Spectral Statistics of Directed Networks with Random Link Model Transpose-Asymmetry

TL;DR

This paper extends spectral analysis methods to large-scale directed networks with transpose-asymmetric distributions, providing efficient spectral density approximations crucial for filter design.

Contribution

It introduces a novel spectral density approximation approach for transpose-asymmetric directed networks, expanding the applicability of spectral analysis techniques.

Findings

Spectral density approximations are accurate for large transpose-asymmetric networks.

Numerical simulations confirm the effectiveness of the proposed spectral analysis.

Application to consensus filters demonstrates practical utility.

Abstract

Stochastic network influences complicate graph filter design by producing uncertainty in network iteration matrix eigenvalues, the points at which the graph filter response is defined. While joint statistics for the eigenvalues typically elude analysis, predictable spectral asymptotics can emerge for large scale networks. Previously published works successfully analyze large-scale networks described by undirected graphs and directed graphs with transpose-symmetric distributions, focusing on consensus acceleration filter design for time-invariant networks as an application. This work expands upon these results by enabling analysis of certain large-scale directed networks described by transpose-asymmetric distributions. Specifically, efficiently computable spectral density approximations are possible for transpose-asymmetric percolation network models with node-transitive symmetry group and normal mean matrix. Numerical simulations support the derived approximations and application to consensus filters.