#' co-butterfly graphs
#' List all possible co-butterfly subgraphs based on given FIVE nodes. Note that co-butterfly is the complement graph of butterfly based on give five nodes.
#' @param x The vector representing nodes
#' @return A matrix listing edges of co-butterfly graphs
#' @examples
#' co_butterfly(c(1:5))
co.butterfly = function(x){
if(length(x) != 5){
stop('The number of nodes should be FIVE!')
}
x = sort(x)
mtx = matrix(NA, ncol = 4)
for(i in 1: length(x)){
temp_rest = x[-i]
temp_c4 = c4(temp_rest)
mtx = rbind(mtx, temp_c4)
}
return(mtx[-1, ])
}
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