In this paper we study the edge-magicness of graphs with equal size and order, and we use such graphs and digraph products in order to construct labelings of different classes and of different graphs. We also study super edge-magic labelings of 2-regular graphs with exactly two components and their implications to other labelings. The strength of the paper lays on the techniques used, since they are not only used in order to provide labelings of many different types of families of graphs, but they also show interesting relations among well studied types of labelings. We are able to obtain, in this way, deep results relating different types of labelings.