Information distance index (IDI)
The
information distance index
(IDI) is an entropy-based centrality measure that quantifies node importance based on its distances to all other nodes in the network [2]. The index of node \(i\) is defined as
\begin{equation*}
c_{\text{IDI}}(i) = - \sum_{j \neq i} \frac{d_{ij}}{\sum_{k=1}^N d_{ik}} \log_2 \frac{d_{ij}}{\sum_{k=1}^N d_{ik}},
\end{equation*}
where \(d_{ij}\) is the shortest-path distance from node \(i\) to node \(j\), and \(N\) is the total number of nodes in the network.
The IDI measure captures how uniformly a node is positioned with respect to all others: higher IDI values indicate nodes whose distances to the rest of the network are more evenly distributed, highlighting their central role in connecting the network.