How can I find all available path for each Vertices which won’t cause a cycle? What algorithm to use? Please be brief and provide links if possible, and ask questions if something is not clear from the wonderful diagram below 🙂

I am not looking for a shortest path or anything like that. Instead I just want to know which paths I can still draw on my graph without causing a loop/cycle. For example L4 can goto L1, L2, L5 AND L2 can goto L5…and so on….
I guess I want a Directed acyclic graph and need help finding out which algorithm to use and how?
Look the Ford Algorithm
http://en.wikipedia.org/wiki/Bellman%E2%80%93Ford_algorithm
Enjoy’,