Simulate a bipartite interaction network using block model
simulate_lbm(con, pi, rho, nr, nc, method = "gnp")A matrix, the connectivity between blocks. If
method = "gnp" then each entry is the probability of interactions
given 2 blocks. If method = "gnm" then each entry is the number of
interactions between 2 blocks.
A vector of the same length as nrow(con),
the block mixture for the row species. If method = "gnp", then
pi is a probability vector, if method = "gnm", then
pi is the number of species per block, must sum to nr.
A vector of the same length as ncol(con),
the block mixture for the column species. If method = "gnm", then
rho is a probability vector, if method = "gnm", then
rho is the number of species per block, must sum to nc.
The number of row Species
The number of column Species
One of "gnp" (the default) where the blocks size and
number of interactions is random and "gnm" where the blocks size and
number of interactions are fixed.
A list of 3 elements:
A The incident matrix of size nrxnc
Z A vector of length nr, the block assignment of the row
species
W A vector of length nc, the block assignment of the column
species
# For a random number of interactions and blocks sizes
con <- matrix(c(.5,.3,.3,.1), 2, 2)
pi <- c(.25,.75)
rho <- c(1/3, 2/3)
nr <- 50
nc <- 30
simulate_lbm(con, pi, rho, nr, nc, method = "gnp")
#> $A
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
#> [1,] 0 0 0 0 0 0 0 1 1 0 0 0 1
#> [2,] 1 0 0 0 0 0 1 0 1 0 0 0 0
#> [3,] 0 0 1 0 0 0 0 0 0 0 0 0 0
#> [4,] 1 0 0 0 0 0 1 0 0 0 0 1 0
#> [5,] 0 0 0 0 0 0 0 0 0 0 0 1 0
#> [6,] 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [7,] 1 1 1 0 0 0 1 0 1 0 1 1 0
#> [8,] 0 0 0 0 0 0 1 0 1 0 0 0 0
#> [9,] 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [10,] 0 0 0 0 0 1 1 0 1 0 0 0 1
#> [11,] 0 0 0 0 0 0 0 0 0 0 0 1 0
#> [12,] 1 0 0 0 0 0 0 0 0 0 0 0 0
#> [13,] 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [14,] 1 0 0 0 1 0 1 0 1 1 0 0 0
#> [15,] 1 0 0 1 0 0 0 0 1 0 0 0 0
#> [16,] 0 1 0 0 0 0 0 0 1 0 0 1 0
#> [17,] 0 0 0 0 0 0 1 0 1 0 1 0 0
#> [18,] 0 0 1 0 0 0 0 0 0 1 0 1 0
#> [19,] 1 1 1 0 0 0 0 0 0 0 0 1 0
#> [20,] 1 0 0 0 0 0 0 0 0 0 0 0 0
#> [21,] 1 0 0 0 0 0 1 0 0 0 0 0 0
#> [22,] 0 0 0 0 0 0 0 0 1 0 0 0 0
