Definition:Graph (Graph Theory)/Size

Definition

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

The size of $G$ is the count of its edges.

That is, the size of a graph $G = \struct {V, E}$ is $\card E$.

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 size of $G$ is the cardinality of $E$:

$\card E = 4$

Also see

A size zero graph is called an edgeless graph.

Sources

• 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Chapter $1$: Mathematical Models: $\S 1.3$: Graphs
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): size (of a graph)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): size: 1. (of a graph)