\begin{definition}[Definition:Connectivity]
Let $G$ be a graph.
Then $\kappa \left({G}\right)$, the '''connectivity''' of $G$, is the smallest $k \in \Z_{>0}$ such that $G$ is $k$-connected. 
If $G$ is disconnected, or if $G$ has fewer than 2 vertices, then $\kappa \left({G}\right) = 0$.
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\end{definition}