DAG Traversal with Cycle Detection

Concepts: pyDAGCycleDetect, pyTopoSort, py3ColorDFS

Pure trees cannot have cycles. Data pipeline DAGs can — accidentally. A cyclic dependency in an Airflow DAG (table A depends on B, B depends on C, C depends on A) causes an infinite loop and must be caught before execution. The industry-standard algorithm is 3-color DFS: white means unvisited, gray means currently in the DFS call stack (in-progress), black means fully processed. If you encounter a gray node during DFS, you found a cycle. This is exactly what Airflow's DAG validator runs on startup. 3-Color Cycle Detection Topological Sort via DFS (Reverse Post-Order) If there is no cycle, you can compute a valid execution order using topological sort. The DFS approach: after fully processing a node (all its descendants are done), append it to a result list. Then reverse that list. The resu