Index of CENTRality (Icentr) is a centrality measure developed to evaluate the performance of transportation networks [2]. Icentr defines the centrality of a node based on the weights of its incident edges, which in turn depend on the distances between nodes. For unweighted networks, the centrality of node \(i\) is defined as\[c_{Icentr}(i) = \sum_{(j,k) \in \mathcal{L}} \frac{1}{2^{w(j,k)}},\]where \(\mathcal{L}\) is the set of edges in the network and\[w(j,k) =\begin{cases}\max(d_{ij}, d_{ik}), & d_{ij} \neq d_{ik}, \\d_{ij} + 1, & d_{ij} = d_{ik},\end{cases}\]with \(d_{ij}\) denoting the shortest-path distance between nodes \(i\) and \(j\). Icentr assigns higher centrality to nodes connected via shorter paths, reflecting their greater accessibility and potential influence within the network. Mussone et al. [2] also extend Icentr to weighted networks, where both node and edge weights are considered in the computation.

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] Mussone, L., Viseh, H., & Notari, R. (2022). Novel centrality measures and applications to underground networks. Physica A: Statistical Mechanics and its Applications, 589, 126595. doi: 10.1016/j.physa.2021.126595.