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Abstract:
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Modularity-based optimization methods are commonly used in practice to identify clusters and structure in graph-valued data. Here, we investigate the theoretical asymptotic properties of different modularity functions in large networks, beginning with stochastic blockmodel graphs. Our results include deriving asymptotic limiting distributions for modularity-based statistics in the large-network limit, accompanied by perturbation analysis of low rank matrices in the presence of noise. We apply our results to hypothesis testing problems for random graphs and to the analysis of uncertainty in computed modularity measures.
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