The Laplacian of a signed graph.
Arguments
- g
igraph object with a sign edge attribute.
- norm
Whether to calculate the normalized Laplacian. See definitions below.
- sparse
Logical scalar, whether to return the result as a sparse matrix. The Matrix package is required for sparse matrices.
Details
See laplacian_matrix of igraph for more details. In the signed case, D is a diagonal matrix containing the absolute values of row sums of the signed adjacency matrix.
Examples
library(igraph)
g <- sample_islands_signed(3, 10, 5 / 10, 1)
laplacian_matrix_signed(g)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
#> [1,] 2 0 0 0 0 -1 0 0 -1 0 0 0 0
#> [2,] 0 2 0 0 -1 0 0 -1 0 0 0 0 0
#> [3,] 0 0 3 -1 -1 -1 0 0 0 0 0 0 0
#> [4,] 0 0 -1 4 0 -1 0 0 -1 -1 0 0 0
#> [5,] 0 -1 -1 0 5 0 -1 -1 0 -1 0 0 0
#> [6,] -1 0 -1 -1 0 4 0 -1 0 0 0 0 0
#> [7,] 0 0 0 0 -1 0 3 -1 0 0 0 0 0
#> [8,] 0 -1 0 0 -1 -1 -1 4 0 0 0 0 0
#> [9,] -1 0 0 -1 0 0 0 0 3 -1 0 0 0
#> [10,] 0 0 0 -1 -1 0 0 0 -1 4 0 0 0
#> [11,] 0 0 0 0 0 0 0 0 0 0 2 -1 0
#> [12,] 0 0 0 0 0 0 0 0 0 0 -1 4 0
#> [13,] 0 0 0 0 0 0 0 0 0 0 0 0 5
#> [14,] 0 0 0 0 0 0 0 0 0 0 0 0 -1
#> [15,] 0 0 0 0 0 0 0 0 0 0 0 -1 0
#> [16,] 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [17,] 0 0 0 0 0 0 0 0 0 0 0 0 -1
#> [18,] 0 0 0 0 0 0 0 0 0 0 0 -1 -1
#> [19,] 0 0 0 0 0 0 0 0 0 0 0 -1 -1
#> [20,] 0 0 0 0 0 0 0 0 0 0 -1 0 -1
#> [21,] 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [22,] 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [23,] 0 0 0 0 0 0 0 0 0 1 0 0 0
#> [24,] 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [25,] 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [26,] 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [27,] 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [28,] 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [29,] 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [30,] 0 0 0 0 0 0 1 0 0 0 0 0 0
#> [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25]
#> [1,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [3,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [4,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [5,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [6,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [7,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [8,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [9,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [10,] 0 0 0 0 0 0 0 0 0 1 0 0
#> [11,] 0 0 0 0 0 0 -1 0 0 0 0 0
#> [12,] 0 -1 0 0 -1 -1 0 0 0 0 0 0
#> [13,] -1 0 0 -1 -1 -1 -1 0 0 0 0 0
#> [14,] 3 0 -1 -1 0 0 0 0 0 0 0 0
#> [15,] 0 3 -1 0 0 -1 0 0 0 0 0 0
#> [16,] -1 -1 4 0 -1 0 -1 0 0 0 0 0
#> [17,] -1 0 0 3 0 -1 0 0 0 0 0 0
#> [18,] 0 0 -1 0 4 0 -1 0 0 0 0 0
#> [19,] 0 -1 0 -1 0 6 -1 0 0 0 0 1
#> [20,] 0 0 -1 0 -1 -1 5 0 0 0 0 0
#> [21,] 0 0 0 0 0 0 0 3 -1 -1 0 0
#> [22,] 0 0 0 0 0 0 0 -1 7 -1 -1 -1
#> [23,] 0 0 0 0 0 0 0 -1 -1 8 -1 0
#> [24,] 0 0 0 0 0 0 0 0 -1 -1 4 0
#> [25,] 0 0 0 0 0 1 0 0 -1 0 0 5
#> [26,] 0 0 0 0 0 0 0 0 0 0 0 -1
#> [27,] 0 0 0 0 0 0 0 0 -1 -1 -1 0
#> [28,] 0 0 0 0 0 0 0 -1 -1 -1 0 -1
#> [29,] 0 0 0 0 0 0 0 0 0 -1 -1 0
#> [30,] 0 0 0 0 0 0 0 0 -1 -1 0 -1
#> [,26] [,27] [,28] [,29] [,30]
#> [1,] 0 0 0 0 0
#> [2,] 0 0 0 0 0
#> [3,] 0 0 0 0 0
#> [4,] 0 0 0 0 0
#> [5,] 0 0 0 0 0
#> [6,] 0 0 0 0 0
#> [7,] 0 0 0 0 1
#> [8,] 0 0 0 0 0
#> [9,] 0 0 0 0 0
#> [10,] 0 0 0 0 0
#> [11,] 0 0 0 0 0
#> [12,] 0 0 0 0 0
#> [13,] 0 0 0 0 0
#> [14,] 0 0 0 0 0
#> [15,] 0 0 0 0 0
#> [16,] 0 0 0 0 0
#> [17,] 0 0 0 0 0
#> [18,] 0 0 0 0 0
#> [19,] 0 0 0 0 0
#> [20,] 0 0 0 0 0
#> [21,] 0 0 -1 0 0
#> [22,] 0 -1 -1 0 -1
#> [23,] 0 -1 -1 -1 -1
#> [24,] 0 -1 0 -1 0
#> [25,] -1 0 -1 0 -1
#> [26,] 4 0 -1 -1 -1
#> [27,] 0 6 -1 -1 -1
#> [28,] -1 -1 7 -1 0
#> [29,] -1 -1 -1 6 -1
#> [30,] -1 -1 0 -1 7
laplacian_matrix_signed(g, norm = TRUE)
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 1.0000000 0.0000000 0.0000000 0.0000000 0.0000000 -0.3535534
#> [2,] 0.0000000 1.0000000 0.0000000 0.0000000 -0.3162278 0.0000000
#> [3,] 0.0000000 0.0000000 1.0000000 -0.2886751 -0.2581989 -0.2886751
#> [4,] 0.0000000 0.0000000 -0.2886751 1.0000000 0.0000000 -0.2500000
#> [5,] 0.0000000 -0.3162278 -0.2581989 0.0000000 1.0000000 0.0000000
#> [6,] -0.3535534 0.0000000 -0.2886751 -0.2500000 0.0000000 1.0000000
#> [7,] 0.0000000 0.0000000 0.0000000 0.0000000 -0.2581989 0.0000000
#> [8,] 0.0000000 -0.3535534 0.0000000 0.0000000 -0.2236068 -0.2500000
#> [9,] -0.4082483 0.0000000 0.0000000 -0.2886751 0.0000000 0.0000000
