# Spatiotemporal Patterns of Risk Propagation in Complex Financial Networks
## 2 Literature Review  
Complex financial systems are made up of multiple components (nodes), which is a typical example of complex networks. In a complex financial network, the allocation of resources and the interaction between elements imply the flow of information. The study of information flow such as risk propagation flow in the financial system is very important, attracting researchers from various fields. In the past, the research mainly focused on two aspects: either the topological structure or modeling. The research methods of the topological structure are mainly divided into three categories: correlation coefficient, Granger causality test, and entropy-like method. The correlation coefficient method is the main method used in early research. For example, the information flow between stock markets and future markets were explored in [64]. The correlation coefficient method is useful and easy to implement, whereas it cannot capture the causal relationship between different components. Therefore, the Granger causality test is introduced to describe the information flow in the financial system. For example, [PERSON] [65] utilized this method to characterize information flow for global markets, analyzing the influence of the time scale and efficiency on the flow. In the past decade, physicists have introduced the concept of information entropy into the financial system. A stream of research utilizes entropy-like methods such as the transfer entropy (TE) to characterize information flow in financial systems. The TE can estimate the impact of the history for one time series on another time series, quantifying the direction of information flow. The strengths and directions of information flow between worldwide stock indices has been investigated [21]. Likewise, global information transfer networks (GITN) for different time periods or market states have been constructed with the TE [66; 67]. The information flow between bitcoin and other financial assets was studied by [68]. [PERSON] [69] proposed the transfer entropy coefficient to quantify multi-scale information flow in financial systems. The Renyi transfer entropy (RTE) is applicable to asymmetric and nonlinear data, which can emphasize a special part of the distributions for observations, with wide applicability to various distributions such as fat-tailed distribution. This method is employed to analyze the information flow between different stock markets based on intraday stock data, considering the impact of a crisis [70]. Although the last few decades have witnessed a deeper understanding of topological structures, topological structure analysis cannot identify the specific role of nodes and edges in information flow networks, as well as the dynamic characteristics such as the response time of nodes, due to the financial system evolving with time and being full of random disturbance and complexity. On the other hand, researchers in different fields have adopted different models to study information flow in the financial system. Statistical models are utilized to describe the information flow between various elements. For example, a multi-period continuous information diffusion model was proposed to reveal the term structure of information flow [71]. Besides, agent-based models act as a powerful simulation technique to explore the microscopic mechanism of financial systems [57; 59; 60; 61]. To unveil the microscopic mechanism behind information flow in financial systems, an artificial stock market comprised of agents with limited information has been presented [72]. Epidemic models are also widely applied in the investigation of financial information flow, especially the financial risk propagation information flow [58; 62; 63]. Reference [58] explored how social influence affects individual investors' trading and stock returns with epidemic models [58]. A modeling framework based on epidemic models was proposed to analyze financial contagion during financial crises in [62].