The definition of rings used in this work corresponds to the definition of "primitive rings", first introduced by Marians and used in the R.I.N.G.S. code. Several names referring to the same mathematical object can be found in the literature, and this definition is equivalent to that of "shortest path ring" by Franzblau, of "minimal ring" by Guttman, of "irreducible ring" by Wooten and of "rings" by Goetzke and Klein. A path between vertices y and z of length k is a chain of k edges joining y to z, in which at most two edges share any vertex. A cycle is a closed path, i.e. which returns to its starting point. A ring is a cycle of a graph which contains a shortest path for each pair of vertices.