I had implemented this problem in sml ( imperative programming) . Here is the outline . Find all the nodes that either have an indegree or outdegree of 0 . Such nodes cannot be part of a cycle ( so remove them ) . Next remove all the incoming or outgoing edges from such nodes.
Recursively apply this process to the resulting graph. If at the end you are not left with any node or edge , the graph does not have any cycles , else it has.
