# Definition:Connected (Graph Theory)

This page is about connectedness in graph theory. For other uses, see Definition:Connected.

## Definition

### Vertices

Let $G$ be a graph.

Two vertices $u, v \in G$ are connected if and only if either:

$(1): \quad u = v$
$(2): \quad u \ne v$, and there exists a walk between them.

### Graph

Let $G$ be a graph.

Then $G$ is connected if and only if every pair of vertices in $G$ is connected.