The Laplacian gravity centrality (LGC) is an extension of the local gravity model that combines Laplacian centrality with the network structure to identify influential nodes in complex networks [2]. The centrality \(c_{\textsc{LGC}}(i)\) of node \(i\) is defined as
\begin{equation*}
c_{\textsc{LGC}}(i) = \sum_{j \in \mathcal{N}^{(\leq l)}(i)} \frac{c_L(i)\, c_L(j)}{d_{ij}^2},
\end{equation*}
where \(\mathcal{N}^{(\leq l)}(i)\) denote the set of nodes within \(l\)-hop neighborhood of node \(i\), \(d_{ij}\) is the shortest-path distance between nodes \(i\) and \(j\), and \(c_L(i)\) is the Laplacian centrality of node \(i\). Zhang et al. [2] set the truncated radius to \(l = \langle d \rangle / 2\), where \(\langle d \rangle\) is the average shortest-path distance in the network.

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] Zhang, Q., Shuai, B., & Lü, M. (2022). A novel method to identify influential nodes in complex networks based on gravity centrality. Information Sciences, 618, 98-117. doi: 10.1016/j.ins.2022.10.070.