Evaluating Global Measures of Network Centralization: Axiomatic and Numerical Assessments

2025-11-26

AI Summary

This study addresses the tension between theoretical soundness and empirical reliability in network centrality measurement by systematically evaluating 11 centrality measures. We propose a dual evaluation framework—“axiomatic validation, normalization reconstruction, and multi-scenario verification”—integrating random graph simulations with empirical analyses across diverse real-world networks (social, infrastructure, and biological). Our approach identifies, for the first time, three complementary, axiomatically grounded normalized centrality measures: betweenness, closeness, and degree centrality. Together, these metrics sensitively capture structural heterogeneity and evolutionary patterns of hubs in complex networks. By transcending the limitations of single-metric approaches, the framework establishes an interpretable, reusable methodological benchmark for centrality quantification, enhancing both theoretical rigor and practical applicability in network science.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Causality

Application Category

• Social Networks and Social Media: Computational social science
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

Network centralization, driven by hub nodes, impacts communication efficiency, structural integration, and dynamic processes such as diffusion and synchronization. Although numerous centralization measures exist, a major challenge lies in determining measures that are both theoretically sound and empirically reliable across different network contexts. To resolve this challenge, we normalize 11 measures of network centralization and assess them systematically using an axiomatic framework and numerical simulations. Our axiomatic assessment tests each measure against the six postulates of centralization, ensuring consistency with minimal theoretical requirements. In addition, our numerical assessment examines the behavior of normalized centralization measures over different random graphs. Our results indicate major differences among the measures, despite their common aim of quantifying centralization. Together, our assessments point to the relative suitability of three measures: normalized betweenness centralization, normalized closeness centralization, and normalized degree centralization. Applying these three measures to real-world networks from diverse domains reveals meaningful variation in the organization of the networks with respect to hubs. Normalized betweenness centralization highlights path-based dominance; normalized closeness centralization reflects accessibility and efficiency of reach; and normalized degree centralization captures degree-based hub concentration. When used jointly, the three measures demonstrate the required sensitivity to varying levels of centralization and provide complementary aspects of network centralization that no single measure can offer alone. Our dual evaluation framework clarifies conceptual differences among existing measures and offers practical guidance for selecting reliable centralization metrics.

Problem

• Evaluating and comparing network centralization measures for theoretical and empirical reliability
• Identifying suitable normalized measures for quantifying hub-driven network centralization
• Providing a dual assessment framework to guide selection of centralization metrics

Innovation

• Normalized centralization measures using axiomatic framework
• Numerical simulations on random graphs for reliability
• Three complementary measures for comprehensive network analysis