Integration Centrality

Integration centrality (Valente and Foreman 1998) scores each distance against the diameter $D$, the largest finite hop distance, and sums: $$I(i) = \sum_{j} \left(1 - \frac{d_{ij} - 1}{D}\right),$$ where an unreachable node contributes 0.

Usage

centrality_integration(x, mode = "all", ...)

Arguments

x: Network input accepted by centrality.
mode: Direction for directed networks: "all" (default), "out" or "in".
...: Further arguments to centrality.

Value

A named numeric vector with one score per node, in input node order.

Details

Distances are hop counts, so edge weights are ignored. The sum includes the node itself, which contributes $1 + 1/D$, and is not divided by $n - 1$; the values equal tidygraph::centrality_integration(). mode = "all" treats edges as undirected, "out" uses distances from the node and "in" distances to it. On a network without edges every node scores $n$.

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 .

Examples

centrality_integration(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>        8.5        9.0        9.5        9.0        8.5        8.5        8.0 
#>   Evaluate     Create      Share 
#>        8.5        9.0        8.5