Abstract

As one of the basic tools of statistical analysis, random matrix theory builds a bridge for the study of microscopic and macroscopic properties of complex networks. The eigenvalues of the adjacency matrix of the complex network after mapping correspond to the energy spectrum in the random matrix theory, so the characteristics of the complex network are concentrated in the volatility of the eigenvalue sequence. The eigenvalues of complex networks are analyzed through random matrix theory to find the relationship between their structure and properties. This paper discusses the design and realization of the comprehensive application platform of group enterprise financial management. Based on the current situation of the development of financial management software in domestic and foreign group companies, the thesis gives the goals and tasks of the platform research and design. The enterprise financial management platform has made a business and technical architecture design and has made an in-depth analysis and design of modules such as fund management, budget management, statement management, and accounting management. This paper finds that the critical point threshold makes the results of network community division below this threshold poor, and the results above this threshold are good. Furthermore, the tipping point threshold for the NYSE network is significantly lower than that of the CSM network. This paper further analyzes the dynamic cross-correlation matrix and examines the time-dependent changes in the number of outliers, the number of communities, the degree of network modularity, and the degree of decentralization of industry composition under the condition of two market critical point thresholds. From the magnitude of fluctuation, it is found that the NYSE network is much more stable than the CSM network, which may also be related to the basic characteristics of the two markets, because the capital chain relationship is much more stable than the supply chain relationship.

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