The Global Structure Model (GSM) centrality accounts for self-influence (SI) and global influence (GI) [2]. For node \(i\), the GSM score is defined as
\[
c_{GSM}(i) = SI(i) \cdot GI(i) = e^{k_s(i)/N} \cdot \sum_{j \neq i} \frac{k_s(j)}{d_{ij}},
\]
where \(k_s(i)\) is the \(k\)-shell value of \(i\), \(d_{ij}\) is the shortest-path distance between \(i\) and \(j\) and \(N\) is the total number of nodes in the network. The term \(SI(i)\) reflects intrinsic influence based on the core-periphery position, while \(GI(i)\) captures contributions from all other nodes weighted by distance.

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] Ullah, A., Wang, B., Sheng, J., Long, J., Khan, N., & Sun, Z. (2021). Identification of nodes influence based on global structure model in complex networks. Scientific Reports, 11(1), 6173. doi: 10.1038/s41598-021-84684-x.