely interconnected nodes that are only loosely connected to the rest of the network) are found to coincide with the domains of equal spin value in the minima of a modified Potts spin glass Hamiltonian. Comparing global and local minima of the Hamiltonian allows for the detection of overlapping (``fuzzy'') communities and quantifying the association of nodes to multiple communities as well as the robustness of a community. No prior knowledge of the number of communities has to be assumed.