Rich Club Coefficient

Computes the rich club coefficient for a degree threshold k, the density of ties among nodes with degree above k. It measures the tendency of high-degree nodes to connect to each other. Degrees are taken on the undirected simple skeleton of the network.

Usage

network_rich_club(x, k = NULL, normalized = FALSE, n_random = 10, ...)

Arguments

x

Network input: matrix, igraph, network, cograph_network, or tna object

k

Degree threshold. Only nodes with degree greater than k are included. Default NULL uses the median degree.

normalized

Logical. If TRUE, divide by the mean coefficient of random graphs with the same degree sequence. Default FALSE.

n_random

Number of random graphs for normalization. Default 10.

...

Passed to to_igraph, whose only other argument is directed; anything else raises an "unused argument" error.

Value

Numeric scalar: the rich club coefficient. A normalized value above 1 indicates a rich club effect. NA when fewer than two nodes exceed k.

Reproducibility

When normalized = TRUE the null graphs are drawn from the caller's RNG stream; this function takes no seed argument and does not save or restore .Random.seed. Call set.seed() beforehand for a reproducible result. rich_club() offers a seed argument, confidence intervals, and the full rich club curve.

Examples

network_rich_club(regulation_net, k = 5)
#> [1] 0.6666667