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.


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