Global and local information (GLI) method
The
global and local information
(GLI) method is a hybrid centrality measure that combines global and local node information using degree and \(k\)-shell decomposition [2].
First, the
improved \(k\)-shell score
of node \(i\) is defined as
\[
Iks(i) = k_s(i) + nit(i),
\]
where \(k_s(i)\) is the standard \(k\)-shell index of node \(i\) and \(nit(i)\) denotes the iteration number at which node \(i\) is removed during the \(k\)-shell decomposition.
The \textsc{GLI} centrality of node \(i\) is then given by
\[
c_{\textsc{GLI}}(i) = \exp \left( \frac{Iks(i) + d_i}{\sum_{j=1}^N (Iks(j) + d_j)} \right)
\left( \sum_{j \in \mathcal{N}^{(\leq r)}(i)} \frac{Iks(j) + d_j}{d_{ij}} \right),
\]
where \(d_i\) is the degree of node \(i\), \(d_{ij}\) is the shortest-path distance between nodes \(i\) and \(j\), and \(\mathcal{N}^{(\leq r)}(i)\) denotes the set of nodes within a truncated radius \(r\) from node \(i\).
Yang et al. [2] set \(r = 3\) to reduce computational complexity. This measure integrates a node’s global hierarchical position (via improved \(k\)-shell) with the local connectivity of its neighborhood to better capture its influence in the network.