FindCycle

FindCycle[g] finds a cycle in graph g. FindCycle[g, k, n] finds up to n cycles of length at most k.

Examples

Find a cycle:

g = Graph[{1 -> 2, 2 -> 3, 3 -> 1}]
FindCycle[g]
(* {{1 -> 2, 2 -> 3, 3 -> 1}} *)

Find triangles:

FindCycle[CompleteGraph[5], {3}, All]
(* All 3-cycles in K5 *)

No cycles in a tree:

FindCycle[TreeGraph[{1 -> 2, 1 -> 3}]]
(* {} *)

Please visit the official Wolfram Language Reference for more details.