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A graph-theoretic analysis is undertaken for a compendium of input-output(transfer) metrics of a standard discrete-time linear synchronization model,including lp gains, frequency responses, frequency-band energy, and Markovparameters. We show that these transfer metrics exhibit a spatial degradation,such that they are monotonically nonincreasing along vertex cutsets away froman exogenous input. We use this spatial analysis to characterizesignal-to-noise ratios (SNRs) in diffusive networks driven by process noise,and to develop a notion of propagation stability for dynamical networks.Finally, the formal results are illustrated through an example.

On the Spatial Pattern of Input-Output Metrics for a Network Synchronization Process