Continous-trace $k$-graph $C^{\ast }$-algebras

A characterization is given for directed graphs that yield graph $C^{\ast }$-algebras with continuous trace. This is established for row-finite graphs with no sources first using a groupoid approach, and extended to the general case via the Drinen-Tomforde desingularization. Partial results are given to characterize higher-rank graphs that yield $C^{\ast }$-algebras with continuous trace.