Extended diversity-strength ranking (EDSR)
Extended diversity-strength ranking
(EDSR) further extends the diversity-strength ranking (DSR) measure by incorporating the influence potential of nodes over a wider network range, as proposed by Zareie et al. [2]. The EDSR value of node \(i\) is given by
\begin{equation*}
c_{\text{EDSR}}(i) =\sum_{j \in \mathcal{N}(i)} c_{\text{DSR}}(i) = \sum_{j \in \mathcal{N}(i)}
\left[
\sum_{k \in \mathcal{N}(j)}
\left(
\sum_{p \in \mathcal{N}(k)}
\frac{IKs(p)}{\sum_{q \in \mathcal{N}(k)} IKs(q)}
\log \frac{IKs(p)}{\sum_{q \in \mathcal{N}(k)} IKs(q)}
\right)
\right],
\end{equation*}
where \(\mathcal{N}(i)\) denotes the set of neighbors of node \(i\), and \(IKs(p)\) is the improved \(k\)-shell index of node \(p\) as defined by Liu et al. [3]. The innermost term represents the diversity-strength centrality of node \(k\), the middle summation yields the DSR of node \(j\), and the outermost summation aggregates these across the neighbors of node \(i\). EDSR thus captures multi-level influence by integrating local, second-order, and higher-order structural information. Nodes with high EDSR values lie within regions of strong and diverse influence, indicating their importance in diffusion and spreading processes across the network.