The improved closeness centrality (\textsc{ICC}) is a variation of standard closeness centrality that accounts for the number of shortest paths between nodes [2].
For a node \(i\), the \textsc{ICC} centrality \(c_{\textsc{ICC}}(i)\) is defined as
\[
c_{\textsc{ICC}}(i) = \frac{N-1}{\sum_{j \neq i} d_{ij} \left( \frac{1}{n_{ij}} \right)^{α}},
\]
where \(d_{ij}\) is the shortest-path distance between nodes \(i\) and \(j\), \(n_{ij}\) is the number of shortest paths connecting \(i\) and \(j\), and \(0 \leq α \leq 1\) is a tunable parameter.
Luan et al. [2] show that the \textsc{ICC} performs best for \(α = 0.2\). Note that \textsc{ICC} reduces to standard closeness centrality when \(α = 0\).

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] Luan, Y., Bao, Z., & Zhang, H. (2021). Identifying influential spreaders in complex networks by considering the impact of the number of shortest paths. Journal of Systems Science and Complexity, 34(6), 2168-2181. doi: 10.1007/s11424-021-0111-7.