Rich Club Coefficient — network_rich

Computes the rich club coefficient for a given degree threshold k. Measures the tendency of high-degree nodes to connect to each other. A normalized version compares to random graphs.

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 > k are included. If NULL, uses median degree.
normalized: Logical. Normalize by random graph expectation? 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: rich club coefficient (> 1 indicates rich club effect when normalized). 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

# Scale-free networks often show rich-club effect
if (requireNamespace("igraph", quietly = TRUE)) {
  g <- igraph::sample_pa(50, m = 2, directed = FALSE)
  network_rich_club(g, k = 5)
}
#> [1] 0.4166667