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A block model for node popularity in networks with community structure
Author(s) -
Sengupta Srijan,
Chen Yuguo
Publication year - 2018
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12245
Subject(s) - popularity , stochastic block model , node (physics) , modularity (biology) , computer science , community structure , block (permutation group theory) , consistency (knowledge bases) , theoretical computer science , data mining , complex network , clique percolation method , data science , artificial intelligence , cluster analysis , mathematics , world wide web , statistics , engineering , psychology , social psychology , geometry , structural engineering , biology , genetics
Summary The community structure that is observed in empirical networks has been of particular interest in the statistics literature, with a strong emphasis on the study of block models. We study an important network feature called node popularity, which is closely associated with community structure. Neither the classical stochastic block model nor its degree‐corrected extension can satisfactorily capture the dynamics of node popularity as observed in empirical networks. We propose a popularity‐adjusted block model for flexible and realistic modelling 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 block model modularity in simulations. By analysing the political blogs network, the British Members of Parliament network and the ‘Digital bibliography and library project’ bibliographical network, we illustrate that improved empirical insights can be gained through this methodology.