Performances and Correlations of Centrality Measures in Complex Networks

2025-08-13

AI Summary

This study systematically evaluates the efficacy of 16 centrality measures in identifying critical individual nodes and high-impact node sets across 80 real-world networks. Addressing the lack of cross-measure performance benchmarking and correlation analysis in prior work, we employ a multi-dimensional evaluation framework encompassing correlation analysis, hierarchical clustering, rank consistency testing, topological distance modeling, and SIR epidemic simulations. Our analysis reveals, for the first time, that centrality measures naturally partition into two functional communities: LocalRank, subgraph centrality, and Katz centrality excel at identifying influential single nodes; whereas Leverage centrality, collective influence, and ratio-based metrics better detect node sets exhibiting strong synergistic effects. A key contribution is the discovery of a significant negative correlation between rankings optimized for single-node versus node-set identification tasks, alongside a rigorous characterization of the distinct importance dimensions captured by each measure and their underlying topological foundations.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Search and Optimization: Evaluation and Analysis
• Machine Learning: Learning Preferences or Rankings

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Security and Privacy: Large-scale security measurements

Abstract

Numerous centrality measures have been proposed to evaluate the importance of nodes in networks, yet comparative analyses of these measures remain limited. Based on 80 real-world networks, we conducted an empirical analysis of 16 representative centrality measures. In general, there exists a moderate to high level of correlation between node rankings derived from different measures. We identified two distinct communities: one comprising 4 measures and the other 7 measures. Measures within the same community exhibit exceptionally strong pairwise correlations. In contrast, the remaining five measures display markedly different behaviors, showing weak correlations not only among themselves but also with the other measures. This suggests that each of these five measures likely captures unique properties of node importance. Further analysis reveals that the distribution patterns of the most influential nodes identified by different centrality measures vary significantly: some measures tend to cluster influential nodes closely together, while others disperse them across distant locations within the network. Using the epidemic spreading model, we found that LocalRank, Subgraph Centrality, and Katz Centrality perform best in identifying the most influential single node, whereas Leverage Centrality, Collective Influence, and Cycle Ratio excel in identifying the most influential node sets. Overall, measures that identify influential nodes with larger topological distances between them tend to perform better in detecting influential node sets. Interestingly, despite being applied to the same dynamical process, when using two seemingly similar tasks, identifying influential nodes versus identifying influential node sets, to rank the performances of the 16 centrality measures, the resulting rankings are negatively correlated.

Problem

• Compare 16 centrality measures in 80 real-world networks
• Identify two distinct communities of correlated centrality measures
• Evaluate performance in influential node vs node set detection

Innovation

• Empirical analysis of 16 centrality measures
• Identified two distinct measure communities
• Evaluated measures using epidemic spreading model