# Definition:Component of Graph

## Contents

## Definition

Let $G$ be a graph.

Let $H$ be a subgraph of $G$ such that:

- $H$ is connected

- $H$ is not contained in any connected subgraph of $G$ which has more vertices or edges than $H$ has.

Then $H$ is a **component** of $G$.

## Example

This graph has 4 components:

## Also see

- Definition:Connected Graph: a graph with only one component.

## Sources

- 1977: Gary Chartrand:
*Introductory Graph Theory*... (previous) ... (next): $\S 2.3$