Volume 103, Number 5, September 2013
|Number of page(s)||6|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||01 October 2013|
Analysis of stability of community structure across multiple hierarchical levels
1 School of Management Science and Engineering, Central University of Finance and Economics Beijing 100080, China
2 Academy of Mathematic and Systems Science, Chinese Academy of Sciences - Beijing 100190, China
3 National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences Beijing 100190, China
Received: 28 March 2013
Accepted: 29 August 2013
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.
PACS: 89.75.Hc – Networks and genealogical trees / 89.75.Fb – Structures and organization in complex systems
© EPLA, 2013
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