This is a collection of functions that convert a graph stored as an
igraph object into a desired matrix representation
among adjacency matrix, graph laplacian, modularity matrix or graphon (edge
probability matrix).
Usage
repr_adjacency(network, validate = TRUE)
repr_laplacian(network, validate = TRUE)
repr_modularity(network, validate = TRUE)
repr_graphon(network, validate = TRUE)Arguments
- network
An
igraphobject.- validate
A boolean specifying whether the function should check the class of its input (default:
TRUE).
Value
A numeric square matrix giving the desired network representation recorded in the object's class.
Examples
g <- igraph::sample_smallworld(1, 25, 3, 0.05)
repr_adjacency(g)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
#> [1,] 0 1 0 1 0 0 0 0 0 0 0 0 0
#> [2,] 1 0 1 1 1 0 0 0 0 0 0 0 0
#> [3,] 0 1 0 1 1 1 0 0 0 0 0 0 0
#> [4,] 1 1 1 0 1 1 1 0 0 0 0 0 0
#> [5,] 0 1 1 1 0 1 1 1 0 0 0 0 0
#> [6,] 0 0 1 1 1 0 1 1 1 0 0 0 0
#> [7,] 0 0 0 1 1 1 0 1 0 1 0 0 0
#> [8,] 0 0 0 0 1 1 1 0 1 1 1 0 0
#> [9,] 0 0 0 0 0 1 0 1 0 1 1 1 0
#> [10,] 0 0 0 0 0 0 1 1 1 0 1 1 1
#> [11,] 0 0 0 0 0 0 0 1 1 1 0 1 1
#> [12,] 0 0 0 0 0 0 0 0 1 1 1 0 1
#> [13,] 0 0 0 0 0 0 0 0 0 1 1 1 0
#> [14,] 0 0 0 0 0 0 0 0 0 0 1 1 1
#> [15,] 0 0 0 0 0 0 0 0 0 0 0 1 1
#> [16,] 0 0 0 0 0 0 0 0 0 0 0 0 1
#> [17,] 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [18,] 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [19,] 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [20,] 0 0 0 0 0 0 0 0 1 0 0 0 0
#> [21,] 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [22,] 0 0 1 1 0 0 0 0 0 0 0 0 0
#> [23,] 1 0 0 0 0 0 0 0 0 0 0 0 0
#> [24,] 0 1 0 0 0 1 0 0 0 0 0 0 0
#> [25,] 1 1 1 0 0 0 0 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 1 0 1
#> [2,] 0 0 0 0 0 0 0 0 0 0 1 1
#> [3,] 0 0 0 0 0 0 0 0 1 0 0 1
#> [4,] 0 0 0 0 0 0 0 0 1 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 1 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 1 0 0 0 0 0
#> [10,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [11,] 1 0 0 0 0 0 0 0 0 0 0 0
#> [12,] 1 1 0 0 0 0 0 0 0 0 0 0
#> [13,] 1 1 1 0 0 0 0 0 0 0 0 0
#> [14,] 0 1 1 1 0 0 0 0 0 0 0 0
#> [15,] 1 0 1 1 1 0 0 1 0 0 0 0
#> [16,] 1 1 0 1 1 1 0 0 0 0 0 0
#> [17,] 1 1 1 0 1 1 1 0 0 0 0 0
#> [18,] 0 1 1 1 0 1 1 1 0 0 0 0
#> [19,] 0 0 1 1 1 0 1 1 1 0 0 0
#> [20,] 0 0 0 1 1 1 0 1 1 1 0 0
#> [21,] 0 1 0 0 1 1 1 0 1 1 0 0
#> [22,] 0 0 0 0 0 1 1 1 0 1 1 0
#> [23,] 0 0 0 0 0 0 1 1 1 0 1 1
#> [24,] 0 0 0 0 0 0 0 0 1 1 0 1
#> [25,] 0 0 0 0 0 0 0 0 0 1 1 0
#> attr(,"representation")
#> [1] "adjacency"
