We characterise the topological spaces which arise as the primitive ideal spaces of the Cuntz–Krieger algebras of graphs satisfying condition (K): directed graphs in which every vertex lying on a loop lies on at least two loops. We deduce that the spaces which arise as ${\rm Prim}\;C^*(E)$ are precisely the spaces which arise as the primitive ideal spaces of AF-algebras. Finally, we construct a graph $\wt{E}$ from E such that $C^*(\wt{E})$ is an AF-algebra and ${\rm Prim}\;C^*(E)$ and ${\rm Prim}\;C^*(\wt{E})$ are homeomorphic.