Permutation cycles

A permutation is a sequence of integers from 1 to n of length n containing each number exactly once. For example, $[1]$, $[4, 3, 5, 1, 2]$ , $[3, 2, 1]$ are permutations, and $[1, 1]$, $[4, 3, 1]$, $[2, 3, 4]$ are not. For every permutation, we can make a directed graph by adding an edge from the node $i $ to $P_i$. Such a graph would be a set of disjoint cycles. For example, the graph for the pe