Analysis of stability of community structure across multiple hierarchical levels

TL;DR

This paper introduces a Markov process-based framework to analyze the stability of community structures across multiple hierarchical levels, revealing hidden properties and effectively uncovering multiscale structures.

Contribution

It presents a novel, mathematically grounded method using spectral analysis of a Markov process to detect and analyze hierarchical community structures without resolution limitations.

Findings

Successfully uncovers hierarchical community structures at different scales

Demonstrates effectiveness and efficiency on example networks

Avoids resolution limit problems common in other methods

Abstract

The analysis of stability of community structure is an important problem for scientists from many fields. Here, we propose a new framework to reveal hidden properties of community structure by quantitatively analyzing the dynamics of Potts model. Specifically we model the Potts procedure of community structure detection by a Markov process, which has a clear mathematical explanation. Critical topological information regarding to multivariate spin configuration could also be inferred from the spectral significance of the Markov process. We test our framework on some example networks and find it doesn't have resolute limitation problem at all. Results have shown the model we proposed is able to uncover hierarchical structure in different scales effectively and efficiently.