CONCOR

Convergence of iterated correlations (Breiger, Boorman and Arabie, 1975), a partition of the nodes into positions of structurally equivalent actors.

Usage

concor(A, splits = 1, max_iter = 50, tol = 1e-08)

Arguments

A

A square matrix, or a list of matrices of the same order for multiple relations

splits

Number of successive divisions

max_iter

Maximum number of iterated correlations

tol

Tolerance to decide that the correlations have converged

Value

This function returns the position of each node and the number of positions.

Details

The rows and the columns of the matrix describe how each node relates to the others, so they are stacked into a profile. The correlations between the profiles of every pair of nodes are computed, and the correlations of those correlations are computed again and again. The matrix converges to a matrix of ones and minus ones, which splits the nodes into two positions. The procedure is repeated within each position, so splits divisions give at most \(2^{splits}\) positions.

References

Breiger, R. L., Boorman, S. A. and Arabie, P. (1975). An algorithm for clustering relational data with applications to social network analysis and comparison with multidimensional scaling. Journal of Mathematical Psychology, 12(3), 328–383. doi:10.1016/0022-2496(75)90028-0

Author

Alejandro Espinosa-Rada

Examples

A <- matrix(c(
  0, 1, 1, 0, 0, 0,
  1, 0, 1, 0, 0, 0,
  1, 1, 0, 0, 0, 0,
  0, 0, 0, 0, 1, 1,
  0, 0, 0, 1, 0, 1,
  0, 0, 0, 1, 1, 0
), byrow = TRUE, ncol = 6)
rownames(A) <- letters[1:nrow(A)]
colnames(A) <- rownames(A)

concor(A, splits = 1)
#> $partition
#> a b c d e f 
#> 1 1 1 2 2 2 
#> 
#> $positions
#> [1] 2
#>