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.