Finding all cycles in a directed graph

Hi all,
I have a task I believe I will solve relatively easy if I manage to detect all cycles within a graph that I can build from the data given.
I googled for a while but I couldn't find some explanation that I can use. I came upon refrerences to some publication referred as "Reingold, Nievergelt and Deo 1977", however I could not find some online resources from that ?book?.
AFAIK I can detect whether thre is a cycle using DFS, but I need all cycles.
Please guide me to some online resource that can help me find a suitable algorithm, or if you know such algorithm please post its name so I can find information about it.
Thanks for your cooperation
Mike

Thanks for all those replies!
I still haven't implemented a solution and I have some questions. I googled and skimmed through a book I have and I came up with the definition that topological sorted graph means that all 'paths' lead in one direction (such ordering of the vertices V that for each edge(i, j) in E vertex i is to the left of vertex j).
If I understand correctly your idea, it is to first order the vertices by some criterion and then remove all edges leading in a direction opposite to the sorting direction.
I am not quite sure I understand correctly how to choose the ordering of the vertices. In the beginning of the sorted vertex list we must have vertices with the most possible outgoing edges /as sum of weights/ and least incoming(because these are to be removed), did I understand the idea correctly?
I thought about another solution but I cannot estimate how heavy it will be as processing time: to perform search(maybe DFS) and if I find a cycle - to remove the least heavy edge and continue the search from the position before passing this edge.
I guess it is not applicable since it can escalate to a very time-heavy task, especially if each time we go back.
So I think I will implement the Idea YATArchivist proposed - sorting vertices and removing back-edges, and we'll see what will happen. After all - it's only a contest, I can only win or not win, there are no losers ;)
Thank you for giving your valuable time for sharing thoughts in this thread
Mike

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malcolmmc wrote:
paulcw wrote:
I don't see the need for unsetting the flag. Visited is visited. What needs to be added is to respond when the flag is set to true.You need to clear the flag because the same node might be reached through more than one route without the graph being cyclic (it could be a shared sub-tree).
Only if you encounter a node which is already part of the path you're examining have you found a loop.But not if it's a depth-first search, no?
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11.png ‏15 KB
13.PNG ‏85 KB

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