  Optimal design of consensus acceleration graph filters relates closely to the
eigenvalues of the consensus iteration matrix. This task is complicated by
random networks with uncertain iteration matrix eigenvalues. Filter design
methods based on the spectral asymptotics of consensus iteration matrices for
large-scale, random undirected networks have been previously developed both for
constant and for time-varying network topologies. This work builds upon these
results by extending analysis to large-scale, constant, random directed
networks. The proposed approach uses theorems by Girko that analytically
produce deterministic approximations of the empirical spectral distribution for
suitable non-Hermitian random matrices. The approximate empirical spectral
distribution defines filtering regions in the proposed filter optimization
problem, which must be modified to accommodate complex-valued eigenvalues.
Presented numerical simulations demonstrate good results. Additionally,
limitations of the proposed method are discussed.
