Finding all cycles in a directed graph

Question

How can I find (iterate over) ALL the cycles in a directed graph from/to a given node?

For example, I want something like this:

A->B->A
A->B         


        

Answer 1

Start at node X and check for all child nodes (parent and child nodes are equivalent if undirected). Mark those child nodes as being children of X. From any such child node A, mark it's children of being children of A, X', where X' is marked as being 2 steps away.). If you later hit X and mark it as being a child of X'', that means X is in a 3 node cycle. Backtracking to it's parent is easy (as-is, the algorithm has no support for this so you'd find whichever parent has X').

Note: If graph is undirected or has any bidirectional edges, this algorithm gets more complicated, assuming you don't want to traverse the same edge twice for a cycle.