  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. In particular, 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 topologies on a representative sample
of physics-inspired HPC workloads using the Structure Simulation Toolkit
Macroscale Element Library simulator and demonstrate considerable benefit to
using the LPS construction as the basis of the SpectralFly topology.