repr_laplacian(g)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
#> [1,] 4 -1 0 -1 0 0 0 0 0 0 0 0 0
#> [2,] -1 6 -1 -1 -1 0 0 0 0 0 0 0 0
#> [3,] 0 -1 6 -1 -1 -1 0 0 0 0 0 0 0
#> [4,] -1 -1 -1 7 -1 -1 -1 0 0 0 0 0 0
#> [5,] 0 -1 -1 -1 6 -1 -1 -1 0 0 0 0 0
#> [6,] 0 0 -1 -1 -1 7 -1 -1 -1 0 0 0 0
#> [7,] 0 0 0 -1 -1 -1 5 -1 0 -1 0 0 0
#> [8,] 0 0 0 0 -1 -1 -1 6 -1 -1 -1 0 0
#> [9,] 0 0 0 0 0 -1 0 -1 6 -1 -1 -1 0
#> [10,] 0 0 0 0 0 0 -1 -1 -1 6 -1 -1 -1
#> [11,] 0 0 0 0 0 0 0 -1 -1 -1 6 -1 -1
#> [12,] 0 0 0 0 0 0 0 0 -1 -1 -1 6 -1
#> [13,] 0 0 0 0 0 0 0 0 0 -1 -1 -1 6
#> [14,] 0 0 0 0 0 0 0 0 0 0 -1 -1 -1
#> [15,] 0 0 0 0 0 0 0 0 0 0 0 -1 -1
#> [16,] 0 0 0 0 0 0 0 0 0 0 0 0 -1
#> [17,] 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [18,] 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [19,] 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [20,] 0 0 0 0 0 0 0 0 -1 0 0 0 0
#> [21,] 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [22,] 0 0 -1 -1 0 0 0 0 0 0 0 0 0
#> [23,] -1 0 0 0 0 0 0 0 0 0 0 0 0
#> [24,] 0 -1 0 0 0 -1 0 0 0 0 0 0 0
#> [25,] -1 -1 -1 0 0 0 0 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 -1 0 -1
#> [2,] 0 0 0 0 0 0 0 0 0 0 -1 -1
#> [3,] 0 0 0 0 0 0 0 0 -1 0 0 -1
#> [4,] 0 0 0 0 0 0 0 0 -1 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 -1 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 -1 0 0 0 0 0
#> [10,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [11,] -1 0 0 0 0 0 0 0 0 0 0 0
#> [12,] -1 -1 0 0 0 0 0 0 0 0 0 0
#> [13,] -1 -1 -1 0 0 0 0 0 0 0 0 0
#> [14,] 6 -1 -1 -1 0 0 0 0 0 0 0 0
#> [15,] -1 7 -1 -1 -1 0 0 -1 0 0 0 0
#> [16,] -1 -1 6 -1 -1 -1 0 0 0 0 0 0
#> [17,] -1 -1 -1 6 -1 -1 -1 0 0 0 0 0
#> [18,] 0 -1 -1 -1 6 -1 -1 -1 0 0 0 0
#> [19,] 0 0 -1 -1 -1 6 -1 -1 -1 0 0 0
#> [20,] 0 0 0 -1 -1 -1 7 -1 -1 -1 0 0
#> [21,] 0 -1 0 0 -1 -1 -1 6 -1 -1 0 0
#> [22,] 0 0 0 0 0 -1 -1 -1 7 -1 -1 0
#> [23,] 0 0 0 0 0 0 -1 -1 -1 6 -1 -1
#> [24,] 0 0 0 0 0 0 0 0 -1 -1 5 -1
#> [25,] 0 0 0 0 0 0 0 0 0 -1 -1 5
#> attr(,"representation")
#> [1] "laplacian"
repr_modularity(g)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
#> [1,] -0.1066667 0.84 -0.16 0.8133333 -0.16 -0.1866667 -0.1333333 -0.16 -0.16
#> [2,] 0.8400000 -0.24 0.76 0.7200000 0.76 -0.2800000 -0.2000000 -0.24 -0.24
#> [3,] -0.1600000 0.76 -0.24 0.7200000 0.76 0.7200000 -0.2000000 -0.24 -0.24
#> [4,] 0.8133333 0.72 0.72 -0.3266667 0.72 0.6733333 0.7666667 -0.28 -0.28
#> [5,] -0.1600000 0.76 0.76 0.7200000 -0.24 0.7200000 0.8000000 0.76 -0.24
#> [6,] -0.1866667 -0.28 0.72 0.6733333 0.72 -0.3266667 0.7666667 0.72 0.72
