IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v24y2022i3d10.1007_s11009-021-09900-7.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-021-09900-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-021-09900-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Caron, François & Panero, Francesca & Rousseau, Judith, 2023. "On sparsity, power-law, and clustering properties of graphex processes," LSE Research Online Documents on Economics 119794, London School of Economics and Political Science, LSE Library.
    2. Liu, Yirui & Qiao, Xinghao & Wang, Liying & Lam, Jessica, 2023. "EEGNN: edge enhanced graph neural network with a Bayesian nonparametric graph model," LSE Research Online Documents on Economics 119918, London School of Economics and Political Science, LSE Library.
    3. Yifei Zhou & Shaoyong Li & Yaping Liu, 2020. "Graph-based Method for App Usage Prediction with Attributed Heterogeneous Network Embedding," Future Internet, MDPI, vol. 12(3), pages 1-16, March.
    4. Yun, Seokhoon, 1997. "On Domains of Attraction of Multivariate Extreme Value Distributions under Absolute Continuity," Journal of Multivariate Analysis, Elsevier, vol. 63(2), pages 277-295, November.
    5. Nora Connor & Albert Barberán & Aaron Clauset, 2017. "Using null models to infer microbial co-occurrence networks," PLOS ONE, Public Library of Science, vol. 12(5), pages 1-23, May.
    6. Leto Peel & Tiago P. Peixoto & Manlio De Domenico, 2022. "Statistical inference links data and theory in network science," Nature Communications, Nature, vol. 13(1), pages 1-15, December.
    7. Rafiee, Samira & Salavati, Chiman & Abdollahpouri, Alireza, 2020. "CNDP: Link prediction based on common neighbors degree penalization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    8. Riva Palacio, Alan & Leisen, Fabrizio, 2018. "Integrability conditions for compound random measures," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 32-37.
    9. Lee, Yan-Li & Zhou, Tao, 2021. "Collaborative filtering approach to link prediction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).
    10. Greg Morrison & L Mahadevan, 2012. "Discovering Communities through Friendship," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-9, July.
    11. Olav Kallenberg, 1999. "Multivariate Sampling and the Estimation Problem for Exchangeable Arrays," Journal of Theoretical Probability, Springer, vol. 12(3), pages 859-883, July.
    12. Liu, Zhenfeng & Feng, Jian & Uden, Lorna, 2023. "Technology opportunity analysis using hierarchical semantic networks and dual link prediction," Technovation, Elsevier, vol. 128(C).
    13. Shugang Li & Ziming Wang & Beiyan Zhang & Boyi Zhu & Zhifang Wen & Zhaoxu Yu, 2022. "The Research of “Products Rapidly Attracting Users” Based on the Fully Integrated Link Prediction Algorithm," Mathematics, MDPI, vol. 10(14), pages 1-19, July.
    14. Chunjiang Liu & Yikun Han & Haiyun Xu & Shihan Yang & Kaidi Wang & Yongye Su, 2024. "A Community Detection and Graph-Neural-Network-Based Link Prediction Approach for Scientific Literature," Mathematics, MDPI, vol. 12(3), pages 1-20, January.
    15. Li, Haijun & Wu, Peiling, 2013. "Extremal dependence of copulas: A tail density approach," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 99-111.
    16. Dmitry Arkhangelsky & Guido Imbens, 2023. "Causal Models for Longitudinal and Panel Data: A Survey," Papers 2311.15458, arXiv.org, revised Mar 2024.
    17. Griffin, Jim, 2019. "Two part envelopes for rejection sampling of some completely random measures," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 36-41.
    18. Giorgos Stamatelatos & George Drosatos & Sotirios Gyftopoulos & Helen Briola & Pavlos S. Efraimidis, 2021. "Point-of-interest lists and their potential in recommendation systems," Information Technology & Tourism, Springer, vol. 23(2), pages 209-239, June.
    19. Kai Yang & Yuan Liu & Zijuan Zhao & Xingxing Zhou & Peijin Ding, 2023. "Graph attention network via node similarity for link prediction," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(3), pages 1-10, March.
    20. Mungo, Luca & Lafond, François & Astudillo-Estévez, Pablo & Farmer, J. Doyne, 2023. "Reconstructing production networks using machine learning," Journal of Economic Dynamics and Control, Elsevier, vol. 148(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:24:y:2022:i:3:d:10.1007_s11009-021-09900-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.