Adjusted Index of Centrality (AIC)

The Adjusted Index of Centrality (AIC) is a closeness-based centrality measure introduced by Moxley [2]. For a node \(i\), its AIC centrality, denoted \(c_{AIC}(i)\), is defined as
\begin{equation*}
c_{AIC}(i) = \frac{\sum_{j=1}^N \sum_{k=1}^N (d_{jk} + p \cdot n_j)}{\sum_{j=1}^N (d_{ij} + p \cdot n_i)},
\end{equation*}
where \(d_{jk}\) is the shortest-path distance from node \(j\) to node \(k\), \(n_i\) is the number of nodes unreachable from \(i\), and \(p\) is a penalty parameter chosen such that \(p > \max_{i,j} d_{ij}\). The penalty ensures that nodes with unreachable nodes receive appropriately lower centrality scores.

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] Moxley, R. L., & Moxley, N. F. (1974). Determining Point-Centrality in Uncontrived Social Networks. Sociometry, 37(1), 122-130. doi: 10.2307/2786472.