  Graph signal processing analyzes signals supported on the nodes of a graph by
defining the shift operator in terms of a matrix, such as the graph adjacency
matrix or Laplacian matrix, related to the structure of the graph. With respect
to the graph shift operator, polynomial functions of the shift matrix perform
filtering. An application considered in this paper, convergence acceleration
filters for distributed average consensus may be viewed as lowpass graph
filters periodically applied to the states. Design of graph filters depends on
the shift matrix eigendecomposition. Consequently, random graphs present a
challenge as this information is often difficult to obtain. Nevertheless, the
asymptotic behavior of the shift matrix empirical spectral distribution
provides a substitute for suitable random matrix models. This paper employs
deterministic approximations for empirical spectral statistics from other works
to propose optimization criteria for consensus acceleration filters, evaluating
the results through simulation.
