sk's answer is technically correct. However, my experiences has been that one very rarely has a completely generic graph. Usually, there's additional information about how the graph is built that can remove the NP-completeness from a find_all_cycles() function.

A few items to look for could be:

• You don't have any edges that loopback to the same vertex.
• You can guarantee either an even or odd number of edges leading into or out of every vertex.
• You can break your graph up into sub-graphs where any cycles cannot contain vertices in more than one sub-graph.