#' k2 U k3 graphs
#' List all possible k2 U k3 graphs based on FIVE given nodes. k2 U k3 is the complement of k2,3
#' @param x The vector representing nodes
#' @return A matrix listing edges of k2 U k3 graphs
#' @examples
#' k2_k3(1:5)
k2_k3 = function(x){
if(length(x)!= 5){
stop('The number of nodes should be FIVE!')
}
x = sort(x)
pair3 = combn(x, 3)
k2_k3.mat = matrix(NA, ncol = 4)
for(i in 1:ncol(pair3)){
pair3.vec = sort(pair3[, i])
c3.mat = k3(pair3.vec)
rst = x[! x%in% pair3.vec]
k2_k3.temp = cbind(c3.mat, deToIn(rst[1], rst[2]))
k2_k3.mat = rbind(k2_k3.mat, k2_k3.temp)
}
return(k2_k3.mat[-1, ])
}
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