# Acyclic Graph & Directed Acyclic Graph: Definition, Examples

Descriptive Statistics > Directed Acyclic Graph

Directed acyclic graphs (DAGs) are used to model probabilities, connectivity, and causality. A “graph” in this sense means a structure made from nodes and edges.

• Nodes are usually denoted by circles or ovals (although technically they can be any shape of your choosing).
• Edges are the connections between the nodes. An edge connects two nodes. They are usually represented by lines, or lines with arrows.

DAGs are based on basic acyclic graphs.

## What is an Acyclic Graph?

An acyclic graph is a graph without cycles (a cycle is a complete circuit). When following the graph from node to node, you will never visit the same node twice.

A connected acyclic graph, like the one above, is called a tree. If one or more of the tree “branches” is disconnected, the acyclic graph is a called a forest.

## What is a Directed Acyclic Graph?

A directed acyclic graph is an acyclic graph that has a direction as well as a lack of cycles.

The parts of the above graph are:

• Integer = the set for the Vertices.
• Vertices set = {1,2,3,4,5,6,7}.
• Edge set = {(1,2), (1,3), (2,4), (2,5), (3,6), (4,7), (5,7), (6,7)}.

A directed acyclic graph has a topological ordering. This means that the nodes are ordered so that the starting node has a lower value than the ending node. A DAG has a unique topological ordering if it has a directed path containing all the nodes; in this case the ordering is the same as the order in which the nodes appear in the path.

In computer science, DAGs are also called wait-for-graphs. When a DAG is used to detect a deadlock, it illustrates that a resources has to wait for another process to continue.