We study a class of interconnection networks for multiprocessors, called the Necklace-G network that is based on the base graph G by attaching an array of processors to each two adjacent nodes of G. One of the interesting features of the proposed topology is its scalability while preserving most of the desirable properties of the underlying base network G. We conduct a general study on the topological properties of necklace networks. We first obtain their basic topological parameters, and then present optimal routing and broadcasting algorithms. We also present a unified approach to obtain the topological properties and the VLSI-layout of an arbitrary necklace network based on the properties of the corresponding base network G.