近年来随机图谱理论已成为国内外研究热点，引起了众多学者的广泛研究。本项目主要围绕随机图谱的计算及应用展开深入研究，基于几类随机图模型，研究其对应的若干随机矩阵的谱性质。主要包括：1.研究随机混合图的Hermitian Laplacian矩阵和规范化Hermitian Laplacian矩阵的经验谱分布以及Hermitian邻接矩阵特征值的界。2.研究广义随机混合图的Hermitian邻接矩阵谱半径的渐近界和规范化Hermitian Laplacian矩阵特征值的近似问题。3.研究随机定向图的斜邻接矩阵和斜Randić矩阵的谱半径的渐近界。本项目研究内容涉及图谱理论、概率论、随机矩阵论等，是一个多学科相互交叉的综合性研究课题。一方面通过开发新方法和新工具深入探讨随机图的谱性质，从而丰富和发展随机图谱理论；另一方面，通过随机图谱的理论研究，为解决实际问题提供可靠的科学依据和理论指导。

In recent years, spectral random graph theory has been a research hotspot both at home and abroad, and it has attracted considerable studies from many scholars. This project mainly focuses on the calculation and application of the spectra of random graphs. Based on several random graph models, the spectral properties of several corresponding random matrices are studied. This project mainly includes the following research contents. 1. We will study the empirical spectral distributions of the Hermitian Laplacian matrix and the normalized Hermitian Laplacian matrix, and the bounds of eigenvalues of the Hermitian adjacency matrix of random mixed graphs. 2. We will study the asymptotic bound of the spectral radius of the Hermitian adjacency matrix, and the problem of approximating the eigenvalues of the normalized Hermitian Laplacian matrix of generalized random mixed graphs. 3. We will study the asymptotic bounds of the spectral radii of the skew adjacency matrix and the skew Randić matrix of random oriented graphs. This project involves spectral graph theory, probability theory, random matrix theory etc., and it is an interactional, comprehensive and multidisciplinary research project. On one hand, through the development of new methods and new tools to further explore the spectral properties of random graphs, so as to enrich and develop the spectral random graph theory; on the other hand, through the theoretical research of the spectra of random graphs, it provides reliable scientific basis and theoretical guidance for solving practical problems.