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Pareto dominance

Source: R/dominance.R
pareto_dominance.Rd

Pareto-style dominance across several neighbourhood-inclusion relations (Espinosa-Rada, 2026).

Usage

pareto_dominance(
  inclusions,
  tau = length(inclusions),
  strict = NULL,
  direction = c("dominated", "dominates")
)

Arguments

inclusions

A list of binary matrices where [u, v] = 1 if u is included in v

tau

Minimum number of relations in which u should be weakly dominated by v

strict

An optional list of binary matrices, in the same order as inclusions, where [u, v] = 1 if the inclusion of u in v is strict. If NULL, the asymmetric criterion is used

direction

Whether D[u, v] = 1 means that u is dominated by v (default) or that u dominates v

Value

This function returns a binary dominance matrix D.

Details

Given \(K\) inclusion matrices (e.g. from set_inclusion()), \(u\) is dominated by \(v\) if (i) the neighbourhood of \(u\) is included in the neighbourhood of \(v\) in at least tau relations (weak dominance), and (ii) the dominance is strict in at least one relation.

By default, the dominance is strict when it is asymmetric: the neighbourhood of \(u\) is included in the neighbourhood of \(v\) but not the other way around. Other criteria, such as proper inclusion, can be given in strict (see set_inclusion(proper = TRUE)).

With tau = K every relation should agree (unanimity), with a majority of relations the dominance is less demanding, and with tau = 1 one relation is enough.

References

Espinosa-Rada, A. (2026). Network positions within scholars and intellectual networks. Journal of Informetrics, 20, 101854. doi:10.1016/j.joi.2026.101854

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

X <- matrix(c(
  1, 1, 1, 0,
  1, 1, 0, 0,
  1, 0, 0, 0,
  0, 1, 0, 0,
  0, 0, 1, 1
), byrow = TRUE, ncol = 4)
Y <- matrix(c(
  1, 1, 0,
  1, 0, 0,
  1, 0, 0,
  0, 1, 1,
  0, 0, 1
), byrow = TRUE, ncol = 3)
rownames(X) <- c("a1", "a2", "a3", "a4", "a5")
rownames(Y) <- rownames(X)

pareto_dominance(list(set_inclusion(X), set_inclusion(Y)), tau = 2)
#>    a1 a2 a3 a4 a5
#> a1  0  0  0  0  0
#> a2  1  0  0  0  0
#> a3  1  1  0  0  0
#> a4  0  0  0  0  0
#> a5  0  0  0  0  0