Abstract:

Network data analysis is a fast growing research field with diverse applications spanning several scientific 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 a 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 as well as estimation of node popularities and model parameters, and demonstrate the advantages of the new modularity over the degree-corrected blockmodel modularity in simulations. By analyzing the political blogs network, the British MP network, and the DBLP bibliographical network, we illustrate that improved empirical insights can be gained through this methodology. If time permits, I will also briefly outline some ongoing work on anomaly detection in networks.