A block model for node popularity in networks with community structure

Srijan Sengupta, Yuguo Chen

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)365-386
Number of pages22
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Issue number2
StatePublished - Mar 2018


  • Community detection
  • Degree-corrected block model
  • Likelihood modularity
  • Node popularity
  • Popularity-adjusted block model
  • Stochastic block model

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'A block model for node popularity in networks with community structure'. Together they form a unique fingerprint.

Cite this