Radiality (Valente and Foreman 1998) reverses each distance against the diameter \(D\) and averages over the network: $$R(i) = \frac{1}{n - 1} \sum_{j:\, d_{ij} < \infty} (D + 1 - d_{ij}).$$ Nodes close to the others score high.
Arguments
- x
Network input accepted by
centrality.- mode
Direction for directed networks:
"all"(default),"out"or"in".- ...
Further arguments to
centrality. The measure usesweighted(defaultTRUE),invert_weights(defaultNULL, which inverts for tna input only),alpha(inversion exponent, default 1) andcutoff(largest distance counted, default -1 for no limit).
Details
The sum includes the node itself, which contributes \(D + 1\), and the
values equal centiserve::radiality() on undirected networks.
Unreachable nodes contribute 0. Edge weights are read as distances;
weighted = FALSE uses hop counts, and invert_weights = TRUE
converts a weight \(w\) to the distance \(1/w^\alpha\).
mode = "all" treats edges as undirected, "out" uses
distances from the node and "in" distances to it. The diameter is
taken on the stored edge weights in the direction of the network,
whatever mode and invert_weights are. A single-node network
gives NA.
References
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 .