#> [7,] -0.1333333 -0.20 -0.20 0.7666667 0.80 0.7666667 -0.1666667 0.80 -0.20
#> [8,] -0.1600000 -0.24 -0.24 -0.2800000 0.76 0.7200000 0.8000000 -0.24 0.76
#> [9,] -0.1600000 -0.24 -0.24 -0.2800000 -0.24 0.7200000 -0.2000000 0.76 -0.24
#> [10,] -0.1600000 -0.24 -0.24 -0.2800000 -0.24 -0.2800000 0.8000000 0.76 0.76
#> [11,] -0.1600000 -0.24 -0.24 -0.2800000 -0.24 -0.2800000 -0.2000000 0.76 0.76
#> [12,] -0.1600000 -0.24 -0.24 -0.2800000 -0.24 -0.2800000 -0.2000000 -0.24 0.76
#> [13,] -0.1600000 -0.24 -0.24 -0.2800000 -0.24 -0.2800000 -0.2000000 -0.24 -0.24
#> [14,] -0.1600000 -0.24 -0.24 -0.2800000 -0.24 -0.2800000 -0.2000000 -0.24 -0.24
#> [15,] -0.1866667 -0.28 -0.28 -0.3266667 -0.28 -0.3266667 -0.2333333 -0.28 -0.28
#> [16,] -0.1600000 -0.24 -0.24 -0.2800000 -0.24 -0.2800000 -0.2000000 -0.24 -0.24
#> [17,] -0.1600000 -0.24 -0.24 -0.2800000 -0.24 -0.2800000 -0.2000000 -0.24 -0.24
#> [18,] -0.1600000 -0.24 -0.24 -0.2800000 -0.24 -0.2800000 -0.2000000 -0.24 -0.24
#> [19,] -0.1600000 -0.24 -0.24 -0.2800000 -0.24 -0.2800000 -0.2000000 -0.24 -0.24
#> [20,] -0.1866667 -0.28 -0.28 -0.3266667 -0.28 -0.3266667 -0.2333333 -0.28 0.72
#> [21,] -0.1600000 -0.24 -0.24 -0.2800000 -0.24 -0.2800000 -0.2000000 -0.24 -0.24
#> [22,] -0.1866667 -0.28 0.72 0.6733333 -0.28 -0.3266667 -0.2333333 -0.28 -0.28
#> [23,] 0.8400000 -0.24 -0.24 -0.2800000 -0.24 -0.2800000 -0.2000000 -0.24 -0.24
#> [24,] -0.1333333 0.80 -0.20 -0.2333333 -0.20 0.7666667 -0.1666667 -0.20 -0.20
#> [25,] 0.8666667 0.80 0.80 -0.2333333 -0.20 -0.2333333 -0.1666667 -0.20 -0.20
#> [,10] [,11] [,12] [,13] [,14] [,15] [,16] [,17] [,18] [,19]
#> [1,] -0.16 -0.16 -0.16 -0.16 -0.16 -0.1866667 -0.16 -0.16 -0.16 -0.16
#> [2,] -0.24 -0.24 -0.24 -0.24 -0.24 -0.2800000 -0.24 -0.24 -0.24 -0.24
#> [3,] -0.24 -0.24 -0.24 -0.24 -0.24 -0.2800000 -0.24 -0.24 -0.24 -0.24
#> [4,] -0.28 -0.28 -0.28 -0.28 -0.28 -0.3266667 -0.28 -0.28 -0.28 -0.28
#> [5,] -0.24 -0.24 -0.24 -0.24 -0.24 -0.2800000 -0.24 -0.24 -0.24 -0.24
#> [6,] -0.28 -0.28 -0.28 -0.28 -0.28 -0.3266667 -0.28 -0.28 -0.28 -0.28
#> [7,] 0.80 -0.20 -0.20 -0.20 -0.20 -0.2333333 -0.20 -0.20 -0.20 -0.20
#> [8,] 0.76 0.76 -0.24 -0.24 -0.24 -0.2800000 -0.24 -0.24 -0.24 -0.24
#> [9,] 0.76 0.76 0.76 -0.24 -0.24 -0.2800000 -0.24 -0.24 -0.24 -0.24
#> [10,] -0.24 0.76 0.76 0.76 -0.24 -0.2800000 -0.24 -0.24 -0.24 -0.24
#> [11,] 0.76 -0.24 0.76 0.76 0.76 -0.2800000 -0.24 -0.24 -0.24 -0.24
#> [12,] 0.76 0.76 -0.24 0.76 0.76 0.7200000 -0.24 -0.24 -0.24 -0.24
#> [13,] 0.76 0.76 0.76 -0.24 0.76 0.7200000 0.76 -0.24 -0.24 -0.24
