Small-World Coefficient (Sigma) — network_small

Computes the small-world coefficient $$\sigma = \frac{C / C_{rand}}{L / L_{rand}}$$ where $C$ is the global clustering coefficient, $L$ is the mean shortest path length, and $C_{rand}$ and $L_{rand}$ are their means over Erdos-Renyi graphs with the same numbers of nodes and edges. A directed network is collapsed to undirected first.

Usage

network_small_world(x, n_random = 10, ...)

Arguments

x: Network input: matrix, igraph, network, cograph_network, or tna object
n_random: Number of Erdos-Renyi comparison graphs (same n and m as the observed graph). Default 10.
...: Passed to to_igraph, whose only other argument is directed; anything else raises an "unused argument" error.

Value

Numeric: small-world coefficient sigma. NA when the graph has fewer than 4 nodes, no edges, or an undefined/zero mean path length.

Details

Values above 1 indicate small-world structure.

Reproducibility

The comparison 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. A larger n_random gives a more stable estimate.

Examples

set.seed(1)
network_small_world(regulation_net, n_random = 5)
#> [1] 3.339275