Power set of Graphs of size n

Source: R/powerset.R

Generates the set of all possible binary networks of size n.

powerset(n, directed = TRUE, force = FALSE, chunk_size = 2e+05)

Arguments

n

Integer. Number of edges.
directed

Logical scalar. Whether to generate the power set of directed or undirected graphs,
force

Logical scalar. When TRUE it generates the power set for n>5, otherwise it returns with error.
chunk_size

Number of matrices to process at a time. If n = 5, then stack memory on the computer may overflow if chunk_size is relatively large.

Examples

powerset(2)
#> [[1]]
#>      [,1] [,2]
#> [1,]    0    0
#> [2,]    1    0
#> 
#> [[2]]
#>      [,1] [,2]
#> [1,]    0    1
#> [2,]    1    0
#> 
#> [[3]]
#>      [,1] [,2]
#> [1,]    0    1
#> [2,]    0    0
#> 
#> [[4]]
#>      [,1] [,2]
#> [1,]    0    0
#> [2,]    0    0
#> 
powerset(4, directed = FALSE)
#> [[1]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    0    0
#> [2,]    1    0    0    0
#> [3,]    0    0    0    0
#> [4,]    0    0    0    0
#> 
#> [[2]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    1    0
#> [2,]    1    0    0    0
#> [3,]    1    0    0    0
#> [4,]    0    0    0    0
#> 
#> [[3]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    1    0
#> [2,]    0    0    0    0
#> [3,]    1    0    0    0
#> [4,]    0    0    0    0
#> 
#> [[4]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    0    1
#> [2,]    1    0    0    0
#> [3,]    0    0    0    0
#> [4,]    1    0    0    0
#> 
#> [[5]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    1    1
#> [2,]    1    0    0    0
#> [3,]    1    0    0    0
#> [4,]    1    0    0    0
#> 
#> [[6]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    1    1
#> [2,]    0    0    0    0
#> [3,]    1    0    0    0
#> [4,]    1    0    0    0
#> 
#> [[7]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    0    1
#> [2,]    0    0    0    0
#> [3,]    0    0    0    0
#> [4,]    1    0    0    0
#> 
#> [[8]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    0    0
#> [2,]    1    0    1    0
#> [3,]    0    1    0    0
#> [4,]    0    0    0    0
#> 
#> [[9]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    1    0
#> [2,]    1    0    1    0
#> [3,]    1    1    0    0
#> [4,]    0    0    0    0
#> 
#> [[10]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    1    0
#> [2,]    0    0    1    0
#> [3,]    1    1    0    0
#> [4,]    0    0    0    0
#> 
#> [[11]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    0    1
#> [2,]    1    0    1    0
#> [3,]    0    1    0    0
#> [4,]    1    0    0    0
#> 
#> [[12]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    1    1
#> [2,]    1    0    1    0
#> [3,]    1    1    0    0
#> [4,]    1    0    0    0
#> 
#> [[13]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    1    1
#> [2,]    0    0    1    0
#> [3,]    1    1    0    0
#> [4,]    1    0    0    0
#> 
#> [[14]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    0    1
#> [2,]    0    0    1    0
#> [3,]    0    1    0    0
#> [4,]    1    0    0    0
#> 
#> [[15]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    0    0
#> [2,]    0    0    1    0
#> [3,]    0    1    0    0
#> [4,]    0    0    0    0
#> 
#> [[16]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    0    0
#> [2,]    1    0    0    1
#> [3,]    0    0    0    0
#> [4,]    0    1    0    0
#> 
#> [[17]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    1    0
#> [2,]    1    0    0    1
#> [3,]    1    0    0    0
#> [4,]    0    1    0    0
#> 
#> [[18]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    1    0
#> [2,]    0    0    0    1
#> [3,]    1    0    0    0
#> [4,]    0    1    0    0
#> 
#> [[19]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    0    1
#> [2,]    1    0    0    1
#> [3,]    0    0    0    0
#> [4,]    1    1    0    0
#> 
#> [[20]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    1    1
#> [2,]    1    0    0    1
#> [3,]    1    0    0    0
#> [4,]    1    1    0    0
#> 
#> [[21]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    1    1
#> [2,]    0    0    0    1
#> [3,]    1    0    0    0
#> [4,]    1    1    0    0
#> 
#> [[22]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    0    1
#> [2,]    0    0    0    1
#> [3,]    0    0    0    0
#> [4,]    1    1    0    0
#> 
#> [[23]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    0    0
#> [2,]    1    0    1    1
#> [3,]    0    1    0    0
#> [4,]    0    1    0    0
#> 
#> [[24]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    1    0
#> [2,]    1    0    1    1
#> [3,]    1    1    0    0
#> [4,]    0    1    0    0
#> 
#> [[25]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    1    0
#> [2,]    0    0    1    1
#> [3,]    1    1    0    0
#> [4,]    0    1    0    0
#> 
#> [[26]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    0    1
#> [2,]    1    0    1    1
#> [3,]    0    1    0    0
#> [4,]    1    1    0    0
#> 
#> [[27]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    1    1
#> [2,]    1    0    1    1
#> [3,]    1    1    0    0
#> [4,]    1    1    0    0
#> 
#> [[28]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    1    1
#> [2,]    0    0    1    1
#> [3,]    1    1    0    0
#> [4,]    1    1    0    0
#> 
#> [[29]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    0    1
#> [2,]    0    0    1    1
#> [3,]    0    1    0    0
#> [4,]    1    1    0    0
#> 
#> [[30]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    0    0