#> [14,] -0.24 0.76 0.76 0.76 -0.24 0.7200000 0.76 0.76 -0.24 -0.24
#> [15,] -0.28 -0.28 0.72 0.72 0.72 -0.3266667 0.72 0.72 0.72 -0.28
#> [16,] -0.24 -0.24 -0.24 0.76 0.76 0.7200000 -0.24 0.76 0.76 0.76
#> [17,] -0.24 -0.24 -0.24 -0.24 0.76 0.7200000 0.76 -0.24 0.76 0.76
#> [18,] -0.24 -0.24 -0.24 -0.24 -0.24 0.7200000 0.76 0.76 -0.24 0.76
#> [19,] -0.24 -0.24 -0.24 -0.24 -0.24 -0.2800000 0.76 0.76 0.76 -0.24
#> [20,] -0.28 -0.28 -0.28 -0.28 -0.28 -0.3266667 -0.28 0.72 0.72 0.72
#> [21,] -0.24 -0.24 -0.24 -0.24 -0.24 0.7200000 -0.24 -0.24 0.76 0.76
#> [22,] -0.28 -0.28 -0.28 -0.28 -0.28 -0.3266667 -0.28 -0.28 -0.28 0.72
#> [23,] -0.24 -0.24 -0.24 -0.24 -0.24 -0.2800000 -0.24 -0.24 -0.24 -0.24
#> [24,] -0.20 -0.20 -0.20 -0.20 -0.20 -0.2333333 -0.20 -0.20 -0.20 -0.20
#> [25,] -0.20 -0.20 -0.20 -0.20 -0.20 -0.2333333 -0.20 -0.20 -0.20 -0.20
#> [,20] [,21] [,22] [,23] [,24] [,25]
#> [1,] -0.1866667 -0.16 -0.1866667 0.84 -0.1333333 0.8666667
#> [2,] -0.2800000 -0.24 -0.2800000 -0.24 0.8000000 0.8000000
#> [3,] -0.2800000 -0.24 0.7200000 -0.24 -0.2000000 0.8000000
#> [4,] -0.3266667 -0.28 0.6733333 -0.28 -0.2333333 -0.2333333
#> [5,] -0.2800000 -0.24 -0.2800000 -0.24 -0.2000000 -0.2000000
#> [6,] -0.3266667 -0.28 -0.3266667 -0.28 0.7666667 -0.2333333
#> [7,] -0.2333333 -0.20 -0.2333333 -0.20 -0.1666667 -0.1666667
#> [8,] -0.2800000 -0.24 -0.2800000 -0.24 -0.2000000 -0.2000000
#> [9,] 0.7200000 -0.24 -0.2800000 -0.24 -0.2000000 -0.2000000
#> [10,] -0.2800000 -0.24 -0.2800000 -0.24 -0.2000000 -0.2000000
#> [11,] -0.2800000 -0.24 -0.2800000 -0.24 -0.2000000 -0.2000000
#> [12,] -0.2800000 -0.24 -0.2800000 -0.24 -0.2000000 -0.2000000
#> [13,] -0.2800000 -0.24 -0.2800000 -0.24 -0.2000000 -0.2000000
#> [14,] -0.2800000 -0.24 -0.2800000 -0.24 -0.2000000 -0.2000000
#> [15,] -0.3266667 0.72 -0.3266667 -0.28 -0.2333333 -0.2333333
#> [16,] -0.2800000 -0.24 -0.2800000 -0.24 -0.2000000 -0.2000000
#> [17,] 0.7200000 -0.24 -0.2800000 -0.24 -0.2000000 -0.2000000
#> [18,] 0.7200000 0.76 -0.2800000 -0.24 -0.2000000 -0.2000000
#> [19,] 0.7200000 0.76 0.7200000 -0.24 -0.2000000 -0.2000000
#> [20,] -0.3266667 0.72 0.6733333 0.72 -0.2333333 -0.2333333
#> [21,] 0.7200000 -0.24 0.7200000 0.76 -0.2000000 -0.2000000
#> [22,] 0.6733333 0.72 -0.3266667 0.72 0.7666667 -0.2333333
#> [23,] 0.7200000 0.76 0.7200000 -0.24 0.8000000 0.8000000
#> [24,] -0.2333333 -0.20 0.7666667 0.80 -0.1666667 0.8333333
#> [25,] -0.2333333 -0.20 -0.2333333 0.80 0.8333333 -0.1666667
#> attr(,"representation")
#> [1] "modularity"
repr_graphon(g)
