Measuring Interlayer Dependence of Large Degrees in Multilayer Inhomogeneous Random Graphs

TL;DR

This paper introduces a new estimator for measuring extremal interlayer dependence in multilayer networks, validated through real-world Reddit data, revealing insights into user interaction patterns influenced by financial and seasonal factors.

Contribution

It develops a novel upper tail dependence estimator for multilayer networks using multivariate regular variation, with proven consistency and practical application.

Findings

Reveals interlayer dependence patterns in Reddit communities.

Shows influence of financial markets on user interactions.

Highlights seasonal effects on engagement.

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.