The longest cycle problem includes the special case of finding a
Hamiltonian cycle (a cycle that visits every node exactly once), and is therefore NP-complete. This means you will not find an efficient solution, only something along the lines of a brute-forcing. I couldn't find much info on the longest-cycle problem, but you can reduce the longest-path problem to the Hamiltonian cycle problem as follows:
If you have a graph with V vertices, take all size-V subsets of vertices, then all size-(V-1) subsets, etc.. For each of these subsets of vertices, determine if there's a Hamiltonian cycle. The first subset of nodes you encounter that contains a Hamiltonian cycle is the longest cycle in your original graph.
The Hamiltonian cycle problem is very common, and you should be able to find a lot of literature on the subject. However, any code is going to be exponential (with the possible exception of some special class of graphs perhaps).
It may be time to rethink a way through this problem. Is there is a way to do it without needing the longest cycle? This page has some good suggestions for rethinking problems involving Hamiltonian cycles. For instance, perhaps you can solve the same problem only by needing an Eulerian cycle, which is much easier to compute.
blokhead
