We initiate the program of extending to higher-rank graphs (k-graphs) the geometric classification of directed graph C * -algebras, as completed in the 2016 paper of Eilers, Restorff, Ruiz, and Sørensen [ERRS16]. To be precise, we identify four "moves," or modifications, one can perform on a k-graph Λ, which leave invariant the Morita equivalence class of its C * -algebra C * (Λ). These moves -insplitting, delay, sink deletion, and reduction -are inspired by the moves for directed graphs described by Sørensen [Sø13] and Bates-Pask [BP04]. Because of this, our perspective on k-graphs focuses on the underlying directed graph. We consequently include two new results, Theorem 2.3 and Lemma 2.9, about the relationship between a k-graph and its underlying directed graph.1 A graph E has finitely many vertices iff C * (E) is unital.

We initiate the program of extending to higher-rank graphs (k-graphs) the geometric classification of directed graph $C^*$ -algebras, as completed in Eilers et al. (2016, Preprint). To be precise, we identify four “moves,” or modifications, one can perform on a k-graph $\Lambda $ , which leave invariant the Morita equivalence class of its $C^*$ -algebra $C^*(\Lambda )$ . These moves—in-splitting, delay, sink deletion, and reduction—are inspired by the moves for directed graphs described by Sørensen (Ergodic Th. Dyn. Syst. 33(2013), 1199–1220) and Bates and Pask (Ergodic Th. Dyn. Syst. 24(2004), 367–382). Because of this, our perspective on k-graphs focuses on the underlying directed graph. We consequently include two new results, Theorem 2.3 and Lemma 2.9, about the relationship between a k-graph and its underlying directed graph.