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In this paper, we propose a method that extends the persistence-basedtopological data analysis (TDA) that is typically used for characterizingshapes to general networks. We introduce the concept of the community tree, atree structure established based on clique communities from the cliquepercolation method, to summarize the topological structures in a network from apersistence perspective. Furthermore, we develop efficient algorithms toconstruct and update community trees by maintaining a series of clique graphsin the form of spanning forests, in which each spanning tree is built on anunderlying Euler Tour tree. With the information revealed by community treesand the corresponding persistence diagrams, our proposed approach is able todetect clique communities and keep track of the major structural changes duringtheir evolution given a stability threshold. The results demonstrate itseffectiveness in extracting useful structural insights for time-varying socialnetworks.

Efficient Community Detection in Large-Scale Dynamic Networks Using Topological Data Analysis