 The Yoneda Lemma asserts that "C"op embeds in Set"C" as a full subcategory.In the graph example the embedding represents "C"op as the subcategory of Set"C" whose two objects are "V' " as the one-vertex no-edge graph and "E' " as the two-vertex one-edge graph (both as functors), and whose two nonidentity morphisms are the two graph homomorphisms from "V' " to "E' " (both as natural transformations).The natural transformations from "V' " to an arbitrary graph (functor) "G" constitute the vertices of "G" while those from "E' " to "G" constitute its edges.