k-shell hybrid method (ksh)
The
\(k\)-shell hybrid method
(ksh) is a centrality measure that combines the \(k\)-shell decomposition and degree information within the framework of gravitational centrality [2]. Specifically, the centrality score \( c_{\mathrm{ksh}}(i) \) of node \( i \) is defined as
\begin{equation*}
c_{\mathrm{ksh}}(i) = \sum_{j \in \mathcal{N}^{(\leq l)}(i)}
\frac{\sqrt{k_s(i) + k_s(j)} + μ\,d_j}{d_{ij}^2},
\end{equation*}
where \( \mathcal{N}^{(\leq l)}(i) \) denotes the set of nodes within the \( l \)-hop neighborhood of node \( i \), \( d_{ij} \) is the shortest path distance between nodes \( i \) and \( j \), \( k_s(i) \) and \( k_s(j) \) represent the \(k\)-shell indices of nodes \( i \) and \( j \), respectively, \( d_j \) is the degree of node \( j \), and \( μ \in (0,1) \) is a tunable parameter that balances the contributions of the two components.
Namtirtha et al. [2] recommend using \( l = 3 \) and \( μ = 0.4 \) for optimal performance.