Dyad Census

Classifies every dyad (unordered pair of nodes) in a directed network into one of three mutually exclusive states: mutual (M, edges in both directions), asymmetric (A, an edge in exactly one direction), or null (N, no edge between the pair). The dyad census is the dyad-level companion to triad_census and underlies dyad-based reciprocity.

Usage

dyad_census(x, directed = NULL, ...)

Arguments

x: Network input: matrix, igraph, network, cograph_network, or tna object.
directed: Logical or NULL. If NULL (default), auto-detect from matrix symmetry. Set TRUE to force directed, FALSE to force undirected.
...: Additional arguments passed to to_igraph.

Value

A tidy data.frame of class "cograph_dyad_census" with one row per dyad type and columns:

type: Character: "mutual", "asymmetric", or "null".
count: Integer: number of dyads of that type.
proportion: Numeric: count divided by the total number of dyads (\(n(n-1)/2\)).

The dyad-based reciprocity \(2M / (2M + A)\) is attached as the "reciprocity" attribute.

Details

For undirected networks every present edge is counted as a mutual dyad and the asymmetric count is always zero, so the census reduces to a present/absent split. The total number of dyads is \(n(n-1)/2\) regardless of direction.

References

Wasserman, S., & Faust, K. (1994). Social Network Analysis: Methods and Applications. Cambridge University Press.

Examples

# Directed network with a mix of mutual and asymmetric ties
adj <- matrix(c(
  0, 1, 1, 0,
  1, 0, 0, 1,
  0, 0, 0, 1,
  0, 0, 0, 0
), 4, 4, byrow = TRUE)
rownames(adj) <- colnames(adj) <- LETTERS[1:4]
cograph::dyad_census(adj)
#> Dyad Census
#> =================================== 
#>        type count proportion
#>      mutual     1  0.1666667
#>  asymmetric     3  0.5000000
#>        null     2  0.3333333
#> 
#>   Dyads: 6   Directed: TRUE 
#>   Reciprocity (2M / (2M + A)): 0.4