  In recent years, graph theoretic considerations have become increasingly
important in the design of HPC interconnection topologies. One approach is to
seek optimal or near-optimal families of graphs with respect to a particular
graph theoretic property, such as diameter. In this work, we consider
topologies which optimize the spectral gap. We study a novel HPC topology,
SpectralFly, designed around the Ramanujan graph construction of Lubotzky,
Phillips, and Sarnak (LPS). We show combinatorial properties, such as diameter,
bisection bandwidth, average path length, and resilience to link failure, of
SpectralFly topologies are better than, or comparable to, similarly constrained
DragonFly, SlimFly, and BundleFly topologies. Additionally, we simulate the
performance of SpectralFly on a representative sample of micro-benchmarks using
the Structure Simulation Toolkit Macroscale Element Library simulator and study
cost-minimizing layouts, demonstrating considerable benefit of the SpectralFly
topology.
