On Symmetry for Network Virtual Topology

General networks such as Internet are complex heterogeneous networks, which are constructed by many different organizations, and so become non-effective ones. Therefore one constructed a level of software over networks which is called overlay or virtual topology. In this paper we present principle of symmetry for general network topology by using Cayley graph models and show its necessity to improving network performance. We explain the main conclusions of the paper by many examples in optical, wireless and peer-to-peer networks.