Potts model based on a Markov process computation solves the community structure problem effectively

TL;DR

This paper introduces a Markov process-based Potts model framework that effectively uncovers hierarchical community structures and determines the optimal number of communities in complex networks.

Contribution

It presents a novel Markov process approach to analyze Potts model dynamics, revealing hierarchical community structures and stability measures.

Findings

Successfully identifies hierarchical community structures

Determines optimal number of communities and stability

Validated through theoretical analysis and experiments

Abstract

Potts model is a powerful tool to uncover community structure in complex networks. Here, we propose a new framework to reveal the optimal number of communities and stability of network structure by quantitatively analyzing the dynamics of Potts model. Specifically we model the community structure detection Potts procedure by a Markov process, which has a clear mathematical explanation. Then we show that the local uniform behavior of spin values across multiple timescales in the representation of the Markov variables could naturally reveal the network's hierarchical community structure. In addition, critical topological information regarding to multivariate spin configuration could also be inferred from the spectral signatures of the Markov process. Finally an algorithm is developed to determine fuzzy communities based on the optimal number of communities and the stability across multiple timescales. The effectiveness and efficiency of our algorithm are theoretically analyzed as well as experimentally validated.