# Definition:Graph (Graph Theory)/Informal Definition

## Informal Definition

A **graph** is intuitively defined as a pair consisting of a set of vertices and a set of edges.

### Vertex

Let $G = \left({V, E}\right)$ be a graph.

The **vertices** (singular: **vertex**) are the elements of $V$.

Informally, the **vertices** are the points that are connected by the edges.

In the above, the **vertices** (singular: **vertex**) are the points $A, B, C, D, E, F, G$ which are marked as dots.

### Edge

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

The **edges** are the elements of $E$.

In the above, the edges are $AB, AE, BE, CD, CE, CF, DE, DF, FG$.