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Network design, as it is currently practiced, involves putting devices together to create a network. However, a network is more than the sum of its parts, both in terms of the services it provides, and the potential for bugs. Devices are important, but their combination into a network should follow from expression of high-level policy, not the minutiae of network device configuration. Ideally we want to consider the network as a whole object. In this paper we develop generalized graph products that allow the mathematical design of a network in terms of small subgraphs that directly express business policy. The result is a flexible algebraic description of networks suitable for manipulation and proof. The approach is more than just design - it allows for analysis of existing networks providing an understanding of the policies used in their construction, something which can be difficult if the original designers no longer work on that network. We apply the approach to several real world networks to demonstrate how it can provide insight, and improve design.