  We give various necessary and sufficient conditions for an AF-algebra to be
isomorphic to a graph C*-algebra, an Exel-Laca algebra, and an ultragraph
C*-algebra. We also explore consequences of these results. In particular, we
show that all stable AF-algebras are both graph C*-algebras and Exel-Laca
algebras, and that all simple AF-algebras are either graph C*-algebras or
Exel-Laca algebras. In addition, we obtain a characterization of AF-algebras
that are isomorphic to the C*-algebra of a row-finite graph with no sinks.
