What follows is a continuation of the general theory developed in Chapter IV. This prolongation was more or less inspired by the excellent Paris These of Felix Pham. Briefly speaking it deals with the subgraphs, open or closed, of the basic graph G. The geometric methods of Chapter IV continue to prevail. For I continue to believe that they are more suitable for an Introduction to our theory, more so indeed than the very abstruse methods utilized by all previous authors.