The Risk Monitoring of the Financial Ecological Environment in Chinese Outward Foreign Direct Investment Based on a Complex Network

: Aiming at the risk problem of ﬁnancial ecological environment in outward foreign direct investment (OFDI), this paper constructs a risk monitoring model of the ﬁnancial ecological environment based on complex network theory, and analyzes the general laws of ﬁnancial risk evolution in Chinese OFDI by using data from 2008 to 2017 in 20 countries. First, the key risk factors are found through centrality analysis, then the correlation between risk indicators is obtained by cohesive subgroup analysis. Finally, we calculate network density, clustering coe ﬃ cient and global e ﬃ ciency to explore the time-spatial laws of the ﬁnancial risk evolution in OFDI are obtained. At the same time, Kruskal’s algorithm is used to generate the minimum spanning tree (MST), and the change trend of risk transmission path is obtained. The results show that the following four risk indicators: M2 / GDP, foreign exchange reserve, stock exchange turnover rate, total government debt as a percentage of GDP play an important role in the whole risk network and are the key nodes of risk evolution. The internal ﬁnancial risks in Pakistan, the United States, Israel and Poland are more complex and highly transmissible. The risk transmission path based on MST shows that Australia and Bulgaria play an important role in risk transmission, and the length of risk transmission path has an overall upward trend. The conclusions of this study have guiding signiﬁcance for overseas investment companies to prevent investment risks and ensure their sustainable development overseas.


Introduction
With the deepening of economic globalization and financial liberalization, international capital flows have gradually accelerated, and enterprises have begun to carry out large-scale cross-border investment activities. Since 2000, Chinese enterprises' OFDI has shown a rapid growth trend. According to the "2018 China Foreign Direct Investment Statistics Bulletin" (this report is available online at http://hzs.mofcom.gov.cn/article/date/201512/20151201223578.shtml) jointly issued by the Ministry of Commerce and other departments, in 2018, China's total net OFDI reached $143.04 billion, ranking the second in the world. The continuous expansion of Chinese enterprises' OFDI also means that China will face greater risks of OFDI. According to the China Global Investment Tracker database (a database was built by The Heritage Foundation; is https://www.heritage.org/) from 2005 to 2018, there were 3061 overseas investment and construction transactions for Chinese companies and 269 troubled transactions involving a total amount of US $381.02 billion. Compared with domestic investment, OFDI often faces a more complex and changeable international environment, and the field of OFDI is also increasingly diversified, which makes the risks of Chinese OFDI increasingly complex, emerging the characteristics of dynamic, comprehensive and complex. In this paper, the financial risk factors of OFDI are regarded as nodes of a complex network and the relationship between risk factors are regarded as the edge, thus forming a financial risk network in OFDI. It can be well combined with the real environment factors to analyze the characteristics of OFDI financial risks by using various parameters of complex network.
The innovation of this article is that in previous studies, risk assessments often considered risks to be independent and there is no correlation between indicators. However, in reality, risks cannot be completely unrelated. Therefore, considering the correlation between risks, this study introduces the complex network theory into the field of OFDI risks, constructing the risk monitoring model of financial ecological environment in an innovative manner. Firstly, this model considers the correlation and transitivity of risks, and measures the correlation and transitivity of risks by calculating network density and clustering coefficient. Secondly, this model finds out the key risk factors and the order of importance of the risk factors by calculating degree centrality, closeness centrality, betweenness centrality and eigenvector centrality of risk, and analyses the internal indicator correlation of financial risk evolution. Finally, the complex network model takes risk factors as nodes, different from most previous studies that all took entities such as financial markets or financial institutions as nodes. On the dimension of the model, most previous studies are based on the time dimension. This paper adds the spatial dimension and analyses the regional characteristics of risks and finds the shortest path of risk evolution based on MST. This model breaks through the traditional risk research methods, from the macro level to the micro level, the cause of the risk is explored.

