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.

References

[1] Shvydun, S. (2025). Zoo of Centralities: Encyclopedia of Node Metrics in Complex Networks. arXiv: 2511.05122 https://doi.org/10.48550/arXiv.2511.05122
[2] Zareie, A., Sheikhahmadi, A., & Jalili, M. (2019). Influential node ranking in social networks based on neighborhood diversity. Future Generation Computer Systems, 94, 120-129. doi: 10.1016/j.future.2018.11.023.
[3] Liu, Z., Jiang, C., Wang, J., & Yu, H. (2015). The node importance in actual complex networks based on a multi-attribute ranking method. Knowledge-Based Systems, 84, 56-66. doi: 10.1016/j.knosys.2015.03.026.