# Difference between Oriented Graph and Directed Acyclic Graphs (DAG)

Definition of Oriented Graph:

Basically directed graphs can have an arrow going from $$A$$ to $$B$$ and an arrow going from $$B$$ to $$A$$. Oriented graphs can have at most one arrow between any two vertices $$A$$ and $$B$$.

Definition of Directed Acylic Graph (DAG)

In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a finite directed graph with no directed cycles.

An edge from $$A$$ to $$B$$ and another from $$B$$ to $$A$$ is a cycle right ?

Then if Oriented graphs already do not have such a cycle then how are they different from DAGs ? Unless of course DAGs need some other constraint satisfied ? In that case what are they ?

You are right that $$A \rightarrow B \rightarrow A$$ would be a directed cycle, but they can be longer. For instance, consider a graph with three vertices $$A,B,C$$ and edges $$A\rightarrow B, B\rightarrow C, C\rightarrow A$$. Such a graph is oriented, but it is not a DAG, because there is a cycle.