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.
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 NPcomplete.
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