I will discuss the recent paper, (${ K}_{H,|A|-e(A)},\leq$) -homogeneous-universal graphs, by Aref'ev. In this paper Aref'ev restricts himself to a class K of finite structures with finite relations. The class K is determined by a lattice H, with lattice points (|A|,y(A)) where A is a finite substructure in the class K, and y is a dimension function: y=|A|-e(A). This function y then gives the notion of strong embeddings and amalgamation of finite structures A in K into a model M. In the paper he shows that if M is a countable (${ K}_{H,|A| -e(A)},\leq$)-homogeneous-universal graph), then M is in one of three different classes of graphs, depending only on the lattice H for the class K.