The local H-index (LH-index) [2] is a semi-local centrality measure and an improved version of the traditional H-index, also known as the lobby index or \(l\)-index [3]. The local H-index of a node \(i\), denoted by \(c_{LH}(i)\), is defined as
\begin{equation*}
c_{LH}(i) = h(i) + \sum_{j \in \mathcal{N}(i)} h(j),
\end{equation*}
where \(h(i)\) denotes the H-index of node \(i\), and \(\mathcal{N}(i)\) represents the set of its neighbors. Thus, the local H-index accounts for both the H-index of a node and those of its 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] Liu, Q., Zhu, Y. X., Jia, Y., Deng, L., Zhou, B., Zhu, J. X., & Zou, P. (2018). Leveraging local h-index to identify and rank influential spreaders in networks. Physica A: Statistical Mechanics and its Applications, 512, 379-391. doi: 10.1016/j.physa.2018.08.053.
[3] Korn, A., Schubert, A., & Telcs, A. (2009). Lobby index in networks. Physica A: Statistical Mechanics and its Applications, 388(11), 2221-2226. doi: 10.1016/j.physa.2009.02.013.