IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v190y2025ics0304414925002066.html

Emergence of multivariate extremes in multilayer inhomogeneous random graphs

Author

Listed:
  • Cirkovic, Daniel
  • Wang, Tiandong
  • Cline, Daren B.H.

Abstract

In this paper we develop a multilayer inhomogeneous random graph model (MIRG). Layers of the MIRG may consist of both single-edge and multi-edge graphs. In the single layer case, it has been shown that the regular variation of the weight distribution underlying the inhomogeneous random graph implies the regular variation of the typical degree distribution. We extend this correspondence to the multilayer case by showing that multivariate regular variation of the weight distribution implies multivariate regular variation of the asymptotic degree distribution. Furthermore, under suitable assumptions, the extremal dependence structure present in the weight distribution will be adopted by the asymptotic degree distribution. By considering the asymptotic degree distribution, a wider class of Chung–Lu and Norros–Reittu graphs may be incorporated into the MIRG layers. Additionally, we prove consistency of the Hill estimator when applied to degrees of the MIRG that have a tail index greater than 1. Simulation results indicate that, in practice, hidden regular variation may be consistently detected from an observed MIRG. Finally, we analyze user interactions on Reddit and observe that they exhibit properties of the MIRG.

Suggested Citation

  • Cirkovic, Daniel & Wang, Tiandong & Cline, Daren B.H., 2025. "Emergence of multivariate extremes in multilayer inhomogeneous random graphs," Stochastic Processes and their Applications, Elsevier, vol. 190(C).
    • Handle: RePEc:eee:spapps:v:190:y:2025:i:c:s0304414925002066
    DOI: 10.1016/j.spa.2025.104762
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414925002066
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2025.104762?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 2000. "Scale-free characteristics of random networks: the topology of the world-wide web," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 281(1), pages 69-77.
    2. Basrak, Bojan & Planinić, Hrvoje, 2019. "A note on vague convergence of measures," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 180-186.
    3. Einmahl, John & He, Y., 2022. "Extreme Value Inference for General Heterogeneous Data," Discussion Paper 2022-017, Tilburg University, Center for Economic Research.
    4. Einmahl, John & He, Y., 2022. "Extreme Value Inference for General Heterogeneous Data," Other publications TiSEM fd8dd91c-086f-40e6-ac29-3, Tilburg University, School of Economics and Management.
    5. Réka Albert & Hawoong Jeong & Albert-László Barabási, 1999. "Diameter of the World-Wide Web," Nature, Nature, vol. 401(6749), pages 130-131, September.
    6. John H. J. Einmahl & Fan Yang & Chen Zhou, 2021. "Testing the Multivariate Regular Variation Model," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(4), pages 907-919, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Han, Zhuoye & Wang, Tiandong, 2026. "Measuring interlayer dependence of large degrees in multilayer inhomogeneous random graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 682(C).

    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. Salcedo-Sanz, S. & Cuadra, L., 2019. "Quasi scale-free geographically embedded networks over DLA-generated aggregates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1286-1305.
    2. Mohammad Ghaderi, 2020. "Public Health Interventions in the Face of Pandemics: Network Structure, Social Distancing, and Heterogeneity," Working Papers 1193, Barcelona School of Economics.
    3. Ghaderi, Mohammad, 2022. "Public health interventions in the face of pandemics: Network structure, social distancing, and heterogeneity," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1016-1031.
    4. Mohammad Ghaderi, 2020. "Public health interventions in the face of pandemics: network structure, social distancing, and heterogeneity," Economics Working Papers 1732, Department of Economics and Business, Universitat Pompeu Fabra.
    5. Jackson, Matthew O. & Rogers, Brian W., 2005. "Search in the formation of large networks: How random are socially generated networks?," Working Papers 1216, California Institute of Technology, Division of the Humanities and Social Sciences.
    6. Chen, Qinghua & Shi, Dinghua, 2006. "Markov chains theory for scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(1), pages 121-133.
    7. Yao, Xin & Zhang, Chang-shui & Chen, Jin-wen & Li, Yan-da, 2005. "On the formation of degree and cluster-degree correlations in scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 661-673.
    8. Mohd-Zaid, Fairul & Kabban, Christine M. Schubert & Deckro, Richard F. & White, Edward D., 2017. "Parameter specification for the degree distribution of simulated Barabási–Albert graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 141-152.
    9. Ruiz Vargas, E. & Mitchell, D.G.V. & Greening, S.G. & Wahl, L.M., 2014. "Topology of whole-brain functional MRI networks: Improving the truncated scale-free model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 151-158.
    10. Giacomello, Giampiero & Picci, Lucio, 2003. "My scale or your meter? Evaluating methods of measuring the Internet," Information Economics and Policy, Elsevier, vol. 15(3), pages 363-383, September.
    11. Ormerod, Paul & Roach, Andrew P, 2004. "The Medieval inquisition: scale-free networks and the suppression of heresy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 339(3), pages 645-652.
    12. He, He & Yang, Bo & Hu, Xiaoming, 2016. "Exploring community structure in networks by consensus dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 342-353.
    13. Zheng, Mingbo & Zhang, Xinyu, 2025. "Digitalization and renewable energy development: Analysis based on cross-country panel data," Energy, Elsevier, vol. 319(C).
    14. Castagna, Alina & Chentouf, Leila & Ernst, Ekkehard, 2017. "Economic vulnerabilities in Italy: A network analysis using similarities in sectoral employment," GLO Discussion Paper Series 50, Global Labor Organization (GLO).
    15. Pascal Billand & Christophe Bravard & Sudipta Sarangi, 2011. "Resources Flows Asymmetries in Strict Nash Networks with Partner Heterogeneity," Working Papers 1108, Groupe d'Analyse et de Théorie Economique Lyon St-Etienne (GATE Lyon St-Etienne), Université de Lyon.
    16. Elias Carroni & Paolo Pin & Simone Righi, 2020. "Bring a Friend! Privately or Publicly?," Management Science, INFORMS, vol. 66(5), pages 2269-2290, May.
    17. Duan, Shuyu & Wen, Tao & Jiang, Wen, 2019. "A new information dimension of complex network based on Rényi entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 529-542.
    18. Baek, Seung Ki & Kim, Tae Young & Kim, Beom Jun, 2008. "Testing a priority-based queue model with Linux command histories," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3660-3668.
    19. Freddy Hern�n Cepeda L�pez, 2008. "La topolog�a de redes como herramienta de Seguimiento en el sistema de Pagos de Alto Valor en Colombia," Borradores de Economia 4676, Banco de la Republica.
    20. Chung-Yuan Huang & Chuen-Tsai Sun & Hsun-Cheng Lin, 2005. "Influence of Local Information on Social Simulations in Small-World Network Models," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 8(4), pages 1-8.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:eee:spapps:v:190:y:2025:i:c:s0304414925002066. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.