This function returns the relational composition of the given matrices. The compound relations define the paths and the social process flows of the given matrices (Pattison, 1993). However, those whom they link may or may not be aware of them. The compound relations allow us to identify "the possibly very long and devious chains of effects propagating withing concrete social systems through links of various kinds" (Lorrain & White, 1971: 50).
Usage
compound_relation(l = list(), comp = 3, matrices = FALSE, equate = FALSE)Arguments
- l
A list of matrices.
- comp
A number with the length of paths to form the compound relation.
- matrices
Whether to return the resulting matrices of the compound relations.
- equate
Whether to return the semigroup equations.
Value
This function provides the composition or concatenation of compound relations and the primitives of the matrices.
References
Boorman, Scott A. and White, Harrison C. (1976) Social Structure from Multiple Networks. II. Role Structures. American Journal of Sociology. 81(6): 1384-1446.
Lorrain, Francois and White, Harrison C. (1971) Structural Equivalence of Individuals in Social Networks. Journal of Mathematical Sociology. 1: 49-80
Pattison, Philippa (1993) Algebraic Models for Social Networks. Cambridge University Press.
Examples
A <- matrix(c(
0, 1, 0, 0,
1, 0, 0, 0,
1, 1, 0, 1,
0, 0, 1, 0
), byrow = TRUE, ncol = 4)
rownames(A) <- letters[1:NCOL(A)]
colnames(A) <- rownames(A)
B <- matrix(c(
0, 1, 0, 0,
1, 0, 0, 0,
0, 0, 0, 1,
0, 0, 1, 0
), byrow = TRUE, ncol = 4)
rownames(B) <- letters[1:NCOL(B)]
colnames(B) <- rownames(B)
cmp <- compound_relation(list(A, B), comp = 2, matrices = TRUE, equate = TRUE)
cmp$compound_relations
#> [1] "a" "b" "ab" "aa" "ba" "bb"
cmp$compound_matrices
#> $a
#> a b c d
#> a 0 1 0 0
#> b 1 0 0 0
#> c 1 1 0 1
#> d 0 0 1 0
#>
#> $b
#> a b c d
#> a 0 1 0 0
#> b 1 0 0 0
#> c 0 0 0 1
#> d 0 0 1 0
#>
#> $ab
#> a b c d
#> a 1 0 0 0
#> b 0 1 0 0
#> c 1 1 1 0
#> d 0 0 0 1
#>
#> $aa
#> a b c d
#> a 1 0 0 0
#> b 0 1 0 0
#> c 1 1 1 0
#> d 1 1 0 1
#>
#> $ba
#> a b c d
#> a 1 0 0 0
#> b 0 1 0 0
#> c 0 0 1 0
#> d 1 1 0 1
#>
#> $bb
#> a b c d
#> a 1 0 0 0
#> b 0 1 0 0
#> c 0 0 1 0
#> d 0 0 0 1
#>
cmp$equated
#> [1] "No reduced equation"