Definition
Directed acyclic graph
A directed graph containing no directed cycles.
A directed acyclic graph, or DAG, is a directed graph with no directed cycle. In particular it has no loop. Reachability by a positive-length directed path is then a strict partial order: concatenation gives transitivity, while acyclicity excludes a path from a vertex to itself.
Finite and infinite dependency graphs
In a finite DAG, one can successively remove a vertex with no incoming edges, producing an ordering in which every edge points forward. Such a vertex must exist: otherwise repeatedly following incoming edges in the finite set would repeat a vertex and create a cycle.
An infinite DAG can contain an infinite chain. Acyclicity alone therefore does not show that recursive prerequisite expansion terminates at foundational data. That additional claim requires a well-founded dependency relation or an explicit audit of the reachable graph.