Networks Multiscale Entropy Analysis

2025-10-13

AI Summary

This study addresses the challenge of quantifying structural complexity and predictability of complex networks across multiple scales. We propose a multiscale structural entropy analysis framework based on spectral graph dimensionality reduction. Integrating compressive entropy theory with spectral graph coarsening techniques, the framework systematically characterizes the evolution of structural entropy during network coarse-graining, identifying three universal structural regimes: stable, increasing, and hybrid. Unlike conventional single-scale entropy methods, our approach overcomes scale limitations and demonstrates broad applicability across real-world biological, social, and transportation networks. Empirical evaluation shows that it significantly enhances discriminative capability for network predictability, enables consistent classification of network families, and supports hierarchical characterization of structural complexity.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Machine Learning: Graph-based Machine Learning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Social Networks and Social Media: Social media analysis through the lenses of networks
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Extending entropy analysis to multiscale network representations
• Quantifying structural complexity across hierarchical network patterns
• Improving network predictability assessment through multiscale entropy

Innovation

• Multiscale entropy framework using spectral graph reduction
• Quantifying structural entropy evolution during network coarsening
• Capturing complexity across multiple network scales