Local Rich Club Score

For each node, measures whether it preferentially directs its strongest ties toward prominent nodes. A score > 1 means the node's ties to prominent nodes are stronger than average.

Usage

rich_club_local(
  x,
  prominence = NULL,
  rich = c("k", "s"),
  directed = NULL,
  digits = NULL,
  sort_by = "score",
  ...
)

Arguments

x: Network input: matrix, igraph, network, cograph_network, or tna object.
prominence: Integer or logical vector indicating which nodes are prominent (1/TRUE = prominent), OR a numeric threshold. If NULL, nodes above median degree (or strength) are prominent.
rich: Character. "k" (degree, default) or "s" (strength). Used when prominence is NULL or a threshold.
directed: Logical or NULL. Default NULL (auto-detect).
digits: Integer or NULL. Round scores. Default NULL.
sort_by: Character or NULL. Column to sort by (descending). Default "score".
...: Currently unused; directed is already an explicit argument above and to_igraph accepts no others.

Value

A plain data frame with one row per node and columns node (node label) and score, sorted by sort_by descending ("score" by default; pass sort_by = NULL to keep node order). Values > 1 indicate the node directs disproportionately strong ties to prominent nodes; a node with no neighbors, no prominent neighbor, or zero mean tie weight scores 1.

Details

For each node i: \(r_i = \bar{w}_{i \to rich} / \bar{w}_i\)

References

Opsahl, T., Colizza, V., Panzarasa, P. & Ramasco, J.J. (2008). Prominence and control: The weighted rich-club effect. Physical Review Letters, 101, 168702.

Examples

adj <- matrix(c(0,5,3,1, 5,0,4,2, 3,4,0,1, 1,2,1,0), 4, 4)
rownames(adj) <- colnames(adj) <- c("A", "B", "C", "D")
cograph::rich_club_local(adj, prominence = c(1, 1, 0, 0))
#>   node    score
#> 1    A 1.666667
#> 2    B 1.363636
#> 3    C 1.312500
#> 4    D 1.125000