  Given a $k$-graph $\Lambda$ and an element $p$ of $\NN^k$, we define the dual
$k$-graph, $p\Lambda$. We show that when $\Lambda$ is row-finite and has no
sources, the $C^*$-algebras $C^*(\Lambda)$ and $C^*(p\Lambda)$ coincide. We use
this isomorphism to apply Robertson and Steger's results to calculate the
$K$-theory of $C^*(\Lambda)$ when $\Lambda$ is finite and strongly connected
and satisfies the aperiodicity condition.