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0.33333333 0.4652778 0.33333333 0.46527778 0.26666667 0.3472222
#> [2,] 0.46527778 0.5000000 0.52777778 0.68750000 0.55000000 0.3125000
#> [3,] 0.33333333 0.5277778 0.33333333 0.59027778 0.57777778 0.6458333
#> [4,] 0.46527778 0.6875000 0.59027778 0.50000000 0.71250000 0.6250000
#> [5,] 0.26666667 0.5500000 0.57777778 0.71250000 0.80000000 0.7125000
#> [6,] 0.34722222 0.3125000 0.64583333 0.62500000 0.71250000 0.5000000
#> [7,] 0.11111111 0.3472222 0.27777778 0.52777778 0.52222222 0.6458333
#> [8,] 0.11111111 0.2986111 0.16666667 0.29166667 0.46666667 0.5277778
#> [9,] 0.00000000 0.1180556 0.11111111 0.23611111 0.21111111 0.4097222
#> [10,] 0.05555556 0.1180556 0.22222222 0.17361111 0.21111111 0.2916667
#> [11,] 0.00000000 0.0000000 0.05555556 0.11805556 0.11111111 0.2916667
#> [12,] 0.00000000 0.0000000 0.00000000 0.00000000 0.05555556 0.1736111
#> [13,] 0.00000000 0.0000000 0.00000000 0.00000000 0.00000000 0.1458333
#> [14,] 0.00000000 0.0000000 0.00000000 0.00000000 0.00000000 0.0000000
#> [15,] 0.05555556 0.0000000 0.00000000 0.00000000 0.00000000 0.0000000
#> [16,] 0.00000000 0.0000000 0.00000000 0.00000000 0.00000000 0.0000000
#> [17,] 0.00000000 0.0000000 0.00000000 0.00000000 0.00000000 0.0000000
#> [18,] 0.11805556 0.0000000 0.00000000 0.00000000 0.00000000 0.0000000
#> [19,] 0.11111111 0.0000000 0.00000000 0.00000000 0.00000000 0.0625000
#> [20,] 0.11111111 0.0625000 0.12698413 0.07142857 0.00000000 0.0625000
#> [21,] 0.11111111 0.1180556 0.11111111 0.05555556 0.00000000 0.1180556
#> [22,] 0.40972222 0.1875000 0.47222222 0.37500000 0.32500000 0.0625000
#> [23,] 0.38888889 0.2916667 0.27777778 0.29166667 0.11111111 0.1736111
#> [24,] 0.33333333 0.5833333 0.27777778 0.40972222 0.26666667 0.4652778
#> [25,] 0.52777778 0.5625000 0.59027778 0.43750000 0.22500000 0.2500000
#> [,7] [,8] [,9] [,10] [,11] [,12]
#> [1,] 0.11111111 0.11111111 0.00000000 0.05555556 0.00000000 0.00000000
#> [2,] 0.34722222 0.29861111 0.11805556 0.11805556 0.00000000 0.00000000
#> [3,] 0.27777778 0.16666667 0.11111111 0.22222222 0.05555556 0.00000000
#> [4,] 0.52777778 0.29166667 0.23611111 0.17361111 0.11805556 0.00000000
#> [5,] 0.52222222 0.46666667 0.21111111 0.21111111 0.11111111 0.05555556
#> [6,] 0.64583333 0.52777778 0.40972222 0.29166667 0.29166667 0.17361111
#> [7,] 0.22222222 0.38888889 0.27777778 0.44444444 0.22222222 0.22222222
#> [8,] 0.38888889 0.55555556 0.50000000 0.61111111 0.50000000 0.38888889
#> [9,] 0.27777778 0.50000000 0.44444444 0.61111111 0.55555556 0.50000000
#> [10,] 0.44444444 0.61111111 0.61111111 0.55555556 0.66666667 0.55555556
