Preserved order — preserved

Whether a centrality index preserves a dominance relation.

Usage

preserved_order(
  P,
  scores,
  tol = sqrt(.Machine$double.eps),
  direction = c("dominated", "dominates")
)

Arguments

P: A binary dominance matrix
scores: A vector of centrality scores in the same order as the rows of P
tol: Numerical tolerance
direction: Whether P[u, v] = 1 means that u is dominated by v (default) or that u dominates v

Value

This function returns whether the order is preserved and the pairs that violate it.

Details

A centrality index preserves the dominance if no dominated node has a higher score than the node that dominates it (Schoch and Brandes, 2016). Differences smaller than tol are considered ties, as eigenvectors and other iterative scores are only approximated.

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)

P <- neigh_inclusion(A)
preserved_order(P, rowSums(A))
#> $preserved
#> [1] TRUE
#> 
#> $violations
#> [1] dominated        dominating       score_dominated  score_dominating
#> <0 rows> (or 0-length row.names)
#> 
preserved_order(P, betweenness_centrality(A, digraph = FALSE))
#> $preserved
#> [1] TRUE
#> 
#> $violations
#> [1] dominated        dominating       score_dominated  score_dominating
#> <0 rows> (or 0-length row.names)
#>