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 1 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,] 1 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 1 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 1 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 0 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 1 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 0 0 0 0 0
#> [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,] 1 0 0 0 0 0 0 0 0 0 0 0 0
#> [24,] 1 1 0 0 0 0 0 0 0 0 0 0 0
#> [25,] 1 1 0 0 0 0 0 0 0 0 1 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 1 1
#> [2,] 0 0 0 0 0 0 0 0 0 0 1 1
#> [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 0 0 0
#> [11,] 0 0 0 1 0 0 0 0 0 0 0 1
#> [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 0 0 0 0 0 1 0 0
#> [16,] 1 1 0 1 1 1 0 0 0 0 0 0
#> [17,] 1 1 1 0 1 1 1 1 0 0 0 0
#> [18,] 0 0 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 0 1 1 0 0
#> [21,] 0 0 0 1 1 1 0 0 1 1 1 0
#> [22,] 0 0 0 0 0 1 1 1 0 1 1 1
#> [23,] 0 1 0 0 0 0 1 1 1 0 1 1
#> [24,] 0 0 0 0 0 0 0 1 1 1 0 1
#> [25,] 0 0 0 0 0 0 0 0 1 1 1 0
#> attr(,"representation")
#> [1] "adjacency"
repr_laplacian(g)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
#> [1,] 6 -1 -1 -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,] -1 -1 5 -1 -1 -1 0 0 0 0 0 0 0
#> [4,] -1 -1 -1 6 -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 6 -1 -1 -1 0 0 0 0
#> [7,] 0 0 0 -1 -1 -1 6 -1 -1 -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 -1 -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 7 -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 0 -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 -1 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 0 0 0 0 0
#> [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,] -1 0 0 0 0 0 0 0 0 0 0 0 0
#> [24,] -1 -1 0 0 0 0 0 0 0 0 0 0 0
#> [25,] -1 -1 0 0 0 0 0 0 0 0 -1 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 -1 -1
#> [2,] 0 0 0 0 0 0 0 0 0 0 -1 -1
#> [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 0 0 0
#> [11,] 0 0 0 -1 0 0 0 0 0 0 0 -1
#> [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,] 5 -1 -1 -1 0 0 0 0 0 0 0 0
#> [15,] -1 6 -1 -1 0 0 0 0 0 -1 0 0
#> [16,] -1 -1 6 -1 -1 -1 0 0 0 0 0 0
#> [17,] -1 -1 -1 8 -1 -1 -1 -1 0 0 0 0
#> [18,] 0 0 -1 -1 5 -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 5 0 -1 -1 0 0
#> [21,] 0 0 0 -1 -1 -1 0 6 -1 -1 -1 0
#> [22,] 0 0 0 0 0 -1 -1 -1 6 -1 -1 -1
#> [23,] 0 -1 0 0 0 0 -1 -1 -1 7 -1 -1
#> [24,] 0 0 0 0 0 0 0 -1 -1 -1 6 -1
#> [25,] 0 0 0 0 0 0 0 0 -1 -1 -1 6
#> attr(,"representation")
#> [1] "laplacian"
repr_modularity(g)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
#> [1,] -0.24 0.76 0.8000000 0.76 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24
#> [2,] 0.76 -0.24 0.8000000 0.76 0.76 -0.24 -0.24 -0.24 -0.24 -0.24
#> [3,] 0.80 0.80 -0.1666667 0.80 0.80 0.80 -0.20 -0.20 -0.20 -0.20
#> [4,] 0.76 0.76 0.8000000 -0.24 0.76 0.76 0.76 -0.24 -0.24 -0.24
#> [5,] -0.24 0.76 0.8000000 0.76 -0.24 0.76 0.76 0.76 -0.24 -0.24
#> [6,] -0.24 -0.24 0.8000000 0.76 0.76 -0.24 0.76 0.76 0.76 -0.24
#> [7,] -0.24 -0.24 -0.2000000 0.76 0.76 0.76 -0.24 0.76 0.76 0.76
