Exploration of a 3-cliques, as the maximum number of three or more actors who have all possible ties present among themselves
Arguments
- A
A symmetric matrix object.
- list_cliques
Whether to return the list of cliques.
- number
Number of triangles
Value
This function return an edge list of actors participating in 3-cliques.
If list_cliques = TRUE it also return the list of cliques per nodes.
If number = TRUE the output returns the number of 3-cliques in the matrix.
References
Luce, R.D. and Perry, A.D. (1949). A method of matrix analysis of group structure. Psychometrika, 14: 95-116.
Roethlisberger, F.J. and Dickson, W.J. (1939). Management and the Worker. Harvard University Press, Cambridge, MA.
Wasserman, S. and Faust, K. (1994). Social network analysis: Methods and applications. Cambridge University Press.
Examples
A <- matrix(c(
0, 1, 1, 0, 0, 0, 0, 1, 0,
1, 0, 1, 0, 0, 0, 0, 0, 0,
1, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 1, 0, 0, 0,
0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 1, 0, 0, 1, 1, 0,
0, 0, 0, 0, 0, 1, 0, 1, 0,
1, 0, 0, 0, 0, 1, 1, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0
), byrow = TRUE, ncol = 9)
rownames(A) <- letters[1:nrow(A)]
colnames(A) <- rownames(A)
clique_table(A, list_cliques = TRUE, number = TRUE)
#> $table
#> node triad300
#> [1,] "a" "1"
#> [2,] "b" "1"
#> [3,] "c" "1"
#> [4,] "f" "2"
#> [5,] "g" "2"
#> [6,] "h" "2"
#>
#> $n_triangles
#> [1] 2
#>
#> $neighbours
#> $neighbours$a
#> [1] "a" "b" "c"
#>
#> $neighbours$b
#> [1] "a" "b" "c"
#>
#> $neighbours$c
#> [1] "a" "b" "c"
#>
#> $neighbours$f
#> [1] "f" "g" "h"
#>
#> $neighbours$g
#> [1] "f" "g" "h"
#>
#> $neighbours$h
#> [1] "f" "g" "h"
#>
#>