# Definition:Graph (Graph Theory)/Order

## Definition

Let $G = \struct {V, E}$ be a graph.

The order of $G$ is the cardinality of its vertex set.

That is, the order of $G$ is $\card V$.

## Examples

### Arbitrary Order $4$ Graph

Let $G = \struct {V, E}$ be the graph defined as:

$V = \set {v_1, v_2, v_3, v_4}$.
$E = \set {\set {\tuple {v_1, v_2}, \tuple {v_2, v_1} }, \set {\tuple {v_1, v_3}, \tuple {v_3, v_1} }, \set {\tuple {v_2, v_3}, \tuple {v_3, v_2} }, \set {\tuple {v_3, v_4}, \tuple {v_4, v_3} } }$

Then the order of $G$ is the cardinality of $V$:

$\card V = 4$

## Also see

An order zero graph is the null graph.