Definition:Connected (Graph Theory)

This page is about Connected in the context of Graph Theory. For other uses, see 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.

Also see

• Definition:$k$-Connected
• Definition:Connectivity
• Definition:Adjacent (Graph Theory)

• Results about connectedness in the context of graph theory can be found here.