Financial Risk and OFDI
Risk originates from uncertainty. In April 2007, the Risk Management Working Group of the Technical Authority of the International Organization for Standardization (ISO) discussed and formulated the "ISO 31,000 Risk Management Principles and Implementation Guidelines" as an international standard for risk management. The standard defines risk as "effect of uncertainty on objectives", which reveals the essence of risk accurately. Based on the definition of risk, this paper defines the environmental risks of OFDI as the uncertainty caused by the changes of the host country's macro environment, that is, the fluctuation of the host country's environmental factors. Scholars generally believe that the factors affecting the OFDI of enterprises include political risk, economic risk, and so on. The "International Country Risk Guide (ICRG)" (the ICRG assessment methodology was established in 1980 by the American International Reporting Group. In 1992, the founder of the ICRG assessment methodology switched to the PRS Group. ICRG conducts monthly risk assessments for 140 countries and conducts annual risk assessments for 26 countries. The ICRG assessment method provides a comprehensive assessment of three types of risk indicators (political, financial, and economic) and their 22 variables) published by the PRS Group divides national risks into political risk, economic risk and financial risk. Meldrum classified national risks into economic risk, transfer risk, exchange rate risk, location or neighborhood risk, sovereign risk and political risk [20]. Thomas and Grosse believe that the level of economic development, economic openness and political risk of the host country are the main factors affecting the risks of OFDI [21]. Al Khattab et al. pointed out that the risks faced in international investment projects mainly include natural, financial, cultural and political risks [22]. Based on the previous research results, this paper believes that the macro risk of OFDI can be divided into political risk, legal risk, financial risk, social risk and natural risk.
Among them, financial risk mainly refers to the possibility of foreign capital losses caused by changes in the stability of a country's financial system and financial markets, foreign debt quality, balance of payments and exchange fluctuations. Financial risk is one of the most important factors in the face of various types of risk sources for OFDI of contemporary enterprises, and it is also the most direct risk, mainly including exchange rate risk, interest rate risk and financing risk. In the whole process of OFDI, enterprises will be affected by exchange rate movements, which will affect the transaction price and the conversion income of accounting reports. Therefore, exchange rate risk should be paid attention to by enterprises. Interest rate risk refers to the possibility of loss due to the change of market interest rate. Financing risk mainly occur in the process of raising funds. Whether the huge amount of funds needed for OFDI can be raised in a timely manner, and the level of financing cost will obviously affect the performance of OFDI. In previous studies, Harris and Ravenscraft demonstrated that the wealth effects of cross-border mergers and acquisitions (M&As) cannot be explained by industry and tax variables. But it is positively related to the weakness of the U.S. dollar, indicating a significant role for exchange rate movements in OFDI [23]. Kiymaz verified that financial risk has a significant impact on the wealth effect of US cross-border M&As enterprises, and the wealth effect of cross-border M&As in developed countries is higher [24].

Research Status of Financial Risk Monitoring
Since the Asian financial crisis in 1998, government regulators have paid more attention to financial risk, and financial risk monitoring has once become a hot topic in academia. According to different research perspectives, financial risk monitoring research can be divided into the risk monitoring of some financial institutions within the financial system and the monitoring of the overall risk level of the financial system. The methods used are the model method based on market data and the index method based on macro data. We compared different methods from these two dimensions. The specific contents are shown in Table 1. The premise is to assume that the attributes are independent of each other It can be seen from the above literature that the measurement methods of systemic financial risk in domestic and foreign academic circles are rich and diverse, and each method has its own advantages and disadvantages. The model method based on market data mainly uses the loss of financial institutions as the unit to measure the contribution to systemic risk, and the construction method is mainly aimed at banks.These methods can track and monitor the systemic risk of financial institutions in real time based on the stock price data of financial institutions, which has good timeliness. However, the shortcoming of these methods is that they focus on analyzing the systemic risk of single financial institution. When multiple financial institutions are involved in each other's influence and contact, these methods lose their advantages. In addition, due to the limited availability of data in actual operation, it will take a long time to collect and arrange information, which is not conducive to dynamic monitoring and early warning of systematic risks.
In order to monitor the macro financial risk status of OFDI target countries, the indicator methods based on macro-data are more effective. The general idea is to construct the indicator system first and then combine it with other risk monitoring models. However, the existing researches only measure the systemic financial risk from one side, but fail to fully reveal the inherent complexity of systemic financial risk. Although the above methods can monitor the risk status systematically and comprehensively, they cannot effectively capture the multi-level characteristics such as path, speed, scope and depth of systemic risk network transmission. Therefore, the complex network analysis method is increasingly concerned by academia and regulatory authorities. Allen and Gale first used this method to study the relationship between financial structure and risk contagion [38]. Gai and Kapadia find that financial systems exhibit a robust-yet-fragile tendency: while the probability of contagion may be low, the effects can be extremely widespread when problems occur [39]. However, the existing related literature [40,41] focuses on the contagion effect between financial institutions or financial markets, and there are fewer studies using complex networks to study the internal evolution of financial risk.

