The Generalized gravity centrality (GGC), also known as the clustering gravity model [2], is a variant of the gravity model that incorporates both degree and clustering coefficient to evaluate the “mass” or influence of a node [3]. The centrality of node \(i\) is defined as
\[
c_{GGC}(i) = \sum_{j \in \mathcal{N}^{(\leq r)}(i)} \frac{sp_i \, sp_j}{d_{ij}^2},
\]
where \(d_{ij}\) is the shortest distance between nodes \(i\) and \(j\), and \(\mathcal{N}^{(\leq r)}\) denotes the set of nodes within radius \(r\) of node \(i\).
The spreading ability of a node is given by
\[
sp_i = d_i \, e^{α c_i},
\]
where \(d_i\) and \(c_i\) are the degree and clustering coefficient of node \(i\), and \(α\) is a tunable parameter controlling the influence of the clustering coefficient. Li et al. [3] suggest \(α = 2\) in their experiments.

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] Zhao, J., Wen, T., Jahanshahi, H., & Cheong, K. H. (2022). The random walk-based gravity model to identify influential nodes in complex networks. Information Sciences, 609, 1706-1720. doi: 10.1016/j.ins.2022.07.084.
[3] Li, H., Shang, Q., & Deng, Y. (2021). A generalized gravity model for influential spreaders identification in complex networks. Chaos, Solitons & Fractals, 143, 110456. doi: 10.1016/j.chaos.2020.110456.