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 or NULL. Consider edge direction? Default NULL, which follows the directedness of the converted graph.

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.

...

Currently unused; directed is already an explicit argument above and to_igraph accepts no others.

Value

Numeric global efficiency. For unweighted simple graphs this is in \([0, 1]\); weighted graphs can exceed 1 when edge distances are below 1.

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)  # 0.75
#> [1] 0.75