Improved Global Structure Model (IGSM)
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.