Monitoring of Financial Ecological Environment based on Complex Network
Complex systems emerged as an independent discipline in the 1990s, while complex network method emerged in the late 1990s, which is considered as an effective method to study complex system. Since the pioneering work of WS small-world network model [42] and the BA scale-free network model [43] was published, there has been a upsurge of research on complex networks in various fields. Network theory has been gradually applied to economic and social science fields, such as financial networks [44], traffic networks [45] and social networks [46]. Network theory is also widely used to study contagion problems, such as the disease infection [47], herding effects in social sciences [48] and information transmission [49], etc. In recent years, complex network theory has been widely used in the study of risk contagion, and some scholars have studied the characteristics and evolutionary mechanism of risk transmission of complex network organizations [50].
The basic idea of complex network is to model a real complex system using network analysis method, then collect information between nodes and their edges in complex network, and study the properties of complex network nodes and edges through statistical analysis. The main advantage of complex network is that it can simplify the analysis process of problems. The internal evolution of risks is complex and difficult to observe, but complex network can obtain the law of risk evolution by calculating and analyzing different network parameters, so as to realize the monitoring for risk evolution. The main idea is to construct the complex network by using the financial risk indicators of OFDI as the nodes in the network, and the complex network can be constructed from two dimensions of time and space. We can find out the key risks by analyzing the centrality parameters, obtain the correlation of risk indicators by cohesive subgroup analysis. At the same time, we can use the network density, clustering coefficient, and global efficiency to analyze the connectivity and transitivity of the risks, so as to gain the time-spatial laws of the financial risk evolution in OFDI.

Ideas and Theoretical Prerequisites for Model Construction
Based on the previous analysis, this paper uses the complex network to construct the the risk monitoring model of financial ecological environment in OFDI. The basic idea is shown in Figure 1. For the financial risk network in OFDI generated by this paper, we first need to explore the prerequisites for its generation, so that the network model can be generated by UCINET (social network analysis software compiled by a group of network analysts at the University of California, Irvine) software.
Prerequisite 1: The financial risk indicators of OFDI are regarded as the nodes of complex network. Although the risk indicators that constitute the risk indicator system of OFDI are different, and the influence path of these factors on OFDI is also quite different, we treat all risk indicators as nodes of the financial risk network, except that they have certain differences in importance.
Prerequisite 2: The edges in the financial risk network in OFDI denote the correlation between indicators. In a general complex network, the edges of the network denote the correlation between nodes. Similarly, in the financial risk network in OFDI, the existence of the edge is also determined by whether there is a correlation between the risk indicators. When there is a correlation between the indicators, there are connected edges between the two nodes. When there is no correlation, there is no connected edge between the two nodes. Although there may be different types of correlation between the indicators, here we still only use one edge to connect the two nodes. That is to say, in the financial risk network in OFDI constructed in this paper, we only study whether there are edge between two nodes, instead of considering how many edges will be formed between two nodes. On the one hand it simplifies the model; On the other hand, it has no significant impact on the key parameters of risk transmission, which will be reflected in the following studies.
Prerequisite 3: Regarding the direction of the network, although the influence between the nodes is directional, and the complex ne twork can be divided into a directed network and an undirected network, but this has little to do with our research. We believe that the correlations between any two risk indicators are mutual, so this paper uses a undirected network complex network for modeling and research.
Based on the above basic prerequisites, this paper regards the financial risk indicators of OFDI as nodes and the correlation between nodes as edges, thus forming a financial risk network in OFDI.

