Diversity-strength centrality (DSC) is an entropy-based measure that quantifies node importance based on neighbor diversity, influence spread, and intensity [2]. The centrality of node \(i\) is defined as
\begin{equation*}
c_{\text{DSC}}(i) = - \sum_{j \in \mathcal{N}(i)} \frac{IKs(j)}{\sum_{l \in \mathcal{N}(i)} IKs(l)} \log \frac{IKs(j)}{\sum_{l \in \mathcal{N}(i)} IKs(l)},
\end{equation*}
where \(\mathcal{N}(i)\) is the set of neighbors of node \(i\) and \(IKs(j)\) is the improved \(k\)-shell index of node \(j\) as defined in [3]. This term captures the relative influence of neighbors, and the entropy reflects the diversity of their influence.
Zareie et al. [2] propose two extensions of DSC:


  1. Diversity-strength ranking (DSR) , which sums the DSC scores of a node's neighbors: \begin{equation*} c_{\text{DSR}}(i) = \sum_{j \in \mathcal{N}(i)} c_{\text{DSC}}(j), \end{equation*}

  2. Extended diversity-strength ranking (EDSR) , which sums the DSR scores of a node's neighbors: \begin{equation*} c_{\text{EDSR}}(i) = \sum_{j \in \mathcal{N}(i)} c_{\text{DSR}}(j). \end{equation*}


Nodes with high DSC values are influential not only individually but also through the diversity and strength of their neighbors, reflecting both local and extended network influence.

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.