Extended hybrid characteristic centrality (EHCC)
The
Extended Hybrid Characteristic Centrality
(EHCC) extends the hybrid characteristic centrality (HCC) by incorporating the contributions of a node's neighbors [2]. The EHCC of node \(i\) is defined as
\begin{equation*}
c_{EHCC}(i) = c_{HCC}(i) + \sum_{j \in \mathcal{N}(i)} c_{HCC}(j),
\end{equation*}
where \(\mathcal{N}(i)\) denotes the set of neighbors of node \(i\) and \(c_{HCC}(i)\) is the HCC score of node \(i\), given by
\begin{equation*}
c_{HCC}(i) = \frac{d^{ex}(i)}{\max_j d^{ex}(j)} + \frac{pos(i)}{\max_j pos(j)},
\end{equation*}
with \(d^{ex}(i)\) representing the extended degree of node \(i\), and \(pos(i)\) denoting the iteration at which node \(i\) is removed during the E-shell decomposition.
Nodes with high EHCC values are influential both due to their own structural position in the network and the importance of their immediate neighbors.