The semi-global triangular centrality evaluates node importance based on the number of triangles associated with a node and its extended neighborhood, including nodes up to two hops away [2]. For a node \(i \in \mathcal{N}\), the centrality \(c_{st}(i)\) is defined as
\[
c_{st}(i) = \sum_{j \in \mathcal{N}^{(\leq r)}(i) \cup \{i\}} \frac{\Delta(j)}{2^{d_{ij}}},
\]
where \(\Delta(j)\) is the number of triangles that include node \(j\), \(d_{ij}\) is the shortest-path distance between nodes \(i\) and \(j\), and \(\mathcal{N}^{(\leq r)}(i)\) denotes the set of nodes within distance \(r=2\) from node \(i\).
The semi-global triangular centrality was validated using the susceptible-infected-recovered (SIR) epidemic model on nine real-world networks and outperformed ten classical centrality measures in identifying effective spreaders.

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] Namtirtha, A., Dutta, B., & Dutta, A. (2022). Semi-global triangular centrality measure for identifying the influential spreaders from undirected complex networks. Expert Systems with Applications, 206, 117791. doi: 10.1016/j.eswa.2022.117791.