Correlation centrality (CoC)
The correlation centrality (CoC) quantifies the influence of a node based on its correlation with all other nodes in the network [2]. Specifically, the influence of node \(i\) depends on the harmonic centrality of other nodes and the distances from node \(i\) to these nodes. The centrality of node \(i\) is defined as\begin{equation*}c_{CoC}(i) = \frac{1}{N^2} \sum_{j=1}^N \left( \frac{σ_{ij}}{d_{ij}^α} \sum_{k=1}^N \frac{1}{d_{jk}} \right),\end{equation*}where \(σ_{ij}\) is the number of shortest paths from node \(i\) to node \(j\), \(d_{ij}\) is the shortest distance from node \(i\) to node \(j\), and \(α\) is an impact factor. Wenli et al. [2] use \(α = 3\). Correlation centrality assigns higher values to nodes that are close to highly central nodes, reflecting both the number of paths a node participates in and the overall accessibility of the network. We remark that the term “correlation” emphasizes that a node’s centrality depends on its relationship with other nodes’ centrality, rather than on a statistical correlation coefficient.