# Graph

A simple undirected graph is a tuple of $V$, the vertex set, and $E \subset V \times V$, an edge set. This is normally referred to as $G = (V, E)$. As this is undirected, an edge $e = (x,y)$ is the same as the edge $e = (y,x)$, so if we define an equivalence relation $(x,y) \sim (y,x)$ for all $x,y \in V$, then it is fairer to say $E \subset V \times V / \sim$.