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Distributed networked systems form an essential resource for computation and applications ranging from commercial, military, scientific, and research communities. Allocation of resources on a given infrastructure is realized through various mapping systems that are tailored towards specific use cases of the requesting applications. While HPC system requests demand compute resources heavy on processor and memory, cloud applications may demand distributed web services that are composed of networked processing and some memory. All resource requests allocate on the infrastructure with some form of network connectivity. However, during mapping of resources, the features and topology constraints of network components are typically handled indirectly through abstractions of user requests. This paper is on a novel graph representation that enables precise mapping methods for distributed networked systems. The proposed graph representations are demonstrated to allocate specific network components and adjacency requirements of a requested graph on a given infrastructure. Furthermore, we report on application of business policy requirements that resulted in increased utilization and a gradual decrease in idle node count as requests are mapped using our proposed methods.