Indicator System Construction
Regarding the financial risk indicator system, some scholars [51,52] adopted the indicator system of the International Country Risk Guide (ICRG) database. The database selected five indicators including foreign debt/GDP, foreign debt/total exports, current account/total exports, net liquidity and exchange rate stability to evaluate financial risks.
Some scholars [53] have supplemented the indicator system from the perspective of banks. In addition, scholars [54] have constructed the indicator system from the perspectives of financial institutions, stock market, bond market, currency market, foreign exchange market, real estate market and government departments. Based on the literature reading and analysis, this paper refers to the practices of Tao and Zhu [54] and analyzes the influencing factors of financial risks from four dimensions: interest rate risk, exchange rate risk, capital market risk and financing risk. Considering the availability of data and the representation of indicators, this paper constructs a financial risk indicator system as shown in Table 2.

Construction of Correlation Coefficient Matrix and Adjacency Matrix
Based on the above-mentioned financial risk indicator system for OFDI, the financial risk factors of OFDI faced by enterprises are quantified, and the correlation coefficient matrix is established by calculating the correlation coefficient between indicators. It is possible that the correlation coefficient is negative, but this paper only considers the closeness of the relationship between the two indicators without considering the directionality. Therefore, in order to deal with the problem conveniently, we uniformly take the positive value.
The relationship between nodes can be determined by the adjacency matrix. Whether there are edges between two nodes depends mainly on the correlation between nodes. According to the correlation coefficient matrix, the correlation coefficient between the two indicators can be obtained. To further determine whether the two nodes are connected by the edge, it is necessary to determine a threshold value according to the actual situation. If the correlation coefficient between the two indicators is less than the value, the nodes will not be connected, otherwise the two nodes will be connected. In this way, the adjacency matrix A = (a ij ) of financial risk factors for OFDI can be established, the meaning of a ij is as follows: a ij = 1, Node i is connected to node j 0, Node i is not connected to node j

Construction of Financial Risk Network in OFDI
Complex network usually consists of a set of nodes and edges, which can be illustrated by graphs. For the financial risk network in OFDI, it consists of risk indicators and the correlations between risk indicators. The adjacency matrix constructed based on the correlation coefficient matrix reflects the relationship between risk indicators, so the financial risk network in OFDI can be constructed by this matrix. In order to construct the financial risk network in OFDI, the following definitions are given: According to the above definitions, the financial risk network in OFDI can be constructed based on the adjacency matrix. It can be denoted by G = (V,E). Suppose there are N nodes and M edges in the network. V = {Q,ν 1 , . . . ,ν n } is used to denote the set of nodes, and nodes denote risk environmental factors. E = {e 1 ,e 2 , . . . ,e m } is used to denote the set of edges, edges denote the correlation between nodes.

Key Parameters of Risk Monitoring Model of Financial Ecological Environment
Based on the network model constructed in the previous paper and the characteristics of financial risk network in OFDI, this paper selects the following six network parameters as the key indicators of the risk monitoring model of financial ecological environment.

Key Risk Factors for OFDI
Centrality is an important parameter in complex network analysis. The centrality of nodes reflects the importance of nodes to some extent. However, there are some limitations in measuring the importance of financial risk indicators based on degree centrality. Therefore, this paper introduces parameters of betweenness centrality and closeness centrality, which can better reflect the influence of financial risk indicators from the aspects of direction and weight.

Degree Centrality
In undirected networks, degree centrality refers to the number of nodes connected to node n i . If a node is directly connected with many other nodes, it means that the node has a higher degree centrality. The degree centrality of node n i can be expressed as follows: In the study of risk network of OFDI, degree centrality should be given practical meaning, because there is more than a simple quantitative relationship between the degree centrality and network nodes (risk indicators) in the risk network of OFDI. For example, some risk indicators have a large degree of centrality, but the risks they generate are not large, while some risk indicators have a small degree of centrality, but they play an important role in the generation of risks. In the financial risk network, degree centrality indicates the correlation between a financial risk indicator and other risk indicators. The greater the degree centrality, the more important the indicator is. By calculating the degree centrality of risk indicators, we can find out the key risk indicators in financial risk.

