Index of CENTRality (Icentr)
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.