# Nonempty finite trees: connectivity, cycles, and unique paths

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)



## [Nonempty finite trees: connectivity, cycles, and unique paths](https://ocme.evemisslab.com/en/atlas/atlas-tree/)

A finite simple undirected graph is a tree only when nonempty, connected, and acyclic; retain singleton, degree-one leaf, and new-edge cycle conventions.

atlas-tree · canonical_mko

[Nonempty finite trees: connectivity, cycles, and unique paths](https://ocme.evemisslab.com/en/mko/mko-tree/)

## Prerequisite nodes


- [Finite simple undirected graphs](https://ocme.evemisslab.com/en/atlas/atlas-graph/)