Symmetrize a Directed Network

Combines each pair of opposite arcs into one undirected edge. The result is an undirected network, so measures that branch on directedness see the change.

Usage

symmetrize(
  x,
  method = c("max", "min", "mean", "sum", "mutual", "upper", "lower"),
  keep_format = FALSE,
  directed = NULL
)

Arguments

x

Network input.

method

How to combine w[i, j] and w[j, i]:

"max": (default) the larger of the two; on a binary network this is sna's "weak" rule
"min": the smaller of the two
"mean": their average
"sum": their total
"mutual": keep only reciprocated pairs, taking the smaller weight; on a binary network this is sna's "strong" rule
"upper": take the upper triangle and mirror it
"lower": take the lower triangle and mirror it

keep_format

Logical. Return the input format when TRUE.

directed

Logical or NULL. Directedness to read the input with; the result is always undirected.

Value

An undirected cograph_network, or the input format when keep_format = TRUE. The weight matrix satisfies isSymmetric(). Zero is how this representation stores "no edge", so any pair whose combined weight is exactly zero disappears: every unreciprocated arc under method = "mutual", and a cancelling pair under "sum". A cograph_edges_dropped warning says how many.

Details

"max", "min", "mean" and "sum" combine two values only where both arcs exist; an unreciprocated edge keeps its own weight rather than being compared against the zero that stands for the missing arc. That distinction matters for signed networks, where comparing a negative weight against a structural zero would delete the edge. Use "mutual" when an edge should survive only if it was reciprocated.

References

Butts, C. T. (2008). Social network analysis with sna. Journal of Statistical Software, 24(6), 1–51.

Examples

adj <- matrix(c(0, .5, 0,
                .2, 0, .7,
                0, .1, 0), 3, 3, byrow = TRUE)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")

symmetrize(adj, method = "max")
#> Cograph network: 3 nodes, 2 edges ( undirected )
#> Source: matrix 
#>   Nodes (3): A, B, C
#>   Edges: 2 / 3 (density: 66.7%)
#>   Weights: [0.500, 0.700]  |  mean: 0.600
#>   Strongest edges:
#>     B -- C  0.700
#>     A -- B  0.500
#> Layout: none 
#>   Use as.data.frame() for the edge table, as.data.frame(what = "nodes") for the nodes.
symmetrize(adj, method = "mean")
#> Cograph network: 3 nodes, 2 edges ( undirected )
#> Source: matrix 
#>   Nodes (3): A, B, C
#>   Edges: 2 / 3 (density: 66.7%)
#>   Weights: [0.350, 0.400]  |  mean: 0.375
#>   Strongest edges:
#>     B -- C  0.400
#>     A -- B  0.350
#> Layout: none 
#>   Use as.data.frame() for the edge table, as.data.frame(what = "nodes") for the nodes.
symmetrize(adj, method = "mutual")
#> Cograph network: 3 nodes, 2 edges ( undirected )
#> Source: matrix 
#>   Nodes (3): A, B, C
#>   Edges: 2 / 3 (density: 66.7%)
#>   Weights: [0.100, 0.200]  |  mean: 0.150
#>   Strongest edges:
#>     A -- B  0.200
#>     B -- C  0.100
#> Layout: none 
#>   Use as.data.frame() for the edge table, as.data.frame(what = "nodes") for the nodes.