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Directed hybrid random networks mixing preferential attachment with uniform attachment mechanisms

Author

Listed:
  • Tiandong Wang

    (Texas A&M University)

  • Panpan Zhang

    (University of Pennsylvania)

Abstract

Motivated by the complexity of network data, we propose a directed hybrid random network that mixes preferential attachment (PA) rules with uniform attachment rules. When a new edge is created, with probability $$p\in (0,1)$$ p ∈ ( 0 , 1 ) , it follows the PA rule. Otherwise, this new edge is added between two uniformly chosen nodes. Such mixture makes the in- and out-degrees of a fixed node grow at a slower rate, compared to the pure PA case, thus leading to lighter distributional tails. For estimation and inference, we develop two numerical methods which are applied to both synthetic and real network data. We see that with extra flexibility given by the parameter p, the hybrid random network provides a better fit to real-world scenarios, where lighter tails from in- and out-degrees are observed.

Suggested Citation

  • Tiandong Wang & Panpan Zhang, 2022. "Directed hybrid random networks mixing preferential attachment with uniform attachment mechanisms," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(5), pages 957-986, October.
    • Handle: RePEc:spr:aistmt:v:74:y:2022:i:5:d:10.1007_s10463-022-00827-5
    DOI: 10.1007/s10463-022-00827-5
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    References listed on IDEAS

    as
    1. Panpan Zhang & Hosam M. Mahmoud, 2020. "On Nodes of Small Degrees and Degree Profile in Preferential Dynamic Attachment Circuits," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 625-645, June.
    2. Nash, John C., 2014. "On Best Practice Optimization Methods in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 60(i02).
    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.
    4. Smith, Brian J., 2007. "boa: An R Package for MCMC Output Convergence Assessment and Posterior Inference," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 21(i11).
    5. Hunter, David R. & Goodreau, Steven M. & Handcock, Mark S., 2008. "Goodness of Fit of Social Network Models," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 248-258, March.
    6. Gao, Fengnan & van der Vaart, Aad, 2017. "On the asymptotic normality of estimating the affine preferential attachment network models with random initial degrees," Stochastic Processes and their Applications, Elsevier, vol. 127(11), pages 3754-3775.
    7. Tiandong Wang & Sidney I. Resnick, 2018. "Multivariate Regular Variation of Discrete Mass Functions with Applications to Preferential Attachment Networks," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 1029-1042, September.
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    Cited by:

    1. Panpan Zhang, 2023. "On Several Properties of A Class of Hybrid Recursive Trees," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-20, March.

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