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Abstract:
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Network data analysis is a rapidly growing research field with diverse applications spanning several scienti fic disciplines. The community structure observed in empirical networks has been of particular interest in the statistics literature, with a strong emphasis on the study of blockmodels. In this paper we study an important network feature called node popularity, which is closely associated with community structure. Neither the classical stochastic blockmodel nor its degree-corrected extension can satisfactorily capture the dynamics of node popularity as observed in empirical networks. We propose a popularity-adjusted blockmodel for flexible and realistic modeling of node popularity. We establish consistency of likelihood modularity for community detection under the proposed model, and demonstrate the advantages of the new modularity over the degree-corrected blockmodel modularity in simulations. By analyzing the political blogs network and the British MP network, we illustrate that improved empirical insights can be gained through this methodology.
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