# Connected component

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

[Catalogue presentation and source-binding data](https://ocme.evemisslab.com/data/i18n/catalogue.en.json)



## [Connected component](https://ocme.evemisslab.com/en/atlas/atlas-connected-component/)

In a finite undirected simple graph, connected components are exactly the vertex equivalence classes defined by the existence of a path.

atlas-connected-component · canonical_mko

[Connected component](https://ocme.evemisslab.com/en/mko/mko-connected-component/)

## Prerequisite nodes


- [Graph walks and simple paths](https://ocme.evemisslab.com/en/atlas/atlas-graph-walk-simple-path/)
- [Equivalence relation](https://ocme.evemisslab.com/en/atlas/atlas-equivalence-relation/)
- [Finite simple undirected graphs](https://ocme.evemisslab.com/en/atlas/atlas-graph/)