This does not look as a cycle or a circle to me.

Why not?

1 2
  2 3
1   3

DO YOU SEE IT NOW?
 [1,--2]
  |   |
  |  [2,3]
  |     |
 [1,----3]
[download]

To elaborate further ... One might dispute (or rather get confused) if the graph is directed or not¹, but in either case it's certainly not a tree.

            1
           /|
          2 |
           \| 
            3
[download]

edit

Furthermore asking for the "shortest" path in a tree doesn't make much sense, there is by definition exactly one between any two nodes.

Cheers Rolf

_{(addicted to the Perl Programming Language and ☆☆☆☆ :)}

¹) the definition above circumvents the problem by postulating an undirected graph.