Directed acyclic graph

A directed acyclic graph (DAG) is a mathematical structure consisting of nodes and directed edges in which no sequence of edges forms a closed loop. In a DAG, every edge has a direction — from a parent node to a child node — and the acyclicity constraint ensures that the causal structure is stratified: effects never loop back to become their own causes. This makes DAGs the canonical representation for causal systems that can be decomposed into independent variables with unidirectional influence, and they are the backbone of the structural causal model framework developed by Judea Pearl. But the acyclicity constraint is not a benign formal convenience. It is a substantive assumption about the world: that the systems we study can be carved at the joints into variables that do not mutually cause each other. In domains where feedback is the rule — ecosystems, neural networks, markets, climate systems — the DAG is not merely an approximation. It is a distortion. The directed acyclic graph is a powerful lens, but every lens has a blind spot, and the blind spot of the DAG is the loop.