#> [10,] 0.0000000 0.0000000 0.0000000 -0.2500000 -0.2236068 0.0000000
#> [11,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [12,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [13,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [14,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [15,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [16,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [17,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [18,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [19,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [20,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [21,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [22,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [23,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [24,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [25,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [26,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [27,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [28,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [29,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [30,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [,7] [,8] [,9] [,10] [,11] [,12]
#> [1,] 0.0000000 0.0000000 -0.4082483 0.0000000 0.0000000 0.0000000
#> [2,] 0.0000000 -0.3535534 0.0000000 0.0000000 0.0000000 0.0000000
#> [3,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [4,] 0.0000000 0.0000000 -0.2886751 -0.2500000 0.0000000 0.0000000
#> [5,] -0.2581989 -0.2236068 0.0000000 -0.2236068 0.0000000 0.0000000
#> [6,] 0.0000000 -0.2500000 0.0000000 0.0000000 0.0000000 0.0000000
#> [7,] 1.0000000 -0.2886751 0.0000000 0.0000000 0.0000000 0.0000000
#> [8,] -0.2886751 1.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [9,] 0.0000000 0.0000000 1.0000000 -0.2886751 0.0000000 0.0000000
#> [10,] 0.0000000 0.0000000 -0.2886751 1.0000000 0.0000000 0.0000000
#> [11,] 0.0000000 0.0000000 0.0000000 0.0000000 1.0000000 -0.3535534
#> [12,] 0.0000000 0.0000000 0.0000000 0.0000000 -0.3535534 1.0000000
#> [13,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [14,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [15,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 -0.2886751
#> [16,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [17,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [18,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 -0.2500000
#> [19,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 -0.2041241
#> [20,] 0.0000000 0.0000000 0.0000000 0.0000000 -0.3162278 0.0000000
#> [21,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [22,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [23,] 0.0000000 0.0000000 0.0000000 0.1767767 0.0000000 0.0000000
#> [24,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [25,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [26,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [27,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [28,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [29,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [30,] 0.2182179 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [,13] [,14] [,15] [,16] [,17] [,18]
#> [1,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [2,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [3,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [4,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [5,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [6,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [7,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [8,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [9,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [10,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [11,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [12,] 0.0000000 0.0000000 -0.2886751 0.0000000 0.0000000 -0.2500000
#> [13,] 1.0000000 -0.2581989 0.0000000 0.0000000 -0.2581989 -0.2236068
#> [14,] -0.2581989 1.0000000 0.0000000 -0.2886751 -0.3333333 0.0000000
#> [15,] 0.0000000 0.0000000 1.0000000 -0.2886751 0.0000000 0.0000000
#> [16,] 0.0000000 -0.2886751 -0.2886751 1.0000000 0.0000000 -0.2500000
#> [17,] -0.2581989 -0.3333333 0.0000000 0.0000000 1.0000000 0.0000000
#> [18,] -0.2236068 0.0000000 0.0000000 -0.2500000 0.0000000 1.0000000
#> [19,] -0.1825742 0.0000000 -0.2357023 0.0000000 -0.2357023 0.0000000
#> [20,] -0.2000000 0.0000000 0.0000000 -0.2236068 0.0000000 -0.2236068
