Definition:Simple Graph/Formal Definition

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.

Also presented as
It is usually more convenient to express the elements of the edge set as doubletons, of the form $\set {v_a, v_b}$.

Also defined as
Some sources impose the condition that $V \ne \O$.

Some sources also define a (simple) graph as one such that $V$ is a finite set.