---
tag: 0FFAYNMAJZ
kind: definition
name: Connected graph
msc: [05C40]
defines: 0KWFFMDF8T
uses: [0J8XE7W68F]
sources:
  - url: https://en.wikipedia.org/wiki/Connectivity_(graph_theory)
    locator: Connected vertices and graphs
---

## Definition

A [[graph|0JD5C82QMB]] $G$ is connected if its vertex set is nonempty and any two vertices of $G$ are [[reachable|0J8XE7W68F]] from each other.

## Remarks

The empty graph, with no vertices, is not connected under this convention. Some authors call it connected.
A graph is connected if and only if it has exactly one [[connected component|01VVP10MWJ]].
The [[cycle graphs|0QQ0F12962]], the [[path graphs|075WR6W3Y3]] and the [[trees|0MJ0JS72DZ]] are connected.

## Explanations

### L1 human

A graph is connected when it is in one piece.
From any vertex you can reach any other vertex along edges.