#> [11,] 0.22222222 0.50000000 0.55555556 0.66666667 0.66666667 0.61111111
#> [12,] 0.22222222 0.38888889 0.50000000 0.55555556 0.61111111 0.55555556
#> [13,] 0.05555556 0.33333333 0.38888889 0.55555556 0.61111111 0.61111111
#> [14,] 0.12698413 0.23809524 0.30952381 0.30952381 0.50793651 0.56349206
#> [15,] 0.00000000 0.16666667 0.27777778 0.27777778 0.33333333 0.50000000
#> [16,] 0.00000000 0.05555556 0.18253968 0.18253968 0.25396825 0.30952381
#> [17,] 0.00000000 0.00000000 0.11111111 0.16666667 0.27777778 0.27777778
#> [18,] 0.00000000 0.00000000 0.00000000 0.06250000 0.18055556 0.23611111
#> [19,] 0.00000000 0.00000000 0.05555556 0.00000000 0.11111111 0.22222222
#> [20,] 0.05555556 0.05555556 0.12698413 0.05555556 0.05555556 0.18253968
#> [21,] 0.00000000 0.00000000 0.05555556 0.00000000 0.00000000 0.00000000
#> [22,] 0.17361111 0.11805556 0.12500000 0.00000000 0.00000000 0.00000000
#> [23,] 0.11111111 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [24,] 0.16666667 0.11111111 0.00000000 0.11111111 0.00000000 0.00000000
#> [25,] 0.34722222 0.11805556 0.00000000 0.00000000 0.00000000 0.00000000
#> [,13] [,14] [,15] [,16] [,17] [,18] [,19]
#> [1,] 0.00000000 0.0000000 0.05555556 0.00000000 0.0000000 0.1180556 0.11111111
#> [2,] 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000 0.0000000 0.00000000
#> [3,] 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000 0.0000000 0.00000000
#> [4,] 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000 0.0000000 0.00000000
#> [5,] 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000 0.0000000 0.00000000
#> [6,] 0.14583333 0.0000000 0.00000000 0.00000000 0.0000000 0.0000000 0.06250000
#> [7,] 0.05555556 0.1269841 0.00000000 0.00000000 0.0000000 0.0000000 0.00000000
#> [8,] 0.33333333 0.2380952 0.16666667 0.05555556 0.0000000 0.0000000 0.00000000
#> [9,] 0.38888889 0.3095238 0.27777778 0.18253968 0.1111111 0.0000000 0.05555556
#> [10,] 0.55555556 0.3095238 0.27777778 0.18253968 0.1666667 0.0625000 0.00000000
#> [11,] 0.61111111 0.5079365 0.33333333 0.25396825 0.2777778 0.1805556 0.11111111
#> [12,] 0.61111111 0.5634921 0.50000000 0.30952381 0.2777778 0.2361111 0.22222222
#> [13,] 0.50000000 0.6904762 0.55555556 0.53571429 0.3055556 0.2083333 0.25000000
#> [14,] 0.69047619 0.5714286 0.63492063 0.57142857 0.5634921 0.3303571 0.30952381
#> [15,] 0.55555556 0.6349206 0.55555556 0.76190476 0.7222222 0.6527778 0.50000000
#> [16,] 0.53571429 0.5714286 0.76190476 0.57142857 0.6190476 0.5982143 0.56349206
#> [17,] 0.30555556 0.5634921 0.72222222 0.61904762 0.5555556 0.5277778 0.55555556
