Analysis of stability of community structure across multiple hierarchical levels

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 structures by quantitatively analyzing the dynamics of the 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 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 does not have resolution limitation problems at all. Results have shown the model we proposed is able to uncover the hierarchical structure in different scales effectively and efficiently.