Global importance of nodes (GIN)
The
global importance of nodes
(GIN) quantifies the influence of a node by combining its degree, representing its direct connectivity, with its potential impact on other nodes, weighted by their degrees and distances within the network [2]. The GIN centrality of node \(i\) is defined as
\begin{equation*}
c_{GIN}(i) =
\begin{cases}
e^{\frac{α d_i}{N}} \cdot \sum_{j \neq i} \frac{β d_j}{d_{ij}}, & \text{if } d_i \neq 0, \\
0, & \text{if } d_i = 0,
\end{cases}
\end{equation*}
where \(d_i\) is the degree of node \(i\), \(d_{ij}\) is the shortest-path distance between nodes \(i\) and \(j\), and \(α\) and \(β\) are tunable parameters. Zhao et al. [2] set \(α = β = 1\) in their analysis. Hence, the GIN measure captures both the direct connectivity of a node, measured by its degree, and the potential influence on other nodes, weighted by their degrees and the shortest-path distances within the network.