#> [23,] 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [24,] 1 1 0 0 1 0 1 0 1 0 0 0 0
#> [25,] 1 0 0 0 0 0 0 1 0 0 1 0 1
#> [26,] 1 0 0 0 0 0 0 0 0 0 0 0 1
#> [27,] 1 1 0 0 1 0 1 0 0 1 0 0 0
#> [28,] 0 0 1 0 0 0 0 0 0 0 0 1 0
#> [29,] 1 1 1 0 0 0 1 0 0 0 1 0 0
#> [30,] 0 0 0 0 0 0 0 0 0 0 1 0 0
#> [31,] 1 0 0 0 0 0 0 1 0 0 0 1 0
#> [32,] 0 0 0 1 0 0 1 0 0 0 0 0 0
#> [33,] 0 0 0 0 0 0 0 0 1 0 0 0 0
#> [34,] 1 1 0 0 1 0 0 0 0 0 0 0 0
#> [35,] 1 1 0 0 1 0 0 0 0 0 1 0 0
#> [36,] 0 0 0 0 0 0 1 0 1 1 0 0 0
#> [37,] 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [38,] 1 0 1 0 0 0 0 0 0 0 0 0 0
#> [39,] 0 1 0 0 1 0 0 0 0 1 1 0 0
#> [40,] 1 0 0 0 0 0 1 0 1 0 0 0 0
#> [41,] 1 0 0 0 0 0 1 0 0 0 0 0 0
#> [42,] 0 0 0 0 0 0 0 0 0 0 1 1 0
#> [43,] 0 1 0 0 0 0 1 0 0 0 0 0 0
#> [44,] 1 0 0 0 0 0 0 0 0 0 0 1 0
#> [45,] 0 0 0 0 0 0 1 0 1 0 0 1 0
#> [46,] 1 0 0 0 0 0 1 0 0 0 0 0 0
#> [47,] 0 1 1 1 0 0 1 0 0 0 1 1 0
#> [48,] 1 0 0 0 0 0 0 0 0 0 0 0 0
#> [49,] 0 0 1 1 0 0 0 0 1 0 0 1 1
#> [50,] 0 0 0 0 0 1 0 0 0 0 0 0 0
#> [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25]
#> [1,] 0 0 1 0 0 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 1 0 0 0 0 1
#> [3,] 0 0 1 0 0 0 0 1 0 0 0 1
#> [4,] 0 1 1 0 0 0 0 0 0 0 0 1
#> [5,] 0 0 1 0 0 1 0 0 0 1 0 0
#> [6,] 0 1 0 0 0 0 1 0 0 0 0 0
#> [7,] 0 0 0 0 0 0 1 0 1 0 0 1
#> [8,] 0 0 1 0 0 1 1 0 0 0 0 0
#> [9,] 0 1 1 0 0 0 0 0 0 0 0 0
#> [10,] 0 1 0 0 0 0 0 0 0 0 0 0
#> [11,] 0 1 0 0 0 0 1 0 0 0 0 0
#> [12,] 0 0 0 0 0 0 0 0 0 0 1 0
#> [13,] 0 0 1 0 0 0 1 0 0 0 0 0
#> [14,] 0 0 0 0 0 0 0 0 0 0 0 1
#> [15,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [16,] 0 1 1 0 0 0 0 0 0 0 1 0
#> [17,] 0 0 0 0 1 0 0 0 0 0 0 0
#> [18,] 0 1 1 0 0 0 1 0 0 0 1 1
#> [19,] 0 0 0 0 0 0 0 0 1 0 0 1
#> [20,] 0 1 1 0 0 0 0 0 0 0 0 0
#> [21,] 0 1 1 0 0 0 0 0 0 0 0 1
#> [22,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [23,] 0 0 0 0 0 0 0 1 0 0 0 1
#> [24,] 0 0 1 0 0 1 0 0 0 0 1 0
#> [25,] 1 1 1 1 0 0 0 1 1 0 0 1
#> [26,] 0 0 0 0 0 0 0 0 0 1 0 0
#> [27,] 0 0 0 0 0 1 0 1 0 0 0 1
#> [28,] 0 1 1 0 0 0 0 0 0 0 0 0
#> [29,] 1 1 1 1 0 0 0 1 0 0 1 0
#> [30,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [31,] 0 0 1 0 0 0 1 0 1 0 0 1
#> [32,] 0 0 0 1 0 0 1 0 1 0 1 0
#> [33,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [34,] 1 0 0 0 1 0 0 0 0 0 0 1
