How to Correctly Detect Dependency Cycles Using Three-State DFS

A common bug in cycle detection code uses a single visited set, which incorrectly flags diamond-shaped dependency graphs as cyclic. The correct approach assigns each node one of three states — unvisited, in-progress, or fully processed — based on classical depth-first search theory. Only an edge pointing back to an in-progress node indicates a true cycle, while an edge to a fully processed node is harmless. This method also captures the exact cycle path, making error messages actionable for engineers. An iterative implementation using an explicit stack demonstrates the technique on a realistic module dependency graph containing both a genuine cycle and a diamond pattern.