A class of doubly stochastic shift operators for random graph signals and their boundedness

A class of doubly stochastic graph shift operators (GSO) is proposed, which is shown to exhibit: (i) lower and upper L2-boundedness for locally stationary random graph signals, (ii) L2-isometry for i.i.d. random graph signals with the asymptotic increase in the incoming neighbourhood size of vertices, and (iii) preservation of the mean of any graph signal - all prerequisites for reliable graph neural networks. These properties are obtained...