gen-state-a-directed-acyclic-graph-precisely-and-explain-why-it-bf5e

State a directed acyclic graph precisely and explain why it matters in 2-3 sentences.

# Directed Acyclic Graph (DAG) **Definition:** A directed acyclic graph is a graph consisting of vertices connected by directed edges, where it is impossible to start at any vertex and follow the directed edges to return back to that same vertex (no cycles exist). **Why it matters:** DAGs are fundamental for representing dependencies and ordering constraints in real-world systems—from task scheduling and build systems to blockchain architectures and causal inference. Their acyclic property guarantees that problems like topological sorting have solutions, enabling us to determine valid orderings for executing dependent tasks without deadlocks or circular dependencies.