  The graph translation operator has been defined with good spectral properties
in mind, and in particular with the end goal of being an isometric operator.
Unfortunately, the resulting definitions do not provide good intuitions on a
vertex-domain interpretation. In this paper, we show that this operator does
have a vertex-domain interpretation as a diffusion operator using a polynomial
approximation. We show that its impulse response exhibit an exponential decay
of the energy way from the impulse, demonstrating localization preservation.
Additionally, we formalize several techniques that can be used to study other
graph signal operators.
