\begin{definition}[Definition:Simple Graph/Formal Definition]
Let $V$ be a set.
Let $\RR$ be an endorelation on $V$ which is antireflexive and symmetric.
Let $E$ be the set whose elements of the form:
:$\set {\tuple {v_a, v_b}, \tuple {v_b, v_a} }$.
where $\tuple {v_a, v_b}$ and $\tuple {v_b, v_a}$ are elements of $\RR$ 
A '''simple graph''' is an ordered pair $G = \struct {V, E}$, where $V$ and $E$ are defined as above.
$V$ is called the vertex set.
$E$ is called the edge set.
\end{definition}