Abstract: The linear correlation between stock returns can be described by Pearson correlation, but the very important non-linear characteristics of stock markets and the correlation between stock returns when extreme events occur are not measured by Pearson correlation. However, correlation information between stock returns that Pearson correlation cannot measure can be provided by Kendall rank correlation and Tail correlation. Therefore, in order to analyze the dependence structure of stocks, it is very important to adopt different correlation measures to characterize the relationship between stock returns. Therefore, based on Pearson correlation, Kendall rank correlation and Tail correlation of stock returns, the evolution characteristics of multilayer network structures of financial institutions in China is empirically studied by this paper.
Firstly, the method of building the multilayer network model of financial institutions is given, which consists of two steps. One is to calculate Pearson, Kendall and Tail correlation of stock returns. The other is to filter the correlation between stocks by using the minimum spanning tree method. Secondly, based on the above model and the financial stock data from October 2010 to March 2018 in China, the evolution characteristics of multilayer network structures of financial institutions is analyzed through the structural indicators, such as average weight, edge uniqueness, degree correlation and similarity in the multilayer network.
Empirical results show that:the average weights of the Kendall and Tail layers are higher than those of the Pearson layer; the trends of average weights of the Pearson and Kendall layers are similar, but the fluctuation amplitude of the former is obviously larger than that of the latter; the trends of edge uniqueness of the Pearson layer and the Kendall layer are very similar, but that of the Tail layer is quite different from them; the degree correlation of any two layers is positive, but it fluctuates sharply with time; the Pearson layer and the Kendall layer have higher similarity, the similarity between the Tail layer and the Pearson layer and the Kendall layer is lower overall; the structural indicators such as average weight, edge uniqueness, degree correlation and similarity in the multilayer network are related to the stock market quotation.From the perspective of the multilayer network theory, the evolutionary characteristics of multilayer correlation among financial institutions in China and its internal relationship with the stock market quotation are explored by this paper, which enriches the study of the multilayer network theory in the financial field. And the relevant research results have a certain practical significance for maintaining the stability of financial markets.

Key words: multilayer network, financial institutions, interrelationship, network structure