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Set inclusion of neighbourhoods

Source: R/dominance.R
set_inclusion.Rd

Inclusion of the neighbourhoods of the rows of an incidence matrix.

Usage

set_inclusion(N, M = N, proper = FALSE)

Arguments

N

An incidence matrix of the neighbourhoods to be included

M

An incidence matrix, with the same dimensions as N, of the including neighbourhoods

proper

Whether the inclusion should be proper

Value

This function returns a binary matrix P where P[u, v] = 1 if N(u) is included in M(v).

Details

The neighbourhoods of the rows can be defined on any set of columns (e.g. papers of authors, or events of actors). N contains the neighbourhood that should be included, and M the neighbourhood in which it should be included. M is the same as N for open neighbourhoods, or can add other elements, such as the node itself, for closed neighbourhoods.

With proper = TRUE the inclusion should be proper, \(N(u) \subsetneq M(v)\), i.e. \(M(v)\) has at least one element that is not in \(N(u)\).

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)
rownames(X) <- c("a1", "a2", "a3", "a4", "a5")
colnames(X) <- c("w1", "w2", "w3", "w4")

set_inclusion(X)
#>    a1 a2 a3 a4 a5
#> a1  0  0  0  0  0
#> a2  1  0  0  0  0
#> a3  1  1  0  0  0
#> a4  1  1  0  0  0
#> a5  0  0  0  0  0