#' x163 graphs
#' List all possible x163 graphs based on given SIX nodes
#' @param x The vector representing nodes
#' @return A matrix listing edges of x163 graphs
#' @examples
#' x163(c(1:6))
x163 = function(x){
if(length(x) != 6){
stop("The number of nodes should be SIX!")
}
pair5 = combn(x, 5)
x163.mat = matrix(NA, ncol = 7)
for(i in 1:ncol(pair5)){
pair5.vec = sort(pair5[, i])
rst = x[! x %in% pair5.vec]
butterfly.mat = butterfly(pair5.vec)
# find the the hub
hub = findNode(2, butterfly.mat)
cnct.mat = paste(rst, '-', hub, sep = '')
butterfly.mat2 = do.call(rbind, replicate(ncol(hub), butterfly.mat, simplify = F))
x163.temp = cbind(butterfly.mat2, cnct.mat)
x163.mat = rbind(x163.mat, x163.temp)
}
return(x163.mat[-1, ])
}
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