Integration centrality
Integration centrality
quantifies how well connected a node is within the network [2, 3]. The integration centrality of node \(i\) is defined as
\begin{equation*}
c_{\mathrm{Integration}}(i) = \frac{\sum_{j \neq i} \left( d_G + 1 - d_{ji} \right)}{N-1},
\end{equation*}
where \(d_G\) is the diameter of \(G\) and \(d_{ji}\) is the length of the shortest path from node \(j\) to node \(i\). Integration effectively inverts distances to provide a closeness-like measure, averaged over all other nodes. High integration centrality indicates that a node can be reached efficiently from most other nodes in the network, whereas low integration centrality indicates that it is more peripheral. For undirected networks, integration centrality coincides with radiality centrality.