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Measuring interlayer dependence of large degrees in multilayer inhomogeneous random graphs

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  • Han, Zhuoye
  • Wang, Tiandong

Abstract

Accurately capturing interlayer dependence is essential for understanding the structure of complex multilayer networks. We propose an upper tail dependence estimator specifically designed for multilayer networks, leveraging multilayer inhomogeneous random graphs and multivariate regular variation to model extremal dependence. We establish the consistency of the estimator and demonstrate its practical effectiveness through real-data analysis of Reddit. Our findings reveal how financial market dynamics influence user interactions in the BitcoinMarkets subreddit and how seasonal trends shape engagement in sports-related subreddits. This work provides a rigorous and practical tool for quantifying extremal dependence across network layers, offering valuable insights into risk propagation and interaction patterns in multilayer systems.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:682:y:2026:i:c:s0378437125008258
    DOI: 10.1016/j.physa.2025.131173
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    References listed on IDEAS

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    1. Das, Bikramjit & Fasen-Hartmann, Vicky, 2018. "Risk contagion under regular variation and asymptotic tail independence," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 194-215.
    2. 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).
    3. Frahm, Gabriel & Junker, Markus & Schmidt, Rafael, 2005. "Estimating the tail-dependence coefficient: Properties and pitfalls," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 80-100, August.
    4. Basrak, Bojan & Planinić, Hrvoje, 2019. "A note on vague convergence of measures," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 180-186.
    5. Xie, Yiwei & Jiao, Feng & Li, Shihan & Liu, Qingfu & Tse, Yiuman, 2022. "Systemic risk in financial institutions: A multiplex network approach," Pacific-Basin Finance Journal, Elsevier, vol. 73(C).
    6. Cai, J. & Einmahl, J.H.J. & de Haan, L.F.M., 2011. "Estimation of extreme risk regions under multivariate regular variation," Other publications TiSEM b7a72a8d-f9bc-4129-ae9b-a, Tilburg University, School of Economics and Management.
    7. Harry Joe & Haijun Li, 2011. "Tail Risk of Multivariate Regular Variation," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 671-693, December.
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