## 1 Introduction
[PERSON] (2014) pointed out that portfolio diversification makes individual investors safer but also establishes a link between them through jointly held assets, which creates an \"endogenous covariance\" between the assets and investors and improves systemic risk by rapidly spreading the impact in the whole system [7]. Based on the endogenous network model, [PERSON] et al. (2018) found that the network structure is closely related to the systemic risk of banks. That is, with the expansion of the network node size, the number of bankrupt banks significantly increases and the systemic risk also significantly increases [8]. [PERSON] et al. (2019) used the data of U.S. commercial banks from 2000 to 2013 and found that bank diversification is related to the increase in systemic risk through empirical analysis. Moreover, the impact of diversification on systemic risk is more significant in large and medium-sized banks [9]. These studies show that there is a close relationship between the systemic risk of a financial network and the network structure. This paper aims to study bank correlation networks. In fact, the correlation network has been widely used in related research in the financial field. For example, [PERSON] [10] first used the stock correlation network to analyze the return correlation of S & P 500 stocks and found a hierarchical clustering structure among stocks. Subsequently, many other researchers analyzed the relationship between the stock market and the topological structure of the network by establishing the stock correlation network [11; 12; 13]. In the stock correlation network, the nodes of the network represent stocks and the connecting edges between nodes represent the price fluctuation association among stocks. Referring to the idea of establishing a stock correlation network, this paper will establish a bank correlation network according to the correlation of many banks' investment portfolios with different types of asset. In a bank correlation network, a network node represents a bank, while the correlation coefficient of the asset portfolio between any two bank nodes is taken as the weight of the connecting edge between the two nodes. It is believed that overlapping portfolios--i.e., the holding of common assets between banks--is a major factor in risk contagion. If banks have many common investment portfolios, risks will be spread among them through asset price fluctuations. At present, many researchers have studied the risk contagion caused by overlapping portfolios and the systemic risk of the financial system, including [PERSON] and [PERSON] [14], [PERSON] et al. [15], [PERSON] and [PERSON] [16], and [PERSON] et al. [17]. Therefore, motivated by these works, we will establish a bank-related network, based on the ratio of investment portfolios between banks, and discuss some potential relationships between network structure and systemic risk. At present, there are still some difficulties in the research of the systemic risk of real financial networks, mainly due to the large scale of real financial networks in which the number of nodes is often in the tens of thousands and the connection of edges is also very complex. The efficiency of studying systemic risk by examining the network average degree, clustering coefficient, asset diversity, leverage, and other general topological characteristics of the whole financial system is often unsatisfactory. Therefore, it is necessary for us to find a method to simplify the financial network model which can divide the network into many sub-networks with different structures and study the differences in risks between different sub-networks. One of the most commonly used methods is community structure division [18]: according to the degree of connection between network nodes, a complex network can be divided into several small communities, with tight connections within the community and sparse connections between the communities. As a topological property of local aggregation, the term community has different practical significance in real networks.