  Granular materials, whose features range from the particle scale to the
force-chain scale to the bulk scale, are usually modeled as either particulate
or continuum materials. In contrast with either of these approaches, network
representations are natural for the simultaneous examination of microscopic,
mesoscopic, and macroscopic features. In this paper, we treat granular
materials as spatially-embedded networks in which the nodes (particles) are
connected by weighted edges obtained from contact forces. We test a variety of
network measures for their utility in helping to describe sound propagation in
granular networks and find that network diagnostics can be used to probe
particle-, curve-, domain-, and system-scale structures in granular media. In
particular, diagnostics of meso-scale network structure are reproducible across
experiments, are correlated with sound propagation in this medium, and can be
used to identify potentially interesting size scales. We also demonstrate that
the sensitivity of network diagnostics depends on the phase of sound
propagation. In the injection phase, the signal propagates systemically, as
indicated by correlations with the network diagnostic of global efficiency. In
the scattering phase, however, the signal is better predicted by meso-scale
community structure, suggesting that the acoustic signal scatters over local
geographic neighborhoods. Collectively, our results demonstrate how the force
network of a granular system is imprinted on transmitted waves.
