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

Compressibility of Network Opinion and Spread States in the Laplacian-Eigenvector Basis