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A block model for node popularity in networks with community structure

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  • Srijan Sengupta
  • Yuguo Chen

Abstract

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.

Suggested Citation

  • Srijan Sengupta & Yuguo Chen, 2018. "A block model for node popularity in networks with community structure," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(2), pages 365-386, March.
    • Handle: RePEc:bla:jorssb:v:80:y:2018:i:2:p:365-386
    DOI: 10.1111/rssb.12245
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    Cited by:

    1. Majid Noroozi & Marianna Pensky, 2022. "The Hierarchy of Block Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 64-107, June.
    2. Li, Mengxue & von Sachs, Rainer & Pircalabelu, Eugen, 2024. "Time-varying degree-corrected stochastic block models," LIDAM Discussion Papers ISBA 2024014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Anirban Dasgupta & Srijan Sengupta, 2022. "Scalable Estimation of Epidemic Thresholds via Node Sampling," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 321-344, June.
    4. Majid Noroozi & Ramchandra Rimal & Marianna Pensky, 2021. "Estimation and clustering in popularity adjusted block model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(2), pages 293-317, April.
    5. Avanti Athreya & Joshua Cape & Minh Tang, 2022. "Eigenvalues of Stochastic Blockmodel Graphs and Random Graphs with Low-Rank Edge Probability Matrices," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 36-63, June.
    6. Vainora, J., 2024. "Latent Position-Based Modeling of Parameter Heterogeneity," Cambridge Working Papers in Economics 2455, Faculty of Economics, University of Cambridge.

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