#> [8,] -0.24 -0.24 -0.2000000 -0.24 0.76 0.76 0.76 -0.24 0.76 0.76
#> [9,] -0.24 -0.24 -0.2000000 -0.24 -0.24 0.76 0.76 0.76 -0.24 0.76
#> [10,] -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.24 0.76 0.76 0.76 -0.24
#> [11,] -0.28 -0.28 -0.2333333 -0.28 -0.28 -0.28 -0.28 0.72 0.72 0.72
#> [12,] -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.24 -0.24 -0.24 0.76 0.76
#> [13,] -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 0.76
#> [14,] -0.20 -0.20 -0.1666667 -0.20 -0.20 -0.20 -0.20 -0.20 -0.20 -0.20
#> [15,] -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24
#> [16,] -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24
#> [17,] -0.32 -0.32 -0.2666667 -0.32 -0.32 -0.32 -0.32 -0.32 -0.32 -0.32
#> [18,] -0.20 -0.20 -0.1666667 -0.20 -0.20 -0.20 -0.20 -0.20 -0.20 -0.20
#> [19,] -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24
#> [20,] -0.20 -0.20 -0.1666667 -0.20 -0.20 -0.20 -0.20 -0.20 -0.20 -0.20
#> [21,] -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24
#> [22,] -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24
#> [23,] 0.72 -0.28 -0.2333333 -0.28 -0.28 -0.28 -0.28 -0.28 -0.28 -0.28
#> [24,] 0.76 0.76 -0.2000000 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24
#> [25,] 0.76 0.76 -0.2000000 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24 -0.24
#> [,11] [,12] [,13] [,14] [,15] [,16] [,17] [,18] [,19]
#> [1,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24
#> [2,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24
#> [3,] -0.2333333 -0.20 -0.20 -0.1666667 -0.20 -0.20 -0.2666667 -0.1666667 -0.20
#> [4,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24
#> [5,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24
#> [6,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24
#> [7,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24
#> [8,] 0.7200000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24
#> [9,] 0.7200000 0.76 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24
#> [10,] 0.7200000 0.76 0.76 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24
#> [11,] -0.3266667 0.72 0.72 -0.2333333 -0.28 -0.28 0.6266667 -0.2333333 -0.28
#> [12,] 0.7200000 -0.24 0.76 0.8000000 0.76 -0.24 -0.3200000 -0.2000000 -0.24
#> [13,] 0.7200000 0.76 -0.24 0.8000000 0.76 0.76 -0.3200000 -0.2000000 -0.24
#> [14,] -0.2333333 0.80 0.80 -0.1666667 0.80 0.80 0.7333333 -0.1666667 -0.20
#> [15,] -0.2800000 0.76 0.76 0.8000000 -0.24 0.76 0.6800000 -0.2000000 -0.24
#> [16,] -0.2800000 -0.24 0.76 0.8000000 0.76 -0.24 0.6800000 0.8000000 0.76
#> [17,] 0.6266667 -0.32 -0.32 0.7333333 0.68 0.68 -0.4266667 0.7333333 0.68
#> [18,] -0.2333333 -0.20 -0.20 -0.1666667 -0.20 0.80 0.7333333 -0.1666667 0.80
#> [19,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 0.76 0.6800000 0.8000000 -0.24
#> [20,] -0.2333333 -0.20 -0.20 -0.1666667 -0.20 -0.20 0.7333333 0.8333333 0.80
#> [21,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 -0.24 0.6800000 0.8000000 0.76
#> [22,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 0.76
#> [23,] -0.3266667 -0.28 -0.28 -0.2333333 0.72 -0.28 -0.3733333 -0.2333333 -0.28
#> [24,] -0.2800000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24
