The Spectral Distribution of Random Mixed Graphs

Abstract

In this work, we propose a random mixed graph model Gn(p(n),q(n)) that incorporates both the classical Erdős-Rényi’s random graph model and the random oriented graph model. We show that the empirical spectral distribution of Gn(p(n),q(n)) converges to the standard semicircle law under some mild condition, and the Monte Carlo simulation highly agrees with our result.

Keywords

• random graph
• mixed graph
• random matrix
• eigenvalues
• empirical spectral distribution