The local structural centrality (LSC) accounts for both the number of nearest and next-nearest neighbors and their topological connections, reflecting that influence depends on local neighborhood size and connectivity [2]. The centrality \( c_{\mathrm{LSC}}(i) \) of node \( i \) is defined as
\begin{equation*}
c_{\mathrm{LSC}}(i) = \sum_{j \in \mathcal{N}(i)}
\left( α |\mathcal{N}^{(\leq 2)}(i)| + (1 - α) \sum_{k \in \mathcal{N}^{(\leq 2)}(j)} c_k \right),
\end{equation*}
where \( \mathcal{N}^{(\leq 2)}(i) \) denotes the set of nearest and next-nearest neighbors of node \( i \),
\( c_k \) is the clustering coefficient of neighbor \( k \),
and \( α \) is a tunable parameter between 0 and 1. In [2], two values of \(α\) are considered: \(α = 0.2\) and \(α = 0.7\).

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, S., Ma, J., Chen, Z., Wang, G., & Xing, C. (2014). Ranking the spreading ability of nodes in complex networks based on local structure. Physica A: Statistical Mechanics and its Applications, 403, 130-147. doi: 10.1016/j.physa.2014.02.032.