In joint work with Shelton, we introduce a generalization of Koszul Algebra. Our class of algebras includes not only Berger’s N-Koszul algebras, but also many graded algebra with defining relations of various different degrees. We show, for example, that Artin-Schelter regular algebras of dimension 4 with 3 generators, 2 cubic relations and 2 quadratic relations belong to this class. This class is closed under twists and twisted tensor products, regular central extensions and Ore extensions. We explore connections between this class and the algebras associated to directed acyclic graphs introduced by Retakh et. al.