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 Markov
parameters. We show that these transfer metrics exhibit a spatial degradation,
such that they are monotonically nonincreasing along vertex cutsets away from
an exogenous input. We use this spatial analysis to characterize
signal-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