Closeness Centrality
Closeness centrality is mainly measured by the reciprocal of the distance from one node to all other nodes (the number of edges passing through the shortest path), which denotes the location characteristics of the node in the network. The larger the value, the closer the node is to the center of the network, and the more important it is. Closeness centrality can be expressed as follows: where d(n i ,n j ) denotes the shortest distance between node n i and node n j . The larger the value of C c (n j ), the closer the node is to the center of the network. In the financial risk network, the closeness centrality is mainly measured by the reciprocal of the shortest distance from one risk indicator to all other indicators, which indicates the location characteristics of risk indicators in the network. The larger the value, the closer the risk indicator is to the center of the network, the more important it is.

Betweenness Centrality
Betweenness centrality refers to the ratio of the number of shortest paths passing through this node to the total number of shortest paths in the network. This parameter can explain the contribution of the node in maintaining the connectivity of the whole network. If there are more shortest paths passing through the node, the larger the value is, the larger the contribution of the node is. The stronger the control ability of the node is, the higher the importance is. Betweenness centrality can be expressed as follows: where g jk denotes the shortest path number from node n j to node n k , and g jk (n i ) denotes the shortest path number from node n j to node n k . In a financial risk network, the higher the betweenness centrality of a risk indicator, the more influential the risk indicator is, and the more important the indicator is.

Eigenvector Centrality
The importance of a node depends on both the number (that is, the degree) of its neighbors and the importance of its neighbors. The idea of eigenvector centrality is that the centrality of a node in a network is closely related to the centrality of its directly connected nodes. If the neighbor node has a larger centrality, the centrality of the node will also be improved. In the financial risk network in OFDI, if the risk contagion intensity or endurance intensity of other risk indicators that have a direct relationship with a risk indicator is greater, the risk transmission intensity or endurance intensity of the risk index will also be increased.
The eigenvector centrality index of the nodes in the network is proportional to the index of all the nodes connected to it, that is: where λ is a constant, x i is the index value of the i-th node, and A is the adjacency matrix of the network.
The matrix X is expressed as X = 1 λ AX, or AX = λX. Compared with other methods, Eigenvector centrality (EC) emphasizes the surrounding environment of a node. The importance of a node depends not only on the number of its neighbors, but also on the importance of its neighbors, which is more suitable for describing the long-term or global influence of nodes. In the financial risk network in OFDI, if the node's EC value is larger, the node is likely to be close to the source of infection or one of the sources of infection, and it is a key node that needs to be focused on or controlled.

Relevance of Financial Risk Indicators for OFDI
When the relationships between some nodes in the network are so close that they are combined into a sub-group, such a group is called a cohesive subgroup in network analysis. The analysis of how many such subgroups exist in the network, the characteristics of the relationship between the members within the subgroups, the characteristics of the relationship between the subgroups, the characteristics of the relationship between the members of one subgroup and the members of another subgroup, etc., are cohesive subgroup analysis. In this study, the correlation between risk indicators was obtained by cohesive subgroup analysis. As far as the financial risks of OFDI are concerned, the clustered risk indicators are more contagious, and the risk subgroups are more likely to evolve within each other. This study explores the correlation between risk indicators from two aspects: faction analysis and density analysis.

Faction Analysis
For the financial risk network in OFDI, cliques refer to the existence of correlations between risk indicators, which means that there is a direct line between any two points in the sub-graph, and the cliques cannot be included by other cliques in the network, that is, the faction is the maximal complete sub-graph. A complete sub-graph contains at least three points, and any two points are directly related.

