Global Efficiency

Computes the global efficiency of a network - the average of the inverse shortest path lengths between all pairs of nodes. Higher values indicate better global communication efficiency. Handles disconnected graphs gracefully (infinite distances contribute 0).

Usage

network_global_efficiency(
  x,
  directed = NULL,
  weights = NULL,
  invert_weights = NULL,
  alpha = 1,
  ...
)

Arguments

x

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

directed

Logical. Consider edge direction? Default TRUE for directed graphs.

weights

Edge weights (NULL for unweighted). Set to NA to ignore existing weights.

invert_weights

Logical or NULL. Invert weights so higher weights = shorter paths? Default NULL which auto-detects: TRUE for tna objects, FALSE otherwise (matching igraph/sna). Set TRUE for strength/frequency weights (qgraph style).

alpha

Numeric. Exponent for weight inversion: distance = 1/weight^alpha. Default 1.

...

Additional arguments passed to to_igraph

Value

Numeric in [0, 1]: global efficiency

Examples

# Complete graph has efficiency 1
k4 <- matrix(1, 4, 4); diag(k4) <- 0
network_global_efficiency(k4)  # 1
#> [1] 1

# Star has lower efficiency
star <- matrix(c(0,1,1,1, 1,0,0,0, 1,0,0,0, 1,0,0,0), 4, 4)
network_global_efficiency(star)  # ~0.83
#> [1] 0.75