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. 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.
    2. Aldous, David J., 1981. "Representations for partially exchangeable arrays of random variables," Journal of Multivariate Analysis, Elsevier, vol. 11(4), pages 581-598, December.
    3. de Haan, L. & Resnick, S., 1987. "On regular variation of probability densities," Stochastic Processes and their Applications, Elsevier, vol. 25, pages 83-93.
    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. Jeong, Yujin & Park, Inchae & Yoon, Byungun, 2019. "Identifying emerging Research and Business Development (R&BD) areas based on topic modeling and visualization with intellectual property right data," Technological Forecasting and Social Change, Elsevier, vol. 146(C), pages 655-672.
    4. 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.
    5. Karimi, Fatemeh & Lotfi, Shahriar & Izadkhah, Habib, 2021. "Community-guided link prediction in multiplex networks," Journal of Informetrics, Elsevier, vol. 15(4).
    6. Yin, Mei, 2022. "Remarks on power-law random graphs," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 183-197.
    7. 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.
    8. Koen Jochmans, 2024. "Nonparametric identification and estimation of stochastic block models from many small networks," Post-Print hal-04672521, HAL.
    9. Xu, Hua & Wang, Minggang & Jiang, Shumin & Yang, Weiguo, 2020. "Carbon price forecasting with complex network and extreme learning machine," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    10. Andreas Spitz & Anna Gimmler & Thorsten Stoeck & Katharina Anna Zweig & Emőke-Ágnes Horvát, 2016. "Assessing Low-Intensity Relationships in Complex Networks," PLOS ONE, Public Library of Science, vol. 11(4), pages 1-17, April.
    11. Qiaoran Yang & Zhiliang Dong & Yichi Zhang & Man Li & Ziyi Liang & Chao Ding, 2021. "Who Will Establish New Trade Relations? Looking for Potential Relationship in International Nickel Trade," Sustainability, MDPI, vol. 13(21), pages 1-15, October.
    12. 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.
    13. Aslan, Serpil & Kaya, Buket & Kaya, Mehmet, 2019. "Predicting potential links by using strengthened projections in evolving bipartite networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 998-1011.
    14. 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.
    15. 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).
    16. Yi He & John H. J. Einmahl, 2017. "Estimation of extreme depth-based quantile regions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 449-461, March.
    17. Xiaowen Xi & Jiaqi Wei & Ying Guo & Weiyu Duan, 2022. "Academic collaborations: a recommender framework spanning research interests and network topology," Scientometrics, Springer;Akadémiai Kiadó, vol. 127(11), pages 6787-6808, November.
    18. Pe[combining cedilla]ski, Marcin, 2011. "Prior symmetry, similarity-based reasoning, and endogenous categorization," Journal of Economic Theory, Elsevier, vol. 146(1), pages 111-140, January.
    19. Angelos Dassios & Junyi Zhang, 2023. "Exact Simulation of Poisson-Dirichlet Distribution and Generalised Gamma Process," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-21, June.
    20. Riva Palacio, Alan & Leisen, Fabrizio, 2018. "Integrability conditions for compound random measures," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 32-37.

    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.