Evaluating Global Measures of Network Centralization: Axiomatic and Numerical Assessments

TL;DR

This paper systematically evaluates 11 network centralization measures using axiomatic and numerical methods, identifying three reliable metrics that capture different aspects of network hub dominance across various contexts.

Contribution

It introduces a dual assessment framework for centralization measures, normalizes and compares them, and provides practical guidance for selecting suitable metrics in network analysis.

Findings

Normalized betweenness, closeness, and degree centralization are most suitable.

Different measures capture distinct aspects of network centralization.

Joint use of three measures offers comprehensive insights into network structure.

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.