We consider a network consisting of N nodes and a certain number of links that could be used to interconnect these nodes. The problem we address is to determine the smallest subset of switching nodes (in which to provide optical or electronic switching capability) necessary and sufficient to provide full end- to-end connectivity among all nodes. It is shown that this selection leads to the minimum number of transceivers needed to achieve full connectivity. We then address the same problem with the additional requirement of survivability, whereby the failure of any one link does not lead to any disconnection in the network. To solve the above stated problems, we present heuristic and optimal algorithms, and we study how the number of switches varies with the number of potential links.