Calculate Edge Centrality Measures — edge

Computes centrality measures for edges in a network and returns a tidy data frame. Unlike node centrality, these measures describe edge importance.

Usage

edge_centrality(
  x,
  measures = "all",
  weighted = TRUE,
  directed = NULL,
  cutoff = -1,
  invert_weights = NULL,
  alpha = 1,
  digits = NULL,
  sort_by = NULL,
  ...
)

edge_betweenness(x, ...)

Arguments

x: Network input (matrix, igraph, network, cograph_network, tna object)
measures: Which measures to calculate. Default "all" calculates all available edge measures. Options: "betweenness", "weight", "overlap", "simmelian", "reciprocity".
weighted: Logical. Use edge weights if available. Default TRUE.
directed: Logical or NULL. If NULL (default), auto-detect from matrix symmetry. Set TRUE to force directed, FALSE to force undirected.
cutoff: Maximum path length for betweenness. Default -1 (no limit).
invert_weights: Logical or NULL. Invert weights for path-based measures? Default NULL (auto-detect: TRUE for tna objects, FALSE otherwise).
alpha: Numeric. Exponent for weight inversion. Default 1.
digits: Integer or NULL. Round numeric columns. Default NULL.
sort_by: Character or NULL. Column to sort by (descending). Default NULL.
...: Additional arguments forwarded to the graph constructor, namely loops and simplify (see centrality).

Value

A base data.frame with one row per edge, in the canonical (row-major) edge order of the input. The first two columns are from and to (character when the input carried node names, numeric indices otherwise); the remaining columns are those the requested measures contribute, as listed in Details. measures = "all" on an undirected input therefore gives from, to, weight, betweenness, overlap, shared_neighbors and triangles, and a directed input adds reciprocated, reverse_weight and weight_ratio.

Named numeric vector of edge betweenness values (named by "from->to").

Details

Edge measures available, with the column(s) each one adds:

betweenness: Number of shortest paths passing through the edge. Adds betweenness.
weight: Original edge weight (1 for an unweighted input). Adds weight.
overlap: Jaccard neighborhood overlap of the edge endpoints. Adds overlap and the raw count shared_neighbors.
simmelian: Number of triangles the edge participates in. Adds triangles (there is no column called simmelian).
reciprocity: Whether the reverse edge exists. Directed only: on an undirected input it warns and adds nothing. Adds reciprocated, reverse_weight and weight_ratio, the last two NA where the edge is not reciprocated.

measures = "all" requests every measure, dropping reciprocity on an undirected input.

Examples

# Create test network
mat <- matrix(c(0,1,1,0, 1,0,1,1, 1,1,0,0, 0,1,0,0), 4, 4)
rownames(mat) <- colnames(mat) <- c("A", "B", "C", "D")

# All edge measures
edge_centrality(mat)
#>   from to weight betweenness overlap shared_neighbors triangles
#> 1    A  B      1           2     0.5                1         1
#> 2    A  C      1           1     1.0                1         1
#> 3    B  C      1           2     0.5                1         1
#> 4    B  D      1           3     0.0                0         0

# Just betweenness
edge_centrality(mat, measures = "betweenness")
#>   from to betweenness
#> 1    A  B           2
#> 2    A  C           1
#> 3    B  C           2
#> 4    B  D           3

# Sort by betweenness to find bridge edges
edge_centrality(mat, sort_by = "betweenness")
#>   from to weight betweenness overlap shared_neighbors triangles
#> 1    B  D      1           3     0.0                0         0
#> 2    A  B      1           2     0.5                1         1
#> 3    B  C      1           2     0.5                1         1
#> 4    A  C      1           1     1.0                1         1
mat <- matrix(c(0,1,1,0, 1,0,1,1, 1,1,0,0, 0,1,0,0), 4, 4)
rownames(mat) <- colnames(mat) <- c("A", "B", "C", "D")
edge_betweenness(mat)
#> A->B A->C B->C B->D 
#>    2    1    2    3