  Graph signal processing (GSP) is an emerging field developed for analyzing
signals defined on irregular spatial structures modeled as graphs. Given the
considerable literature regarding the resilience of infrastructure networks
using graph theory, it is not surprising that a number of applications of GSP
can be found in the resilience domain. GSP techniques assume that the choice of
graphical Fourier transform (GFT) imparts a particular spectral structure on
the signal of interest. We assess a number of power distribution systems with
respect to metrics of signal structure and identify several correlates to
system properties and further demonstrate how these metrics relate to
performance of some GSP techniques. We also discuss the feasibility of a
data-driven approach that improves these metrics and apply it to a water
distribution scenario. Overall, we find that many of the candidate systems
analyzed are properly structured in the chosen GFT basis and amenable to GSP
techniques, but identify considerable variability and nuance that merits future
investigation.