#> [2,]    0    0    1    1
#> [3,]    0    1    0    0
#> [4,]    0    1    0    0
#> 
#> [[31]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    0    0
#> [2,]    0    0    0    1
#> [3,]    0    0    0    0
#> [4,]    0    1    0    0
#> 
#> [[32]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    0    0
#> [2,]    1    0    0    0
#> [3,]    0    0    0    1
#> [4,]    0    0    1    0
#> 
#> [[33]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    1    0
#> [2,]    1    0    0    0
#> [3,]    1    0    0    1
#> [4,]    0    0    1    0
#> 
#> [[34]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    1    0
#> [2,]    0    0    0    0
#> [3,]    1    0    0    1
#> [4,]    0    0    1    0
#> 
#> [[35]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    0    1
#> [2,]    1    0    0    0
#> [3,]    0    0    0    1
#> [4,]    1    0    1    0
#> 
#> [[36]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    1    1
#> [2,]    1    0    0    0
#> [3,]    1    0    0    1
#> [4,]    1    0    1    0
#> 
#> [[37]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    1    1
#> [2,]    0    0    0    0
#> [3,]    1    0    0    1
#> [4,]    1    0    1    0
#> 
#> [[38]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    0    1
#> [2,]    0    0    0    0
#> [3,]    0    0    0    1
#> [4,]    1    0    1    0
#> 
#> [[39]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    0    0
#> [2,]    1    0    1    0
#> [3,]    0    1    0    1
#> [4,]    0    0    1    0
#> 
#> [[40]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    1    0
#> [2,]    1    0    1    0
#> [3,]    1    1    0    1
#> [4,]    0    0    1    0
#> 
#> [[41]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    1    0
#> [2,]    0    0    1    0
#> [3,]    1    1    0    1
#> [4,]    0    0    1    0
#> 
#> [[42]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    0    1
#> [2,]    1    0    1    0
#> [3,]    0    1    0    1
#> [4,]    1    0    1    0
#> 
#> [[43]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    1    1
#> [2,]    1    0    1    0
#> [3,]    1    1    0    1
#> [4,]    1    0    1    0
#> 
#> [[44]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    1    1
#> [2,]    0    0    1    0
#> [3,]    1    1    0    1
#> [4,]    1    0    1    0
#> 
#> [[45]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    0    1
#> [2,]    0    0    1    0
#> [3,]    0    1    0    1
#> [4,]    1    0    1    0
#> 
#> [[46]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    0    0
#> [2,]    0    0    1    0
#> [3,]    0    1    0    1
#> [4,]    0    0    1    0
#> 
#> [[47]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    0    0
#> [2,]    1    0    0    1
#> [3,]    0    0    0    1
#> [4,]    0    1    1    0
#> 
#> [[48]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    1    0
#> [2,]    1    0    0    1
#> [3,]    1    0    0    1
#> [4,]    0    1    1    0
#> 
#> [[49]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    1    0
#> [2,]    0    0    0    1
#> [3,]    1    0    0    1
#> [4,]    0    1    1    0
#> 
#> [[50]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    0    1
#> [2,]    1    0    0    1
#> [3,]    0    0    0    1
#> [4,]    1    1    1    0
#> 
#> [[51]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    1    1
#> [2,]    1    0    0    1
#> [3,]    1    0    0    1
#> [4,]    1    1    1    0
#> 
#> [[52]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    1    1
#> [2,]    0    0    0    1
#> [3,]    1    0    0    1
#> [4,]    1    1    1    0
#> 
#> [[53]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    0    1
#> [2,]    0    0    0    1
#> [3,]    0    0    0    1
#> [4,]    1    1    1    0
#> 
#> [[54]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    0    0
#> [2,]    1    0    1    1
#> [3,]    0    1    0    1
#> [4,]    0    1    1    0
#> 
#> [[55]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    1    0
#> [2,]    1    0    1    1
#> [3,]    1    1    0    1
#> [4,]    0    1    1    0
#> 
#> [[56]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    1    0
#> [2,]    0    0    1    1
#> [3,]    1    1    0    1
#> [4,]    0    1    1    0
#> 
#> [[57]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    0    1
#> [2,]    1    0    1    1
#> [3,]    0    1    0    1
#> [4,]    1    1    1    0
#> 
#> [[58]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    1    1
#> [2,]    1    0    1    1
#> [3,]    1    1    0    1
#> [4,]    1    1    1    0
#> 
#> [[59]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    1    1
#> [2,]    0    0    1    1
#> [3,]    1    1    0    1
#> [4,]    1    1    1    0
#> 
#> [[60]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    0    1
#> [2,]    0    0    1    1
#> [3,]    0    1    0    1
#> [4,]    1    1    1    0
#> 
#> [[61]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    0    0
#> [2,]    0    0    1    1
#> [3,]    0    1    0    1
#> [4,]    0    1    1    0
#> 
#> [[62]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    0    0
#> [2,]    0    0    0    1
#> [3,]    0    0    0    1
#> [4,]    0    1    1    0
#> 
#> [[63]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    0    0
#> [2,]    0    0    0    0
#> [3,]    0    0    0    1
#> [4,]    0    0    1    0
#> 
#> [[64]]
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    0    0
#> [2,]    0    0    0    0
#> [3,]    0    0    0    0
#> [4,]    0    0    0    0
#>