Large-scale strictly nonblocking (SNB) and wide-sense nonblocking (WSNB) networks may be infeasible due to their high cost. In contrast, rearrangeable nonblocking (RNB) networks are more scalable because of their much lower cost. However, RNB networks are not suitable for circuit switching. In this paper, the concept of virtual nonblockingness is introduced. It is shown that a virtual nonblocking (VNB) network functions like an SNB or WSNB network, but it is constructed with the cost of an RNB network. The results indicate that for large-scale circuit switching applications, it is only needed to build VNB networks.