#> [25,] 0.7200000 -0.24 -0.24 -0.2000000 -0.24 -0.24 -0.3200000 -0.2000000 -0.24
#> [,20] [,21] [,22] [,23] [,24] [,25]
#> [1,] -0.2000000 -0.24 -0.24 0.7200000 0.76 0.76
#> [2,] -0.2000000 -0.24 -0.24 -0.2800000 0.76 0.76
#> [3,] -0.1666667 -0.20 -0.20 -0.2333333 -0.20 -0.20
#> [4,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24
#> [5,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24
#> [6,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24
#> [7,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24
#> [8,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24
#> [9,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24
#> [10,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24
#> [11,] -0.2333333 -0.28 -0.28 -0.3266667 -0.28 0.72
#> [12,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24
#> [13,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24
#> [14,] -0.1666667 -0.20 -0.20 -0.2333333 -0.20 -0.20
#> [15,] -0.2000000 -0.24 -0.24 0.7200000 -0.24 -0.24
#> [16,] -0.2000000 -0.24 -0.24 -0.2800000 -0.24 -0.24
#> [17,] 0.7333333 0.68 -0.32 -0.3733333 -0.32 -0.32
#> [18,] 0.8333333 0.80 -0.20 -0.2333333 -0.20 -0.20
#> [19,] 0.8000000 0.76 0.76 -0.2800000 -0.24 -0.24
#> [20,] -0.1666667 -0.20 0.80 0.7666667 -0.20 -0.20
#> [21,] -0.2000000 -0.24 0.76 0.7200000 0.76 -0.24
#> [22,] 0.8000000 0.76 -0.24 0.7200000 0.76 0.76
#> [23,] 0.7666667 0.72 0.72 -0.3266667 0.72 0.72
#> [24,] -0.2000000 0.76 0.76 0.7200000 -0.24 0.76
#> [25,] -0.2000000 -0.24 0.76 0.7200000 0.76 -0.24
#> attr(,"representation")
#> [1] "modularity"
repr_graphon(g)
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0.55555556 0.63333333 0.57777778 0.52777778 0.36507937 0.30952381
#> [2,] 0.63333333 0.60000000 0.70000000 0.65000000 0.68571429 0.34285714
#> [3,] 0.57777778 0.70000000 0.60000000 0.73333333 0.68571429 0.68571429
#> [4,] 0.52777778 0.65000000 0.73333333 0.66666667 0.77380952 0.61904762
#> [5,] 0.36507937 0.68571429 0.68571429 0.77380952 0.57142857 0.71428571
#> [6,] 0.30952381 0.34285714 0.68571429 0.61904762 0.71428571 0.57142857
#> [7,] 0.25000000 0.36666667 0.36666667 0.66666667 0.61904762 0.77380952
#> [8,] 0.18253968 0.17142857 0.34285714 0.30952381 0.57142857 0.57142857
#> [9,] 0.11111111 0.21111111 0.26666667 0.33333333 0.36507937 0.56349206
#> [10,] 0.00000000 0.00000000 0.18333333 0.16666667 0.30952381 0.30952381
#> [11,] 0.05555556 0.00000000 0.00000000 0.15476190 0.14285714 0.28571429
#> [12,] 0.00000000 0.00000000 0.00000000 0.05555556 0.18253968 0.23809524
#> [13,] 0.00000000 0.00000000 0.00000000 0.00000000 0.05555556 0.18253968
#> [14,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [15,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [16,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [17,] 0.06250000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [18,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [19,] 0.11111111 0.05555556 0.00000000 0.00000000 0.00000000 0.00000000
#> [20,] 0.16666667 0.11111111 0.00000000 0.00000000 0.00000000 0.00000000
#> [21,] 0.22222222 0.11111111 0.00000000 0.00000000 0.00000000 0.00000000
