Performances and Correlations of Centrality Measures in Complex Networks

TL;DR

This study empirically compares 16 centrality measures across 80 real-world networks, revealing their correlations, unique properties, and effectiveness in identifying influential nodes and node sets, with implications for network analysis.

Contribution

It provides a comprehensive empirical analysis of centrality measures, identifying communities of similar measures, their correlation patterns, and their relative performance in influence detection tasks.

Findings

High correlation within measure communities

Five measures capture unique node importance properties

Measures with larger topological distances perform better in node set influence detection

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.