  We introduce homotopy groups of digraphs that admit an intuitive description
of grid structures, which is a variation of the GLMY homotopy groups introduced
by Grigor'yan, Lin, Muranov and Yau in [21]. Furthermore, we prove that there
exists a long exact sequence of homotopy groups of digraphs associated to any
based digraph map, that is, there exists a digraph version of the Puppe
sequence.