Density Analysis
That is, external-internal (E-I) index, which is mainly used to analyze the degree of aggregation of subgroups in the overall risk network or the degree of distribution of the overall network. The E-I index is used to measure whether the phenomenon of small groups in a large network is serious. The calculation formula is as follows: where EL denotes the number of relationships between subgroups, IL denotes the number of relationships within the subgroup. The value of this index is between −1 and 1, the closer it is to 1, the more severe the phenomenon of small groups. When the cohesive subgroup density analysis is applied to the field of OFDI risks, if the cohesive subgroup density is high, it means that the risk indicators within the subgroup are closely related and communicate frequently in terms of information transmission, while they are less related to the indicators outside the subgroup.

Correlation of Risk
Network density (R) refers to the closeness of the connection between nodes in the network, which is the ratio of the number of connections actually existing in the network to the maximum number of connections that may exist. For financial risk network, density denotes the closeness of relationship between risk indicators, which can help to study the correlation of risk indicators. Therefore, this paper uses network density to measure the closeness of relationship between risk indicators in financial risk network. If the parameter value is 1, it means that each risk indicator is connected with all other indicators, and the parameter value of 0 means that none of the indicators is connected. For a financial risk network with n risk indicators, the parameter R can be expressed as follows: where L is the actual number of edges in the network and denotes the total number of edges connected by edges between n nodes.

Transitivity of Risk
Clustering coefficient (T) is an important parameter to measure the degree of collectivization of complex networks. It is a local feature quantity, which refers to the probability that two nodes directly connected to a given node are also directly connected to each other. The average clustering coefficient of risk indicators of the network is called network clustering coefficient. In this paper, we use network clustering coefficient to measure the transitivity between risks in financial risk network, which can be expressed as follows: where n denotes the total number of risk indicators in the financial risk network, and m i denotes the number of risk indicators connected with risk indicators i, k i denotes the number of connections between these risk indicators connected with risk indicators i. If a risk network has a high clustering coefficient, it indicates that the risk indicators in the risk network have good connectivity and the transitivity of risk is stronger. For example, if the clustering coefficient of the financial risk network is 0.5, it means that there is a 50% possibility that the two risk indicators connected to the same risk indicator in the network are also connected.

Risk Propagation Efficiency
The risk propagation efficiency € is measured by the global efficiency of the network and reflects the speed of risk information transmission in the financial risk network in OFDI. The concept of global efficiency of the network was proposed by V. Latora in 2001 to calculate the efficiency of the entire network to exchange information. The parameter E can be expressed as follows: where n denotes the total number of risk indicators in the financial risk network, and dij denotes the shortest path length between the two risk factors. E is between 0 and 1. The larger E is, the higher the efficiency of the entire network information exchange is. When E = 1, there is an edge between any two risk factors, that is, the network is fully connected; when E = 0, the shortest path length between any two risk factors is infinite, that is, all risk factors are isolated risks factor. In the financial risk network in OFDI, the global efficiency of the network reflects the speed of risk evolution. The higher the value of this parameter, the faster the risk spreads in the risk network. Based on the financial risk indicators constructed above and the selected monitoring parameters of risk evolution, this paper constructs complex networks from time and space dimensions respectively. Based on the network constructed above, UCINET software can be used to calculate the parameters selected in risk monitoring model of financial ecological environment, and the basic evolution characteristics of the risk network can be obtained by analyzing the key parameters. The monitoring model can find out three basic laws for the financial risk evolution in OFDI: The first is to get key risk factors. The evolutionary dynamics of financial risk are mainly derived from the various risk factors in the above risk indicator system. Therefore, it is important to identify key risks in the environment. The second is the correlation of risk indicators. Analyzing the relationship between indicators can provide a basis for effectively cutting off the transmission path of risk. The third is the overall characteristics of risk. including the time law and spatial law of risk evolution.

