---
tag: 0XNN9Z8E5A
kind: definition
name: Acyclic graph
msc: [05C05]
defines: 0SXHBTNM9T
uses: [07CT9RDY7Q]
sources:
  - url: https://en.wikipedia.org/wiki/Tree_(graph_theory)
    locator: Forest
---

## Definition

A [[graph|0JD5C82QMB]] is acyclic if it has no [[cycle|07CT9RDY7Q]].

## Remarks

An acyclic graph is also called a [[forest|09JP6G9FTA]]. A connected acyclic graph is a [[tree|0MJ0JS72DZ]].
The [[path graphs|075WR6W3Y3]] and the graphs with no edges are acyclic. The [[cycle graphs|0QQ0F12962]] are not.
A finite acyclic graph with $n$ vertices and $c$ components has $n - c$ edges.

## Explanations

### L1 human

A graph is acyclic when you cannot go around any loop in it.
Each edge then splits its piece of the graph in two when you delete it.