中文摘要：

社团结构分析是一项非常重要且具有挑战性的工作,已经引起来自不同领域学者的广泛关注.在该文中,作者创新性地结合Potts模型和Markov动态过程,提出了衡量多尺度社团结构稳定性的完整理论框架.对于给定的网络,该文通过揭示网络社团结构及其自旋动态的局域一致行为之间的关系,可以不使用特定的算法而直接获得社团结构相关的重要隐藏信息,比如社团结构的稳定性和在多个时间尺度的社团结构的最佳数量.它还克服了传统方法的不足,如模块度Q的分辨率局限性问题.进一步基于理论分析,该文给出一个无参数的社团结构探测算法.该算法通过计算每个节点的归属向量,可以识别网络的模糊社团结构,从而在多个层次上描述了每个节点参与重叠社团的程度.同时该文也证明了算法的可扩展性和在实际大型网络上的有效性.

英文摘要：

The analysis of stability of community structure is an important problem for scientists from many fields. Differently from the previous studies, we established a new framework to study the dynamics of Potts model for community structure detection by using the 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 that it does not have resolution limitation problems at all. Finally a parameter-free algorithm is developed to determine fuzzy communities based on the belonging vectors across multiple timescales. Results have shown the model we proposed is able to uncover the hierarchical structure in different scales effectively and efficiently.