Performances and correlations of centrality measures in complex networks

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, node rankings produced by different measures show moderate to high correlations. We identified two distinct communities: one comprising 4 measures and the other comprising 7. Measures within the same community exhibit exceptionally strong pairwise correlations (all exceeding 0.7 as measured by Kendall’s τ). In contrast, the remaining five measures display markedly different behavior, 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. Using the Susceptible-Infected-Recovered (SIR) epidemic spreading model, we evaluated the performance of those considered measures. We found that LocalRank, Subgraph Centrality, and Katz Centrality perform best at identifying the most influential single node. In contrast, Leverage Centrality, Collective Influence, and Cycle Ratio excel at identifying influential node sets. Interestingly, despite using the same dynamical process, the rankings of the 16 centrality measures in identifying a single influential node versus an influential node set are negatively correlated. This reinforces our conviction that there is no one-size-fits-all centrality measure. We further showed that measures generating spatially clustered influential nodes tend to perform better in identifying a single influential node, while measures producing influential nodes with larger distances between them are likely to excel in an identifying influential node set.