Structural similarities

In the literature of social network, Euclidean distance (Burt, 1976) or correlations (Wasserman and Faust, 1994) were considered as measures of structural equivalence.

Usage

dist_sim_matrix(
  A,
  method = c("euclidean", "hamming", "jaccard"),
  bipartite = FALSE
)

Arguments

A

A matrix

method

The similarities/distance currently available are either Euclidean (default), Hamming, or Jaccard.

bipartite

Whether the object is an incidence matrix

Value

This function returns a distance matrix between nodes of the same matrix.

References

Burt, Ronald S. (1976) Positions in networks. Social Forces, 55(1): 93-122.

Wasserman, S. and Faust, K. (1994). Social network analysis: Methods and applications. Cambridge University Press.

Author

Alejandro Espinosa-Rada

Examples

A <- matrix(c(
  0, 1, 0, 0, 1,
  0, 0, 0, 1, 1,
  0, 1, 0, 0, 1,
  0, 0, 1, 1, 0,
  0, 1, 0, 0, 0
), nrow = 5, ncol = 5, byrow = TRUE)
rownames(A) <- letters[1:nrow(A)]
colnames(A) <- rownames(A)
dist_sim_matrix(A, method = "jaccard")
#>           a         b         c         d   e
#> a 0.0000000 0.6666667 0.0000000 1.0000000 0.5
#> b 0.6666667 0.0000000 0.6666667 0.6666667 1.0
#> c 0.0000000 0.6666667 0.0000000 1.0000000 0.5
#> d 1.0000000 0.6666667 1.0000000 0.0000000 1.0
#> e 0.5000000 1.0000000 0.5000000 1.0000000 0.0

A <- matrix(c(
  0, 0, 3, 0, 5,
  0, 0, 2, 0, 4,
  5, 4, 0, 4, 0,
  0, 3, 0, 1, 0,
  0, 0, 0, 0, 2
), nrow = 5, ncol = 5, byrow = TRUE)
dist_sim_matrix(A, method = "euclidean")
#>          [,1]     [,2]     [,3]     [,4]     [,5]
#> [1,] 0.000000 1.414214 9.539392 6.633250 4.242641
#> [2,] 1.414214 0.000000 8.774964 5.477226 2.828427
#> [3,] 9.539392 8.774964 0.000000 5.916080 7.810250
#> [4,] 6.633250 5.477226 5.916080 0.000000 3.741657
#> [5,] 4.242641 2.828427 7.810250 3.741657 0.000000

# Several relations are compared at the same time, stacking the rows and the
# columns of every matrix
B <- matrix(c(
  0, 1, 0, 0, 1,
  1, 0, 0, 0, 1,
  0, 0, 0, 1, 0,
  0, 0, 1, 0, 0,
  1, 1, 0, 0, 0
), nrow = 5, ncol = 5, byrow = TRUE)
dist_sim_matrix(list(A, B), method = "euclidean")
#>           [,1]      [,2]      [,3]     [,4]     [,5]
#> [1,]  0.000000  4.000000 11.618950 7.211103 9.591663
#> [2,]  4.000000  0.000000 11.000000 6.324555 9.055385
#> [3,] 11.618950 11.000000  0.000000 8.306624 8.888194
#> [4,]  7.211103  6.324555  8.306624 0.000000 9.055385
#> [5,]  9.591663  9.055385  8.888194 9.055385 0.000000