#> [22,] 0.27777778 0.16666667 0.08333333 0.08333333 0.00000000 0.00000000
#> [23,] 0.55555556 0.26666667 0.08333333 0.08333333 0.15476190 0.00000000
#> [24,] 0.52222222 0.50000000 0.20000000 0.18333333 0.07142857 0.07142857
#> [25,] 0.50000000 0.47777778 0.26666667 0.25000000 0.23809524 0.18253968
#> [,7] [,8] [,9] [,10] [,11] [,12]
#> [1,] 0.25000000 0.18253968 0.1111111 0.00000000 0.05555556 0.00000000
#> [2,] 0.36666667 0.17142857 0.2111111 0.00000000 0.00000000 0.00000000
#> [3,] 0.36666667 0.34285714 0.2666667 0.18333333 0.00000000 0.00000000
#> [4,] 0.66666667 0.30952381 0.3333333 0.16666667 0.15476190 0.05555556
#> [5,] 0.61904762 0.57142857 0.3650794 0.30952381 0.14285714 0.18253968
#> [6,] 0.77380952 0.57142857 0.5634921 0.30952381 0.28571429 0.23809524
#> [7,] 0.66666667 0.69047619 0.5833333 0.58333333 0.30952381 0.25000000
#> [8,] 0.69047619 0.57142857 0.6349206 0.61904762 0.57142857 0.30952381
#> [9,] 0.58333333 0.63492063 0.5555556 0.69444444 0.56349206 0.38888889
#> [10,] 0.58333333 0.61904762 0.6944444 0.66666667 0.61904762 0.52777778
#> [11,] 0.30952381 0.57142857 0.5634921 0.61904762 0.42857143 0.63492063
#> [12,] 0.25000000 0.30952381 0.3888889 0.52777778 0.63492063 0.55555556
#> [13,] 0.16666667 0.25396825 0.2777778 0.47222222 0.69047619 0.55555556
#> [14,] 0.05555556 0.12698413 0.2222222 0.19444444 0.30952381 0.44444444
#> [15,] 0.00000000 0.07142857 0.1111111 0.20833333 0.26785714 0.59722222
#> [16,] 0.00000000 0.00000000 0.1111111 0.11111111 0.25396825 0.33333333
#> [17,] 0.00000000 0.00000000 0.0625000 0.20833333 0.40178571 0.22916667
#> [18,] 0.00000000 0.00000000 0.0000000 0.00000000 0.05555556 0.16666667
#> [19,] 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.16666667
#> [20,] 0.00000000 0.00000000 0.0000000 0.00000000 0.05555556 0.05555556
#> [21,] 0.00000000 0.00000000 0.0000000 0.00000000 0.05555556 0.05555556
#> [22,] 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.00000000
#> [23,] 0.00000000 0.00000000 0.0000000 0.00000000 0.15476190 0.05555556
#> [24,] 0.00000000 0.00000000 0.0000000 0.00000000 0.10000000 0.00000000
#> [25,] 0.05555556 0.00000000 0.0000000 0.08333333 0.12698413 0.00000000
#> [,13] [,14] [,15] [,16] [,17] [,18]
#> [1,] 0.00000000 0.00000000 0.00000000 0.00000000 0.0625000 0.00000000
#> [2,] 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000
#> [3,] 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000
#> [4,] 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000
#> [5,] 0.05555556 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000
#> [6,] 0.18253968 0.00000000 0.00000000 0.00000000 0.0000000 0.00000000
#> [7,] 0.16666667 0.05555556 0.00000000 0.00000000 0.0000000 0.00000000
#> [8,] 0.25396825 0.12698413 0.07142857 0.00000000 0.0000000 0.00000000
#> [9,] 0.27777778 0.22222222 0.11111111 0.11111111 0.0625000 0.00000000
#> [10,] 0.47222222 0.19444444 0.20833333 0.11111111 0.2083333 0.00000000
#> [11,] 0.69047619 0.30952381 0.26785714 0.25396825 0.4017857 0.05555556
#> [12,] 0.55555556 0.44444444 0.59722222 0.33333333 0.2291667 0.16666667
#> [13,] 0.55555556 0.55555556 0.65277778 0.44444444 0.2916667 0.27777778
#> [14,] 0.55555556 0.44444444 0.59722222 0.50000000 0.5833333 0.33333333
