  The first step for any graph signal processing (GSP) procedure is to learn
the graph signal representation, i.e., to capture the dependence structure of
the data into an adjacency matrix. Indeed, the adjacency matrix is typically
not known a priori and has to be learned. However, it is learned with errors. A
little attention has been paid to modelling such errors in the adjacency
matrix, and studying their effects on GSP methods. However, modelling errors in
the adjacency matrix will enable both to study the graph error effects in GSP
and to develop robust GSP algorithms. In this paper, we therefore introduce
practically justifiable graph error models. We also study, both analytically
when possible and numerically, the graph error effect on the performance of GSP
methods in different types of problems such as filtering of graph signals and
independent component analysis of graph signals (graph decorrelation).
