An Analysis of Correlation and Comparisons Between Centrality Measures in Network Models

Centrality measures are widely utilized in complex networks to assess the importance of nodes. The choice of measure depends on the network type, leading to diverse node rankings. This paper aims to compare various centrality measures by examining their correlations. We specifically focus on the Pearson correlation coefficient and Spearman correlation. Pearson correlation considers node centrality values, while Spearman correlation is based on node ranks. Our study encompasses different network topologies, including random, scale-free, and small-world networks. We investigate how these network structures influence correlation values. The main part of the paper describes the relationship between correlations and network model parameters. Additionally, we explore the impact of global network characteristics on correlations, as well as their direct connection to network parameters. Through a systematic review of literature-based centrality measures, we have identified and selected the most commonly employed ones to investigate their correlation including degree centrality, betweenness centrality, eigenvector centrality, and closeness centrality. Our findings reveal that correlations in random networks are minimally affected by network structure, whereas restructuring significantly impacts correlations in other networks. In particular, we show a notable impact of structural parameter variations on correlations within small-world networks. Furthermore, we demonstrate the substantial influence of fundamental network characteristics such as spectral gap, global efficiency, and majorization gap on correlations. We show that amongst the various properties, the spectral gap stands out as the most valuable indicator for estimating correlations.