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 counterpart of triad_census and is the basis of 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.
...: Passed to to_igraph, which accepts no further arguments. Any argument supplied here raises an error.

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 (NA for a network without edges). The attributes "directed" and "n_dyads" record the directedness and the total number of dyads.

Details

In an undirected network every present edge is counted as a mutual dyad and the asymmetric count is zero. The total number of dyads is \(n(n-1)/2\) in both cases.

References

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

Examples

cograph::dyad_census(regulation_net)
#> Dyad Census
#> =================================== 
#>        type count proportion
#>      mutual     3 0.06666667
#>  asymmetric    24 0.53333333
#>        null    18 0.40000000
#> 
#>   Dyads: 45   Directed: TRUE 
#>   Reciprocity (2M / (2M + A)): 0.2