Calculating higher digraph homotopy groups

Abstract We give the first tractable and systematic examples of nontrivial higher digraph homotopy groups. To do this, we define relative digraph homotopy groups and show that these satisfy a long exact sequence analogous to the relative homotopy groups of spaces. We then define digraph suspension and Hurewicz homomorphisms and show that they commute with each other. The existence of nontrivial digraph homotopy groups then reduces to the existence of corresponding groups in the degree 1 path homology of digraphs.