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Preferential Attachment Random Graphs with Edge-Step Functions

Author

Listed:
  • Caio Alves

    (University of Leipzig)

  • Rodrigo Ribeiro

    (IMPA, Estrada Da. Castorina)

  • Rémy Sanchis

    (Universidade Federal de Minas Gerais)

Abstract

We analyze a random graph model with preferential attachment rule and edge-step functions that govern the growth rate of the vertex set, and study the effect of these functions on the empirical degree distribution of these random graphs. More specifically, we prove that when the edge-step function f is a monotone regularly varying function at infinity, the degree sequence of graphs associated with it obeys a (generalized) power-law distribution whose exponent belongs to (1, 2] and is related to the index of regular variation of f at infinity whenever said index is greater than $$-1$$ - 1 . When the regular variation index is less than or equal to $$-1$$ - 1 , we show that the empirical degree distribution vanishes for any fixed degree.

Suggested Citation

  • Caio Alves & Rodrigo Ribeiro & Rémy Sanchis, 2021. "Preferential Attachment Random Graphs with Edge-Step Functions," Journal of Theoretical Probability, Springer, vol. 34(1), pages 438-476, March.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:1:d:10.1007_s10959-019-00959-0
    DOI: 10.1007/s10959-019-00959-0
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    References listed on IDEAS

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    1. Harry Crane & Walter Dempsey, 2018. "Edge Exchangeable Models for Interaction Networks," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1311-1326, July.
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    Cited by:

    1. Alves, Caio & Ribeiro, Rodrigo & Valesin, Daniel, 2023. "Asymptotic results of a multiple-entry reinforcement process," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 451-489.

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