Measuring Interlayer Dependence of Large Degrees in Multilayer Inhomogeneous Random Graphs

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.