#> [35,] 0 0 0 0 0 0 1 0 0 0 0 1
#> [36,] 0 1 1 0 0 0 1 0 0 0 1 1
#> [37,] 0 0 0 0 0 0 0 0 0 0 0 1
#> [38,] 0 1 0 0 0 0 0 0 1 0 0 0
#> [39,] 0 0 0 0 0 0 1 0 0 0 0 0
#> [40,] 0 0 0 0 0 0 0 0 0 0 0 1
#> [41,] 0 0 0 0 1 0 0 0 1 0 0 0
#> [42,] 1 0 0 0 0 0 0 0 0 0 0 0
#> [43,] 1 1 0 0 0 0 0 0 1 0 0 0
#> [44,] 0 0 0 0 0 0 0 0 0 1 0 0
#> [45,] 0 0 0 0 0 0 1 1 0 1 0 1
#> [46,] 0 0 0 0 0 1 0 0 0 0 0 1
#> [47,] 1 1 1 0 1 0 0 0 1 0 1 1
#> [48,] 1 1 0 0 1 0 0 0 0 0 0 0
#> [49,] 0 0 0 0 0 0 0 1 1 1 1 1
#> [50,] 0 0 0 1 0 1 1 0 0 0 0 0
#> [,26] [,27] [,28] [,29] [,30]
#> [1,] 0 0 0 0 0
#> [2,] 0 0 1 0 0
#> [3,] 1 0 0 0 0
#> [4,] 0 0 0 0 0
#> [5,] 0 0 0 0 0
#> [6,] 0 0 1 0 1
#> [7,] 0 0 0 0 0
#> [8,] 0 0 0 0 1
#> [9,] 0 0 0 0 0
#> [10,] 1 0 0 0 0
#> [11,] 1 0 0 0 0
#> [12,] 0 0 0 0 1
#> [13,] 0 0 1 0 0
#> [14,] 0 0 0 0 1
#> [15,] 0 0 1 0 1
#> [16,] 1 0 1 0 0
#> [17,] 1 0 1 0 1
#> [18,] 0 0 1 0 0
#> [19,] 0 0 0 0 1
#> [20,] 0 0 1 0 0
#> [21,] 0 0 0 0 1
#> [22,] 0 0 0 0 0
#> [23,] 0 0 0 0 1
#> [24,] 0 0 0 0 0
#> [25,] 0 0 1 1 1
#> [26,] 1 0 1 1 1
#> [27,] 1 0 1 0 0
#> [28,] 0 0 0 0 0
#> [29,] 0 0 0 1 0
#> [30,] 1 0 1 0 0
#> [31,] 0 0 1 0 0
#> [32,] 0 0 1 1 0
#> [33,] 0 0 0 0 0
#> [34,] 1 1 1 1 1
#> [35,] 1 0 1 0 0
#> [36,] 1 1 1 0 0
#> [37,] 1 0 0 0 1
#> [38,] 0 0 0 1 0
#> [39,] 0 1 0 0 0
#> [40,] 1 0 0 0 0
#> [41,] 0 0 1 0 0
#> [42,] 0 0 0 1 0
#> [43,] 0 0 0 0 1
#> [44,] 0 0 0 0 0
#> [45,] 0 0 0 0 1
#> [46,] 0 0 1 0 0
#> [47,] 1 0 1 0 1
#> [48,] 0 0 0 1 0
#> [49,] 0 0 1 1 0
#> [50,] 1 0 1 0 1
#>
#> $W
#> [1] 1 2 2 2 2 2 1 2 1 2 2 1 2 2 1 1 2 2 2 1 2 2 2 2 1 1 2 1 2 1
#>
#> $Z
#> [1] 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 1 2 2 1 2 1 2 1 2 2
#> [39] 2 2 2 2 2 2 2 2 1 2 1 2
#>
# For a fixed number of ineractions and blocks sizes
con <- matrix(c(50, 120, 60, 80), 2, 2)
pi <- c(10, 40)
rho <- c(10, 20)
nr <- 50
nc <- 30
simulate_lbm(con, pi, rho, nr, nc, method = "gnm")
#> $A
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
#> [1,] 0 1 1 0 1 1 0 0 0 0 1 0 1
#> [2,] 1 0 0 0 1 1 1 0 1 1 0 0 0
#> [3,] 1 0 1 1 0 1 1 1 1 0 0 0 0
#> [4,] 0 1 0 1 0 0 0 0 0 1 0 0 0
#> [5,] 1 0 1 1 1 0 1 0 0 1 0 0 0
#> [6,] 0 0 0 0 1 0 0 0 0 0 0 1 0
#> [7,] 0 0 1 1 0 1 1 1 1 1 1 0 0
#> [8,] 0 1 0 0 1 1 0 0 1 1 1 0 0
#> [9,] 1 1 0 1 1 1 1 1 0 0 0 1 0
