Intro

A Tree is a graph that satisfies three simple rules:

$1.$ Connected: You can get from any node to any other node.

$2.$ No cycles: There is exactly one path between any two nodes.

$3.$ $n$ nodes means $n-1$ edges.

These three properties are connected. If you have any two of them, you get the third for free. For instance, if a graph is connected and has $n-1$ edges, it cannot have cycles. Trees are the simplest connected graphs. They form the foundation of many data structures and algorithms in computer science.