Definition:K-Connected

Definition
Let $G$ be a graph.

Let $k \in \Z_{>0}$.

Then $G$ is $k$-connected :
 * $\left\lvert{V \left({G}\right) }\right\rvert > k$
 * $G$ is connected
 * $G$ has no vertex cut $W$ with $\left\lvert{W}\right\rvert < k$

Informally:
 * $G$ is connected and has more than $k$ vertices
 * There is no vertex cut of $G$ containing less than $k$ vertices.

Also see

 * Definition:Connectivity