Depending on the data model there are a few ways to deal with cycles. My project involved a friendship graph, and doing queries like "find friends of X", or "find people who like X, who are within 2 degrees of friendship-separation from Y". These are problems where it was okay to have cycles in the graph, as the traversal depth was hard limited. You'll have more problems if you're doing questions like "find the cheapest path from A to B", although there is certainly a way to cope with cycles there as well.