#> [10,] 0 0 1 1 0 1 0 0 1 0 0 0 1
#> [11,] 1 0 1 0 1 1 0 0 0 0 0 0 1
#> [12,] 0 0 0 0 0 1 0 1 1 0 0 0 0
#> [13,] 0 0 1 0 1 1 0 0 1 0 0 1 0
#> [14,] 0 1 1 0 0 0 0 1 0 1 0 1 0
#> [15,] 0 0 1 0 1 0 0 0 1 1 0 0 0
#> [16,] 0 0 0 0 1 0 0 1 0 0 0 0 0
#> [17,] 1 0 0 0 0 0 1 0 1 0 1 0 0
#> [18,] 0 0 0 0 0 0 0 0 0 0 0 1 0
#> [19,] 0 1 0 0 0 1 1 0 0 1 0 0 0
#> [20,] 0 0 0 0 0 0 0 0 0 1 1 0 0
#> [21,] 0 1 1 0 0 0 0 0 0 0 0 0 0
#> [22,] 0 0 0 0 0 0 1 0 1 1 1 0 0
#> [23,] 0 0 0 1 0 0 1 0 0 0 0 0 0
#> [24,] 0 1 0 0 0 0 0 1 0 0 0 0 0
#> [25,] 1 0 0 1 0 0 0 0 0 1 0 0 0
#> [26,] 0 0 0 0 0 0 0 0 0 1 0 0 0
#> [27,] 1 0 1 1 1 1 0 1 0 0 0 0 0
#> [28,] 1 0 0 0 1 0 0 0 1 0 0 0 0
#> [29,] 0 0 1 1 0 0 1 0 1 1 0 0 0
#> [30,] 0 1 1 0 0 0 0 0 0 0 0 0 0
#> [31,] 1 0 0 0 0 0 0 0 0 0 0 0 1
#> [32,] 0 0 0 0 1 0 0 0 0 0 0 0 0
#> [33,] 1 1 1 1 0 1 1 0 0 1 0 0 0
#> [34,] 1 1 1 0 0 0 0 1 1 1 0 0 0
#> [35,] 0 1 1 0 0 1 0 1 1 1 0 0 0
#> [36,] 0 0 0 0 0 1 0 0 0 1 0 0 1
#> [37,] 1 0 0 0 0 0 1 1 1 0 0 0 1
#> [38,] 0 1 0 0 1 0 0 0 0 1 0 0 0
#> [39,] 0 0 0 0 0 0 0 1 0 1 0 0 0
#> [40,] 1 0 0 1 0 1 0 0 0 0 0 0 0
#> [41,] 0 0 1 0 0 0 0 0 0 0 0 0 0
#> [42,] 0 0 0 0 0 0 0 0 1 0 0 0 0
#> [43,] 0 1 0 1 1 1 0 1 0 0 0 0 1
#> [44,] 0 0 0 0 1 0 0 1 0 1 0 0 0
#> [45,] 0 0 1 0 0 0 0 1 0 0 0 0 0
#> [46,] 1 0 1 0 0 0 0 0 0 0 0 0 1
#> [47,] 0 1 0 0 0 1 1 1 0 0 0 0 0
#> [48,] 0 0 0 1 0 0 0 1 0 1 1 0 0
#> [49,] 0 0 0 1 0 0 0 1 1 1 0 0 0
#> [50,] 1 0 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 1 0 0 0 1 0 1 0 1 1
#> [2,] 0 0 0 1 1 0 0 1 0 0 0 0
#> [3,] 0 0 0 0 0 1 0 0 0 0 0 0
#> [4,] 1 1 0 0 0 0 1 1 1 0 0 0
#> [5,] 0 0 0 0 0 0 0 0 1 0 0 0
#> [6,] 1 0 1 1 1 0 0 0 1 0 0 1
#> [7,] 1 0 0 1 0 0 0 1 0 0 1 0
#> [8,] 1 0 1 0 0 0 0 1 0 0 0 0
#> [9,] 0 0 0 1 0 0 1 1 0 0 0 0
#> [10,] 0 1 0 1 1 0 1 0 0 0 0 0
#> [11,] 1 0 0 0 0 0 0 0 0 1 0 0
#> [12,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [13,] 0 1 0 0 0 0 0 0 0 0 0 0
#> [14,] 1 0 0 0 0 0 0 0 0 0 0 0
#> [15,] 0 0 0 0 1 0 0 0 0 1 0 0
#> [16,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [17,] 0 0 0 0 0 1 0 0 0 0 0 0
#> [18,] 0 0 0 0 1 1 1 0 0 0 0 0
#> [19,] 0 0 1 0 0 0 1 1 0 0 0 0
#> [20,] 0 0 1 0 0 0 0 0 0 0 0 0
#> [21,] 0 0 1 0 0 0 0 1 0 0 0 0
#> [22,] 0 0 0 0 0 1 0 0 0 0 0 0
#> [23,] 0 0 1 1 1 0 0 0 0 0 0 0
