How do you detect a cycle in a directed graph?

Use DFS with three states: unvisited, visiting (in current path), and visited. For each node, mark as visiting, recurse on neighbors; if you encounter a visiting node, there's a cycle. After processing all neighbors, mark as visited. Alternative: Kahn's topological sort - if not all nodes are processed (remaining nodes have cycles), a cycle exists. Both are O(V+E). For undirected graphs, track parent during DFS.