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Asymptotic Behavior of Common Connections in Sparse Random Networks

Author

Listed:
  • Bikramjit Das

    (Singapore University of Technology and Design)

  • Tiandong Wang

    (Texas A&M University)

  • Gengling Dai

    (Singapore University of Technology and Design)

Abstract

Random network models generated using sparse exchangeable graphs have provided a mechanism to study a wide variety of complex real-life networks. In particular, these models help with investigating power-law properties of degree distributions, number of edges, and other relevant network metrics which support the scale-free structure of networks. Previous work on such graphs imposes a marginal assumption of univariate regular variation (e.g., power-law tail) on the bivariate generating graphex function. In this paper, we study sparse exchangeable graphs generated by graphex functions which are multivariate regularly varying. We also focus on a different metric for our study: the distribution of the number of common vertices (connections) shared by a pair of vertices. The number being high for a fixed pair is an indicator of the original pair of vertices being connected. We find that the distribution of number of common connections are regularly varying as well, where the tail indices of regular variation are governed by the type of graphex function used. Our results are verified on simulated graphs by estimating the relevant tail index parameters.

Suggested Citation

  • Bikramjit Das & Tiandong Wang & Gengling Dai, 2022. "Asymptotic Behavior of Common Connections in Sparse Random Networks," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 2071-2092, September.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:3:d:10.1007_s11009-021-09900-7
    DOI: 10.1007/s11009-021-09900-7
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    References listed on IDEAS

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    1. de Haan, L. & Resnick, S., 1987. "On regular variation of probability densities," Stochastic Processes and their Applications, Elsevier, vol. 25, pages 83-93.
    2. David Liben‐Nowell & Jon Kleinberg, 2007. "The link‐prediction problem for social networks," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 58(7), pages 1019-1031, May.
    3. Aldous, David J., 1981. "Representations for partially exchangeable arrays of random variables," Journal of Multivariate Analysis, Elsevier, vol. 11(4), pages 581-598, December.
    4. François Caron & Emily B. Fox, 2017. "Sparse graphs using exchangeable random measures," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1295-1366, November.
    5. Adrien Todeschini & Xenia Miscouridou & François Caron, 2020. "Exchangeable random measures for sparse and modular graphs with overlapping communities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(2), pages 487-520, April.
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