  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.
