Spectral Properties of Matrices Associated with Some Directed Graphs

TL;DR

This paper investigates the spectral characteristics of specific non-self-adjoint matrices linked to large directed graphs, revealing eigenvalue convergence to particular curves with some exceptions.

Contribution

It provides new insights into the asymptotic eigenvalue distribution of matrices associated with directed graphs, highlighting convergence patterns and exceptional eigenvalues.

Findings

Eigenvalues asymptotically converge to specific curves.

A finite number of eigenvalues have limits outside these curves.

The results enhance understanding of spectral behavior in directed graph matrices.

Abstract

We study the spectral properties of certain non-self-adjoint matrices associated with large directed graphs. Asymptotically the eigenvalues converge to certain curves, apart from a finite number that have limits not on these curves.