#> [18,] 0.20833333 0.3303571 0.65277778 0.59821429 0.5277778 0.5000000 0.58333333
#> [19,] 0.25000000 0.3095238 0.50000000 0.56349206 0.5555556 0.5833333 0.55555556
#> [20,] 0.30952381 0.2142857 0.38095238 0.42857143 0.5793651 0.6696429 0.63492063
#> [21,] 0.05555556 0.2539683 0.44444444 0.30952381 0.3888889 0.4652778 0.61111111
#> [22,] 0.00000000 0.0000000 0.23611111 0.13392857 0.2361111 0.3125000 0.47222222
#> [23,] 0.00000000 0.0000000 0.16666667 0.18253968 0.1666667 0.1736111 0.27777778
#> [24,] 0.00000000 0.0000000 0.05555556 0.00000000 0.0000000 0.1180556 0.11111111
#> [25,] 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000 0.0625000 0.11805556
#> [,20] [,21] [,22] [,23] [,24] [,25]
#> [1,] 0.11111111 0.11111111 0.4097222 0.3888889 0.33333333 0.5277778
#> [2,] 0.06250000 0.11805556 0.1875000 0.2916667 0.58333333 0.5625000
#> [3,] 0.12698413 0.11111111 0.4722222 0.2777778 0.27777778 0.5902778
#> [4,] 0.07142857 0.05555556 0.3750000 0.2916667 0.40972222 0.4375000
#> [5,] 0.00000000 0.00000000 0.3250000 0.1111111 0.26666667 0.2250000
#> [6,] 0.06250000 0.11805556 0.0625000 0.1736111 0.46527778 0.2500000
#> [7,] 0.05555556 0.00000000 0.1736111 0.1111111 0.16666667 0.3472222
#> [8,] 0.05555556 0.00000000 0.1180556 0.0000000 0.11111111 0.1180556
#> [9,] 0.12698413 0.05555556 0.1250000 0.0000000 0.00000000 0.0000000
#> [10,] 0.05555556 0.00000000 0.0000000 0.0000000 0.11111111 0.0000000
#> [11,] 0.05555556 0.00000000 0.0000000 0.0000000 0.00000000 0.0000000
#> [12,] 0.18253968 0.00000000 0.0000000 0.0000000 0.00000000 0.0000000
#> [13,] 0.30952381 0.05555556 0.0000000 0.0000000 0.00000000 0.0000000
#> [14,] 0.21428571 0.25396825 0.0000000 0.0000000 0.00000000 0.0000000
#> [15,] 0.38095238 0.44444444 0.2361111 0.1666667 0.05555556 0.0000000
#> [16,] 0.42857143 0.30952381 0.1339286 0.1825397 0.00000000 0.0000000
#> [17,] 0.57936508 0.38888889 0.2361111 0.1666667 0.00000000 0.0000000
#> [18,] 0.66964286 0.46527778 0.3125000 0.1736111 0.11805556 0.0625000
#> [19,] 0.63492063 0.61111111 0.4722222 0.2777778 0.11111111 0.1180556
#> [20,] 0.57142857 0.69047619 0.4642857 0.4920635 0.18253968 0.1250000
#> [21,] 0.69047619 0.55555556 0.5277778 0.4444444 0.16666667 0.2361111
#> [22,] 0.46428571 0.52777778 0.3750000 0.5277778 0.59027778 0.3125000
#> [23,] 0.49206349 0.44444444 0.5277778 0.4444444 0.44444444 0.4722222
#> [24,] 0.18253968 0.16666667 0.5902778 0.4444444 0.22222222 0.4722222
#> [25,] 0.12500000 0.23611111 0.3125000 0.4722222 0.47222222 0.5000000
#> attr(,"representation")
#> [1] "graphon"