#> [21,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [22,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [23,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [24,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [25,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [26,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [27,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [28,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [29,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [30,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [,19] [,20] [,21] [,22] [,23] [,24]
#> [1,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [2,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [3,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [4,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [5,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [6,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [7,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [8,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [9,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [10,] 0.0000000 0.0000000 0.0000000 0.0000000 0.1767767 0.0000000
#> [11,] 0.0000000 -0.3162278 0.0000000 0.0000000 0.0000000 0.0000000
#> [12,] -0.2041241 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [13,] -0.1825742 -0.2000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [14,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [15,] -0.2357023 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [16,] 0.0000000 -0.2236068 0.0000000 0.0000000 0.0000000 0.0000000
#> [17,] -0.2357023 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [18,] 0.0000000 -0.2236068 0.0000000 0.0000000 0.0000000 0.0000000
#> [19,] 1.0000000 -0.1825742 0.0000000 0.0000000 0.0000000 0.0000000
#> [20,] -0.1825742 1.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [21,] 0.0000000 0.0000000 1.0000000 -0.2182179 -0.2041241 0.0000000
#> [22,] 0.0000000 0.0000000 -0.2182179 1.0000000 -0.1336306 -0.1889822
#> [23,] 0.0000000 0.0000000 -0.2041241 -0.1336306 1.0000000 -0.1767767
#> [24,] 0.0000000 0.0000000 0.0000000 -0.1889822 -0.1767767 1.0000000
#> [25,] 0.1825742 0.0000000 0.0000000 -0.1690309 0.0000000 0.0000000
#> [26,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [27,] 0.0000000 0.0000000 0.0000000 -0.1543033 -0.1443376 -0.2041241
#> [28,] 0.0000000 0.0000000 -0.2182179 -0.1428571 -0.1336306 0.0000000
#> [29,] 0.0000000 0.0000000 0.0000000 0.0000000 -0.1443376 -0.2041241
#> [30,] 0.0000000 0.0000000 0.0000000 -0.1428571 -0.1336306 0.0000000
#> [,25] [,26] [,27] [,28] [,29] [,30]
#> [1,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [2,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [3,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [4,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [5,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [6,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [7,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.2182179
#> [8,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [9,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [10,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [11,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [12,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [13,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [14,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [15,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [16,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [17,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [18,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [19,] 0.1825742 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [20,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [21,] 0.0000000 0.0000000 0.0000000 -0.2182179 0.0000000 0.0000000
#> [22,] -0.1690309 0.0000000 -0.1543033 -0.1428571 0.0000000 -0.1428571
#> [23,] 0.0000000 0.0000000 -0.1443376 -0.1336306 -0.1443376 -0.1336306
#> [24,] 0.0000000 0.0000000 -0.2041241 0.0000000 -0.2041241 0.0000000
#> [25,] 1.0000000 -0.2236068 0.0000000 -0.1690309 0.0000000 -0.1690309
#> [26,] -0.2236068 1.0000000 0.0000000 -0.1889822 -0.2041241 -0.1889822
#> [27,] 0.0000000 0.0000000 1.0000000 -0.1543033 -0.1666667 -0.1543033
#> [28,] -0.1690309 -0.1889822 -0.1543033 1.0000000 -0.1543033 0.0000000
#> [29,] 0.0000000 -0.2041241 -0.1666667 -0.1543033 1.0000000 -0.1543033
#> [30,] -0.1690309 -0.1889822 -0.1543033 0.0000000 -0.1543033 1.0000000