Pure infiniteness and paradoxicality for graph $C^{\ast }$-algebras

We obtain necessary and sufficient conditions for pure infiniteness of the path groupoid $C^{\ast }$-algebra of a row-finite graph without sinks. In particular we show that for such a path groupoid ${\mathcal{G}}_E$, the properties of being essential principal and the existence of a basis of $($\mathcal{G}$_E^a, 2, 1)$-paradoxical sets for the topology are not only sufficient, but also necessary.