随机矩阵理论运用于金融领域中研究金融相关系数矩阵的相关性，相关系数矩阵是网络构建中的关键因素，本文将随机矩阵理论与网络构建相结合，研究基于随机矩阵的金融网络模型。本文选取上海证券市场的股票数据，将其中的股票数据分成四个阶段，基于随机矩阵理论，讨论金融相关系数矩阵和随机矩阵的特征值统计性质，并在此基础上对现有的去噪方法进行改进，建立更适合构建金融网络的相关系数矩阵，并构建金融网络模型。然后，基于随机矩阵理论和网络的关键节点分析比较去噪前后的金融网络以及噪声网络，发现对网络去噪后仍保留了原始网络的关键重要的信息，而噪声信息对应的是原始网络中度比较小的节点所代表的信息。最后，基于去噪网络，分析金融网络的拓扑结构，如最小生成树、模体和社团结构，发现改进后的金融网络的拓扑性质更加明显，结构更加紧密。%Random matrix theory is applied to study the correlation between different financial correlation coefficient matrices in the financial field. Correlation coefficient matrix is a key factor for constructing a network. In this paper we relate the random matrix theory to the network construction to study the financial networks model in terms of the random matrix. We select the stock data of Shanghai stock market, and divide them into four stages. We discuss the statistical properties of eigenvalues in financial correlation coefficient matrix and random matrix based on the random matrix theory, and improve the existing denoising method to construct the correlation coefficient matrix and to make it more suitable for building financial networks. After that we can build the financial network model. Then we analyze and compare the original financial network, the denoising financial network and the noise financial network in terms of the random matrix theory and the key node of networks. It is found that the primary important information is still in the original network, and the noise information corresponds to the information which the nodes of small degree in the original network include. Finally we analyze the topological structure of the financial networks, such as the minimum spanning tree, the motif and community structure. We also find that the topological properties of the improved financial networks are more remarkable and the topological structure is more compact.
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