The h-index strength is an extension of the weighted h-index that incorporates the influence of a node's neighbors [2]. For node \(i\), the h-index strength \(c_{hs}(i)\) is defined as the sum of the weighted h-indexes of all its neighbors:
\begin{equation*}
c_{hs}(i) = \sum_{j \in \mathcal{N}(i)} c_{wh}(j),
\end{equation*}
where \(\mathcal{N}(i)\) is a set of neighbors of node \(i\) and \(c_{wh}(j)\) denotes the weighted h-index of neighbor \(j\), which is defined in Gao et al. [2].
Nodes with high h-index strength are connected to neighbors with high weighted h-index values, reflecting both local connectivity and the strength of neighboring nodes.

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] Gao, L., Yu, S., Li, M., Shen, Z., & Gao, Z. (2019). Weighted H-index for identifying influential spreaders. Symmetry, 11(10), 1263. doi: 10.3390/sym11101263.