## Definition

From Wikipedia ([source](https://en.wikipedia.org/wiki/Directed_acyclic_graph)):

In [mathematics](https://en.wikipedia.org/wiki/Mathematics), particularly [graph theory](https://en.wikipedia.org/wiki/Graph_theory), and [computer science](https://en.wikipedia.org/wiki/Computer_science), a directed acyclic graph (DAG [/ˈdæɡ/](https://en.wikipedia.org/wiki/Help:IPA/English) ([listen](https://upload.wikimedia.org/wikipedia/commons/5/5a/En-us-DAG.ogg))) is a [directed graph](https://en.wikipedia.org/wiki/Directed_graph) with no [directed cycles](https://en.wikipedia.org/wiki/Cycle_graph#Directed_cycle_graph). That is, it consists of [vertices](https://en.wikipedia.org/wiki/Vertex_(graph_theory)) and [edges](https://en.wikipedia.org/wiki/Edge_(graph_theory)) (also called arcs), with each edge directed from one vertex to another.

<img src="https://hackmd.io/_uploads/rywIzRLo5.png" width="219" height="300" alt="A directed acyclic graph (DAG)"/>

## Why a directed acyclic graph (DAG)

Following directions in a DAG will never form a closed loop. Steps through a DAG are finite. That's the main reason to choose for a DAG.

## Unique properties

From Wikipedia ([source](https://en.wikipedia.org/wiki/Directed_acyclic_graph)):

A directed graph is a DAG if and only if it can be [topologically ordered](https://en.wikipedia.org/wiki/Topological_ordering), by arranging the vertices as a linear ordering that is consistent with all edge directions. 

## Applications

From Wikipedia ([source](https://en.wikipedia.org/wiki/Directed_acyclic_graph)):

DAGs have numerous scientific and computational applications, ranging from biology (evolution, family trees, epidemiology) to information science (citation networks) to computation (scheduling).