The Improved Global Structure Model (IGSM) is a variant of the GSM model in which the \(k\)-shell index is replaced by node degree [2]. The centrality of node \(i\) is defined as
\begin{equation*}
c_{IGSM}(i) = e^{d_i / N} \cdot \sum_{j \neq i} \frac{d_j}{d_{ij}^{\lceil \log_2 \langle d \rangle \rceil}},
\end{equation*}
where \(d_i\) is the degree of node \(i\), \(\langle d \rangle\) is the average degree of the network, \(d_{ij}\) is the shortest path distance between nodes \(i\) and \(j\), and \(\lceil x \rceil\) denotes the smallest integer greater than or equal to \(x\). The exponent in the denominator reduces the contribution of distant nodes while emphasizing the influence of highly connected nodes, providing a balance between local connectivity and global network structure.

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] Zhu, J. C., & Wang, L. W. (2022). An extended improved global structure model for influential node identification in complex networks. Chinese Physics B, 31(6), 068904. doi: 10.1088/1674-1056/ac380d.