Definition:Connected (Graph Theory)

Vertices
Two vertices $u, v \in G$ are connected iff either:


 * $u = v$
 * $u \ne v$, and there exists a walk between them.

Graph
A graph is connected if every pair of vertices in $G$ is connected.

Otherwise, it is called disconnected.

$k$-Connected
A graph $G$ is called $k$-connected for $k \in \Z_{>0}$ if
 * $\left|{V \left({G}\right) }\right| > k$
 * $G$ is connected
 * $G$ has no vertex cut $W$ with $\left|{W}\right| < k$