Volume centrality

Sum of the original-graph degrees of all vertices within volume_radius hops, including the focal vertex. This is the localized volume measure of Wehmuth & Ziviani (DANCE/DACCER). Degrees include edges leaving the neighborhood; they are not recomputed inside the induced subgraph. Radius zero returns degree. Infinite radius returns twice the number of edges in the focal connected component.

Usage

centrality_volume(x, volume_radius = 2, ...)

Arguments

x: Network input accepted by centrality.
volume_radius: Nonnegative integer hop radius, or Inf. Default 2, the local radius investigated by Wehmuth & Ziviani.
...: Additional arguments to centrality. With normalized = TRUE, positive scores are divided by their maximum.

Value

Named numeric vector in input node order.

Details

Uses the simple undirected, unweighted skeleton: either direction creates an edge, parallel edges count once, and self-loops are removed. This is an explicit input projection, not a weighted or directed generalization. Isolates score zero.

References

Wehmuth, K., & Ziviani, A. (2011). Distributed Assessment of Network Centrality. Section II-A, equation 1. https://arxiv.org/abs/1108.1067v1.

Wehmuth, K., & Ziviani, A. (2013). DACCER: Distributed Assessment of the Closeness CEntrality Ranking in complex networks. Computer Networks, 57, 2536-2548. doi:10.1016/j.comnet.2013.05.001 .

Examples

centrality_volume(igraph::make_ring(6), volume_radius = 1)
#> 1 2 3 4 5 6 
#> 6 6 6 6 6 6 
centrality_volume(igraph::make_ring(6), volume_radius = 0)
#> 1 2 3 4 5 6 
#> 2 2 2 2 2 2