With the emergence of new enabling technologies including software-defined networking and network function virtualization, network virtualization has been reemphasized in recent years, such as network slicing in 5G networks. As an important aspect of network virtualization, network topology virtualization is studied in this work-from traditional network embedding toward full network topology virtualization. By full virtualization, the tenant virtual network can specify whatever network topology without knowing the underlying physical network and get the same experience as building a physical network by his own. Based on the switches with a late-binding key extractor, not only one-to-one and many-to-one mapping, but also one-to-many mappings are enabled in full virtualization of network topologies. In this paper, we propose a restricted differential evolution topology virtualization algorithm to achieve efficient mapping from a virtual network to a physical network in full virtualization. Furthermore, migration approaches are carried out to tackle the mapping failure of the virtual network topology. The extensive evaluation results show that the proposed algorithms can accept 30% more virtual network requests and gain more than 25% profit for physical network operators compared with baseline mechanisms.