Understanding The Mapping Of Edges to Nodes In A Graph Theory Problem
$a[0] = 1, a[1] = 2, a[2] = 3$. 

"The arrow from place $i$ points to place $a[i−1]$"

So yes, all $3$ places in this sample point to themselves. It actually says in the explanation that "in each round each token will stay in the same place". 

In the second sample, all three places point towards the first one.

In the third sample, you have a $2$-cycle: $1$ points to $2$ and vice-versa. 

Is everything clear now?