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Poisson Edge Growth and Preferential Attachment Networks

Author

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  • Tiandong Wang

    (Fudan University)

  • Sidney Resnick

    (Cornell University)

Abstract

When modeling a directed social network, one choice is to use the traditional preferential attachment model, which generates power-law tail distributions. In traditional directed preferential attachment, every new edge is added sequentially into the network. However, real datasets often have only coarse timestamps, which means several new edges are created at the same timestamp. Previous analyses on the evolution of social networks reveal that after reaching a stable phase, the growth of edge counts in a network follows a non-homogeneous Poisson process with a constant rate across the day but varying rates from day to day. Taking such empirical observations into account, we propose a modified preferential attachment model with Poisson edge growth, and study its asymptotic behavior. This new model is then fitted to real datasets using an extreme value estimation approach.

Suggested Citation

  • Tiandong Wang & Sidney Resnick, 2023. "Poisson Edge Growth and Preferential Attachment Networks," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-25, March.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-09997-y
    DOI: 10.1007/s11009-023-09997-y
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    References listed on IDEAS

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    1. Gillespie, Colin S., 2015. "Fitting Heavy Tailed Distributions: The poweRlaw Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 64(i02).
    2. Xie, Zheng & Ouyang, Zhenzheng & Li, Jianping, 2016. "A geometric graph model for coauthorship networks," Journal of Informetrics, Elsevier, vol. 10(1), pages 299-311.
    3. Wang, Tiandong & Resnick, Sidney I., 2020. "Degree growth rates and index estimation in a directed preferential attachment model," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 878-906.
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    Cited by:

    1. Natalia Markovich & Marijus Vaičiulis, 2023. "Extreme Value Statistics for Evolving Random Networks," Mathematics, MDPI, vol. 11(9), pages 1-35, May.

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