  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.
