Abstract ¡@¡@Double-loop networks have become one of the most popular architectures in the design of Local Area Networks and distributed memory multiprocessor systems. This is due to its characters of minimal diameter, easy routing, expandability and regularity. The switching mechanism at each node can easily be implemented using building blocks of the same specification. Therefore, double-loop networks have a high degree of reliability and hence very low vulnerability. Let N denote the number of nodes in a double-loop network and d(N) be the best possible diameter with N vertices. Given an N, Bermond et al. [5], Boesch and Wang [7], and Yebra et al. [23] have shown that . This is a well-known lower bound for d(N) and is usually denoted as lb(N). In this paper, what we discuss is finding an optimal topology such that d(N)= lb(N) for any given value of N. We provide a simple formula to find optimal topologies of double-loop networks with N nodes.