--- ## Definition > [!tldr] Definition > A **tree** is a [[graph]] which is [[Connected graph|connected]] and which contains no [[Paths|cycles]]. Notes: - A collection of trees is called a **forest**. That is, a forest is a [[graph]] that has no [[Paths|cycles]] (but which might be disconnected). - In a tree, there is a unique path between any two vertices. That is, given any two vertices, there exists a path from one to the other; and only one such path exists. ## Examples An example of a tree: ![[tree-example1.png|100]] Another example: ![[tree-example2.png|400]] Each of the [[Graph|graphs]] below is a tree, used to model molecular structure in chemistry: ![[tree-example3.png]] This [[graph]] below on the left is not a tree, because it contains a [[Paths|cycle]] ([source](https://www.gatevidyalay.com/tree-data-structure-tree-terminology/)): ![[tree-example4.png]] The image below, taken to be a single [[graph]] with three [[Connected graph|components]], is not a tree, because it is not [[Connected graph|connected]]. But, we can think of it as a forest. ![[tree-example5.png]] ## Resources