#> [15,] 0.65277778 0.59722222 0.75000000 0.59722222 0.6875000 0.29166667
#> [16,] 0.44444444 0.50000000 0.59722222 0.55555556 0.6388889 0.50000000
#> [17,] 0.29166667 0.58333333 0.68750000 0.63888889 0.3750000 0.57638889
#> [18,] 0.27777778 0.33333333 0.29166667 0.50000000 0.5763889 0.55555556
#> [19,] 0.27777778 0.27777778 0.23611111 0.44444444 0.6388889 0.55555556
#> [20,] 0.16666667 0.22222222 0.05555556 0.27777778 0.6458333 0.44444444
#> [21,] 0.16666667 0.22222222 0.05555556 0.27777778 0.6458333 0.44444444
#> [22,] 0.00000000 0.11111111 0.08333333 0.25000000 0.2916667 0.25000000
#> [23,] 0.05555556 0.11111111 0.20833333 0.25000000 0.1458333 0.30555556
#> [24,] 0.00000000 0.00000000 0.10000000 0.05555556 0.1250000 0.11111111
#> [25,] 0.00000000 0.00000000 0.00000000 0.00000000 0.2361111 0.16666667
#> [,19] [,20] [,21] [,22] [,23] [,24]
#> [1,] 0.11111111 0.16666667 0.22222222 0.27777778 0.55555556 0.52222222
#> [2,] 0.05555556 0.11111111 0.11111111 0.16666667 0.26666667 0.50000000
#> [3,] 0.00000000 0.00000000 0.00000000 0.08333333 0.08333333 0.20000000
#> [4,] 0.00000000 0.00000000 0.00000000 0.08333333 0.08333333 0.18333333
#> [5,] 0.00000000 0.00000000 0.00000000 0.00000000 0.15476190 0.07142857
#> [6,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.07142857
#> [7,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [8,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [9,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [10,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [11,] 0.00000000 0.05555556 0.05555556 0.00000000 0.15476190 0.10000000
#> [12,] 0.16666667 0.05555556 0.05555556 0.00000000 0.05555556 0.00000000
#> [13,] 0.27777778 0.16666667 0.16666667 0.00000000 0.05555556 0.00000000
#> [14,] 0.27777778 0.22222222 0.22222222 0.11111111 0.11111111 0.00000000
#> [15,] 0.23611111 0.05555556 0.05555556 0.08333333 0.20833333 0.10000000
#> [16,] 0.44444444 0.27777778 0.27777778 0.25000000 0.25000000 0.05555556
#> [17,] 0.63888889 0.64583333 0.64583333 0.29166667 0.14583333 0.12500000
#> [18,] 0.55555556 0.44444444 0.44444444 0.25000000 0.30555556 0.11111111
#> [19,] 0.55555556 0.44444444 0.50000000 0.47222222 0.36111111 0.21111111
#> [20,] 0.44444444 0.33333333 0.38888889 0.52777778 0.58333333 0.36666667
#> [21,] 0.50000000 0.38888889 0.44444444 0.61111111 0.66666667 0.46666667
#> [22,] 0.47222222 0.52777778 0.61111111 0.50000000 0.66666667 0.63333333
#> [23,] 0.36111111 0.58333333 0.66666667 0.66666667 0.50000000 0.73333333
#> [24,] 0.21111111 0.36666667 0.46666667 0.63333333 0.73333333 0.80000000
#> [25,] 0.27777778 0.16666667 0.22222222 0.55555556 0.66666667 0.67777778
#> [,25]
#> [1,] 0.50000000
#> [2,] 0.47777778
#> [3,] 0.26666667
#> [4,] 0.25000000
#> [5,] 0.23809524
#> [6,] 0.18253968
#> [7,] 0.05555556
#> [8,] 0.00000000
#> [9,] 0.00000000
#> [10,] 0.08333333
#> [11,] 0.12698413
#> [12,] 0.00000000
#> [13,] 0.00000000
#> [14,] 0.00000000
#> [15,] 0.00000000
#> [16,] 0.00000000
#> [17,] 0.23611111
#> [18,] 0.16666667
#> [19,] 0.27777778
#> [20,] 0.16666667
#> [21,] 0.22222222
#> [22,] 0.55555556
#> [23,] 0.66666667
#> [24,] 0.67777778
#> [25,] 0.44444444
#> attr(,"representation")
#> [1] "graphon"