Diversity-strength ranking (DSR)
Diversity-strength ranking
(DSR) is an extension of the diversity-strength centrality (DSC), proposed by Zareie et al. [2], designed to capture influence that extends beyond a node’s immediate neighborhood. The DSR value of node \(i\) is defined as
\begin{equation*}
c_{\text{DSR}}(i) = \sum_{j \in \mathcal{N}(i)} c_{\text{DSC}}(j)= \sum_{j \in \mathcal{N}(i)}
\left(
\sum_{k \in \mathcal{N}(j)}
\frac{IKs(k)}{\sum_{m \in \mathcal{N}(j)} IKs(m)}
\log \frac{IKs(k)}{\sum_{m \in \mathcal{N}(j)} IKs(m)}
\right),
\end{equation*}
where \(\mathcal{N}(i)\) denotes the set of neighbors of node \(i\) and \(IKs(k)\) is the improved \(k\)-shell index of node \(k\) as defined by Liu et al. [3]. The inner summation represents the diversity-strength centrality of neighbor \(j\), while the outer summation aggregates these values for all neighbors of node \(i\). Thus, DSR extends DSC by capturing second-order effects through the influence of neighboring nodes. High DSR values indicate connections to neighbors that are both diverse and influential, reflecting enhanced potential for influence propagation.