Networks Multiscale Entropy Analysis

Abstract

Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction performance, existing methods focus on single-scale representations. This approach often overlooks the rich hierarchical patterns that can exist in real-world networks. In this study, we introduce a multiscale entropy framework that extends previous entropy-based approaches by applying spectral graph reduction. This allows us to quantify how structural entropy evolves as the network is gradually coarsened, capturing complexity across multiple scales. We apply our framework to real-world networks across biological, economic, social, technological, and transportation domains. The results uncover consistent entropy profiles across network families, revealing three structural regimes$\unicode{x2013}$stable, increasing, and hybrid$\unicode{x2013}$that align with domain-specific behaviors. Compared to single-scale models, multiscale entropy significantly improves our ability to determine network predictability. This shows that considering structural information across scales provides a more complete characterization of network complexity. Together, these results position multiscale entropy as a powerful and scalable tool for characterizing, classifying, and assessing the structure of complex networks.