Local and global centrality (LGC)
Local and global centrality
(LGC) identifies influential nodes by integrating both local and global topological properties of a network [2]. The centrality of a node \(i\) is defined as
\[
c_{LGC}(i) = \frac{d_i}{N} \sum_{j \neq i} \frac{\sqrt{d_j + α}}{d_{ij}},
\]
where \(d_i\) is the degree of node \(i\), \(d_{ij}\) is the shortest-path distance between nodes \(i\) and \(j\), and \(α \in [0,1]\) is a parameter that controls the relative influence of neighboring node degrees (e.g., \(α=0.4\)).
Nodes with high LGC scores are those that not only have many connections but are also closely connected to other well-connected nodes, making them critical for information spreading and network cohesion. The effectiveness of LGC has been evaluated on six real-world networks and validated using the Susceptible-Infected-Recovered (SIR) epidemic model.