How about Graph?

Relevant parts from the document -

has_a_cycle

   $g->has_a_cycle

    Returns true if the graph has a cycle, false if not.
find_a_cycle

   $g->find_a_cycle

    Returns a cycle if the graph has one (as a list of vertices), an e
+mpty list if no cycle can be found.

    Note that this just returns the vertices of a cycle: not any parti
+cular cycle, just the first one it finds. A repeated call might find 
+the same cycle, or it might find a different one, and you cannot call
+ this repeatedly to find all the cycles.
[download]

Update: I am looking for cycles in this graph

I hope you are not trying to find out "all" cycles in the graph which is NP-complete.