Finding all cycles in an undirected graph

Question

If I have an undirected graph, how can I get a list of all cycles?

For example, from the following graph, I would want the cycles:

(a,b,d,e,c)
(a,b,c         


        

Answer 1

You presumably want only simple cycles (those that don't repeat a vertex), or there's an infinite number of them. Even then, there can be an exponential number of cycles. Perhaps this isn't the problem you really want to solve?

Answer 2

this is not possible in polynomial time as if possible then we could use this to find all cycles and hence cycle of largest length which implies we can solve hamiltonian cycle problem completely in polynomial time.