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Network performance for a particular application is determined by the latency and bisection bandwidth that are achieved for the set of specific communication patterns used by that application. The number of nodes with which each node might potentially communicate grows linearly as nodes are added, thus, network cost for large systems either becomes a large fraction of machine cost or performance suffers. However, performance-critical communication patterns commonly occurring in real parallel programs rarely require that each node directly communicate with every other node. The number of node pairs actually communicating generally grows far slower than the expected O(N2). Thus, a carefully designed network for a massively parallel system can use relatively narrow switches while still providing single-switch latency and guaranteed pairwise bandwidth for performance-critical communications. This paper introduces sparse flat neighborhood networks (SFNNs), a variant of flat neighborhood networks (FNNs) which are engineered from first principles to efficiently meet these detailed pairwise communication performance criteria.