Dominance pairs — dominance

Comparable and incomparable pairs of a dominance relation.

Usage

dominance_pairs(P, direction = c("dominated", "dominates"))

Arguments

P: A binary dominance matrix (e.g. from neigh_inclusion())
direction: Whether P[u, v] = 1 means that u is dominated by v (default) or that u dominates v

Value

This function returns the number and proportion of comparable pairs, and a table of the unordered pairs, where u < v means that u is dominated by v.

Details

Two nodes are comparable if one is dominated by the other. Centrality indices resolve the incomparable pairs with a total ranking, which is not required by the structure of the network.

References

Schoch, D. and Brandes, U. (2016). Re-conceptualizing centrality in social networks. European Journal of Applied Mathematics, 27(6), 971–985. doi:10.1017/S0956792516000401

Author

Alejandro Espinosa-Rada

Examples

A <- matrix(c(
  0, 1, 1, 1, 0,
  1, 0, 0, 0, 0,
  1, 0, 0, 0, 1,
  1, 0, 0, 0, 0,
  0, 0, 1, 0, 0
), byrow = TRUE, ncol = 5)
rownames(A) <- letters[1:nrow(A)]
colnames(A) <- rownames(A)

dominance_pairs(neigh_inclusion(A))
#> $comparable
#> [1] 7
#> 
#> $incomparable
#> [1] 3
#> 
#> $prop_comparable
#> [1] 0.7
#> 
#> $pairs
#>    u v comparable  direction
#> 1  a b       TRUE      b < a
#> 2  a c      FALSE       <NA>
#> 3  a d       TRUE      d < a
#> 4  a e       TRUE      e < a
#> 5  b c       TRUE      b < c
#> 6  b d       TRUE equivalent
#> 7  b e      FALSE       <NA>
#> 8  c d       TRUE      d < c
#> 9  c e       TRUE      e < c
#> 10 d e      FALSE       <NA>
#>