In this paper, we focus on D=2, the next best value to that of the complete network, and proceeding to somewhat larger (constant) values leading to more economical networks. We show that perfect difference networks (PDNs), which are based on the mathematical notion of perfect difference sets, offer a diameter of 2 in an asymptotically optimal manner. In other words, PDNs allow O (d2) nodes when nodes are of degree d, or, equivalently, have a node degree that grows as the square-root of the network size. The symmetry and rich connectivity of PDNs lead to balanced communication traffic and good fault tolerance for wired network.