The minimum distance diagram of double-loop networks

It is well-known that the minimum distance diagram of a double-loop network yields an L-shape. It is important to know, for a given L-shape, whether there exists a double-loop network realizing it. Necessary and sufficient conditions were given before, but were said to be cumbersome. They also need some clarification. We give new conditions and a simple proof. We also prove that all double-loop networks realizing the same L-shape are isomorphic as the existing proof was given in a Spanish dissertation