Radiality centrality measures how efficiently a node’s ties reach other nodes, emphasizing outward paths [2, 3]. The radiality centrality of node \(i\) is defined as
\begin{equation*}
c_{\mathrm{Radiality}}(i) = \frac{\sum_{j \neq i} \left( d_G + 1 - d_{ij} \right)}{N-1},
\end{equation*}
where \(d_G\) is the diameter of \(G\) and \(d_{ij}\) is the length of the shortest path from node \(i\) to node \(j\). High radiality indicates that a node is, on average, close to other nodes relative to the network diameter, while low radiality indicates a peripheral position. For undirected networks, radiality centrality coincides with integration centrality.

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] Guimaraes, L. L. (1973). Communication integration in modern and traditional social systems: a comparative analysis across twenty communities of Minas Gerais, Brazil. PhD Thesis, Michigan State Univ., East Lansing. doi: 10.25335/jcw2-6990.
[3] Valente, T. W., & Foreman, R. K. (1998). Integration and radiality: Measuring the extent of an individual's connectedness and reachability in a network. Social networks, 20(1), 89-105. doi: 10.1016/S0378-8733(97)00007-5.