We study a change point detection scenario for a dynamic community graph model, which is formed by adding new vertices and randomly attaching them to the existing nodes. The goal of this work is to design a test statistic to detect the merging of communities without solving the problem of identifying the communities. We propose a test that can ascertain when the connectivity between the balanced communities is changing. In addition to the theoretical analysis of the test statistic, we perform Monte Carlo simulations of the dynamic stochastic blockmodel to demonstrate that our test can detect changes in graph topology, and we study a dynamic social-contact graph.
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