An important theoretic interest is to Study the relations between different interconnection networks, and to compare the capability and performance of the network structures. The most popular way to do the investigation is network emulation. Based on the classical voltage graph theory, the authors develop a new representation scheme for interconnection network structures. The new approach is a combination of algebraic methods and combinatorial methods. The results demonstrate that the voltage graph theory is a powerful tool for representing well-known interconnection networks and in implementing optimal network emulation algorithms, and in particular, show that all popular interconnection networks have very simple and intuitive representations under the new scheme. The new representation scheme also offers powerful tools for the study of network routings and emulations. For example, we present very simple constructions for optimal network emulations from the cube-connected cycles networks to the butterfly networks, and from the butterfly networks to the hypercube networks. Compared with the most popular way of network emulation, this new scheme is intuitive and easy to realize, and easy to apply to other network structures.