#' c6 graphs
#' List all possible R graphs based on given SIX nodes
#' @param x The vector representing nodes
#' @return A matrix listing edges of c6 graphs
#' @examples
#' c6(c(1:6))
c6 = function(x){
if(length(x)!=6){
stop("The number of nodes should be SIX!")
}
# start from the first node in the x
start_node = x[1]
# permulate, using p5 function
temp_p5 = p5(x[-1])
# find out the nodes, which start_node will connect to
# frequency of node in each column in temp_p5 is one, should be the nodes
temp_mtx = matrix(NA, ncol = 2)
for(n in 1: nrow(temp_p5)){
temp_tab = as.matrix(table(unlist(strsplit(temp_p5[n,], split = "-"))))
twonodes = as.numeric(rownames(temp_tab)[which(temp_tab[, 1] == 1)])
temp_mtx = rbind(temp_mtx, c(deToIn(1, twonodes[1]), deToIn(1, twonodes[2])))
}
temp_mtx = temp_mtx[-1, ]
return(cbind(temp_p5, temp_mtx))
}
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