k-shell iteration factor (KS-IF)
The
\(k\)-shell iteration factor
(KS-IF) ranks nodes by combining their degree and \(k\)-shell decomposition information [2]. The centrality of node \(i\) is defined as
\begin{equation*}
c_{KS-IF}(i) = δ(i) d_i + \sum_{j \in \mathcal{N}(i)} δ(j) d_j,
\end{equation*}
where \(d_i\) is the degree of node \(i\) and \(δ(i)\) is the \(k\)-shell iteration factor given by
\begin{equation*}
δ(i) = k_s(i) \left( 1 + \frac{n(i)}{m(i)} \right).
\end{equation*}
Here, \(k_s(i)\) is the \(k\)-shell index of node \(i\), \(n(i)\) is the iteration at which node \(i\) is removed, and \(m(i)\) is the total number of iterations in that step. KS-IF combines node degree and \(k\)-shell position to better identify influential nodes.