The Spectral Distribution of Random Mixed Graphs

In this work, we propose a random mixed graph model $G_n(p\left(n\right),q\left(n\right))$ 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 $G_n(p\left(n\right),q\left(n\right))$ converges to the standard semicircle law under some mild condition, and the Monte Carlo simulation highly agrees with our result.