#> [24,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [25,] 1 0 0 0 0 0 0 0 0 1 0 0
#> [26,] 0 0 0 1 0 0 0 0 0 0 0 0
#> [27,] 0 0 0 1 0 1 0 0 0 0 0 0
#> [28,] 0 0 0 0 0 0 1 0 0 0 0 0
#> [29,] 0 0 1 0 0 0 0 0 0 0 0 0
#> [30,] 0 0 0 0 0 1 0 0 0 0 0 0
#> [31,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [32,] 0 1 0 0 1 0 1 0 1 0 0 0
#> [33,] 0 1 0 0 0 0 0 0 0 0 0 0
#> [34,] 1 0 0 0 0 0 0 0 0 0 0 0
#> [35,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [36,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [37,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [38,] 1 0 0 0 0 1 1 1 0 0 0 0
#> [39,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [40,] 0 1 0 0 0 0 0 0 0 0 0 0
#> [41,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [42,] 0 0 0 0 1 0 0 0 0 0 0 0
#> [43,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [44,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [45,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [46,] 0 0 0 0 1 0 0 0 1 0 0 0
#> [47,] 0 0 0 1 0 1 0 0 0 0 0 0
#> [48,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [49,] 1 0 0 1 1 0 1 0 0 0 0 0
#> [50,] 1 0 0 0 0 0 0 0 0 0 0 0
#> [,26] [,27] [,28] [,29] [,30]
#> [1,] 0 0 0 1 0
#> [2,] 1 1 0 1 0
#> [3,] 0 1 1 0 1
#> [4,] 0 1 0 0 0
#> [5,] 1 0 0 1 0
#> [6,] 0 0 0 1 1
#> [7,] 0 0 1 0 1
#> [8,] 1 1 0 0 0
#> [9,] 0 0 0 0 0
#> [10,] 0 0 0 1 1
#> [11,] 0 0 0 0 0
#> [12,] 0 1 0 0 0
#> [13,] 0 0 0 0 0
#> [14,] 0 0 0 1 0
#> [15,] 0 0 0 0 1
#> [16,] 0 0 0 0 0
#> [17,] 0 0 0 0 0
#> [18,] 1 1 0 0 0
#> [19,] 0 0 0 0 0
#> [20,] 0 0 0 0 0
#> [21,] 0 0 0 0 0
#> [22,] 0 0 0 0 0
#> [23,] 0 0 0 0 0
#> [24,] 0 0 0 0 1
#> [25,] 0 0 0 0 0
#> [26,] 0 0 1 0 0
#> [27,] 0 0 0 0 0
#> [28,] 0 0 1 0 0
#> [29,] 1 0 0 0 1
#> [30,] 0 0 1 0 0
#> [31,] 0 0 0 0 0
#> [32,] 0 0 0 0 0
#> [33,] 0 0 0 0 0
#> [34,] 0 0 1 0 0
#> [35,] 0 0 0 0 1
#> [36,] 0 0 0 0 0
#> [37,] 0 1 0 0 0
#> [38,] 0 0 0 0 0
#> [39,] 0 0 0 0 0
#> [40,] 0 0 0 0 0
#> [41,] 0 0 0 0 0
#> [42,] 0 0 0 0 0
#> [43,] 0 1 0 0 0
#> [44,] 0 0 0 0 0
#> [45,] 0 1 0 0 0
#> [46,] 0 0 0 0 0
#> [47,] 0 0 0 0 0
#> [48,] 0 0 1 0 0
#> [49,] 0 0 1 0 0
#> [50,] 0 0 0 0 0
#>
#> $W
#> [1] 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
#>
#> $Z
#> [1] 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
#> [39] 2 2 2 2 2 2 2 2 2 2 2 2
#>