  Opinion-evolution and spread processes on networks (e.g., infectious disease
spread, opinion formation in social networks) are not only high dimensional but
also volatile and multiscale in nature. In this study, we explore whether
snapshot data from these processes can admit terse representations.
Specifically, using three case studies, we explore whether the data are
compressible in the Laplacian-eigenvector basis, in the sense that each
snapshot can be approximated well using a (possibly different) small set of
basis vectors. The first case study is concerned with a linear consensus model
that is subject to a stochastic input at an unknown location; both empirical
and formal analyses are used to characterize compressibility. Second,
compressibility of state snapshots for a stochastic voter model is assessed via
an empirical study. Finally, compressibility is studied for state-level daily
COVID-19 positivity-rate data. The three case studies indicate that state
snapshots from opinion-evolution and spread processes allow terse
representations, which nevertheless capture their rich propagative dynamics.