Data and Sample
According to the "2018 China Foreign Direct Investment Statistics Bulletin", by the end of 2018, Chinese OFDI stock in distributed in 188 countries (regions) around the world. In this paper, 20 countries including Australia, Pakistan, and Brazil were selected as research objects (the 20 countries are: Australia, Pakistan, Brazil, Bulgaria, Poland, The Philippines, Czech Republic, Romania, Malaysia, The United States, Mexico, South Africa, Nigeria, Japan, Saudi Arabia, Ukraine, Singapore, Israel, the United Kingdom, and Zambia), and the financial risk indicators of these countries in 2008-2017 were used as research data. The selection of these 20 countries is based on the following three criteria: (1) Is the investment activity true? The purpose of Chinese investment in these areas is not to take the place as a capital operation center for investment transfer or tax avoidance, but to conduct real investment activities. (2) Is the investment amount large? These 20 sample countries selected in this paper cover a wide range of regions, and Chinese enterprises have a large amount of investment in these countries, so they are widely representative. (3) Is the data available? The financial risk indicators in this paper are all quantitative indicators, which require a large amount of data support. Therefore, in this paper, the countries with large data missing are also excluded.
Based on the above screening conditions, 20 countries are selected as samples. The data on financial risk indicators are collected from WDI, EPS, Sina Finance, and Guo Yan Net. For a small number of missing data, we use the average of previous years or growth rate to calculated approximately.

Network Construction
The dynamic fluctuations in the financial environment within the host country make the network structure time-varying. Therefore, we divide the sample into 10 groups of data according to the year, each group contains 20 countries. Because there is no difference in X 1 in 2010 (X 1 is real effective exchange rate index, it is the ratio (expressed on the base 2010 = 100) of an index of a currency's period-average exchange rate to a weighted geometric average of exchange rates for currencies of selected countries and the euro area), the data for this year is excluded. Then we construct nine networks for 2008 to 2017 by UCINET. Due to length limitations, only the financial risk network in 2008 is shown here, as shown in Figure 2. The time law of risk evolution can be obtained by calculating and analyzing the parameters of each network separately. In addition, as the links between countries get closer, financial risks within host countries not only fluctuate with changes in the country's internal economic environment, but also are affected by international capital flows. The emergence of financial risks in one country will impact other countries, leading to the rapid spread of risks among countries, thus causing changes in global financial risks. In order to study the law of risk evolution among different countries, we divide the sample into 20 groups according to the country, and each group contains 10 years' data from 2008 to 2017, and uses UCINET to construct financial risk networks for 20 countries including Australia, Pakistan and so on. Due to length limitations, only the financial risk network in Australia is shown in this paper, as shown in Figure 3. The spatial law of risk evolution can be obtained by calculating and analyzing the parameters of each network separately.

Degree Centrality
According to the results of UCINET network analysis, the degree centrality of financial risk indicators for OFDI in 2008-2017 is shown in Table 3. Degree centrality can reflect whether a node is directly connected with other nodes. According to the results of degree centrality, the risk nodes with larger degree centrality are: M2/GDP, foreign exchange reserve, stock exchange turnover rate, total government debt as a percentage of GDP. We can find that the most important risk indicator is M2/GDP. M2/GDP is the inflation rate of money supply. The money supply can affect financial risk by affecting credit demand and supply. The inflation rate of money supply reflects the level of economic debt of a country, which is directly proportional to financial risk. The second is foreign exchange reserve, which is mainly used to liquidate the balance of payments deficit and to intervene in the foreign exchange market to maintain the exchange rate of the country's currency. It can effectively resist financial risk. The third is stock exchange turnover rate, which reflects the dynamism of stock transactions and also affects the macroeconomic prosperity. Finally, the total government debt as a percentage of GDP, this indicator reflects the degree of debt of the host government. The higher the debt, the government may adjust the relevant interest rate and tax policy, OFDI enterprises will face greater interest rate risk, which will affect the financial situation of enterprises. To sum up, for enterprises, the above four indicators are the key risk factors, and enterprises should focus on prevention.

Closeness Centrality
According to the results of UCINET network analysis, the closeness centrality of financial risk network in 2008-2017 is shown in Appendix B. Closeness centrality can measure the degree to which a node is not controlled by other nodes. The larger the value, the more the risk indicator is at the core position and the more independent it is. As shown in Appendix B, in the financial risk network, the closeness centrality ranking of the nodes such as M2/GDP, foreign exchange reserve, stock exchange turnover rate, total government debt as a percentage of GDP is relatively high, which is consistent with the results of the degree centrality. It means that these risk indicators are at the core of the network and have strong independence. For example, stock exchange turnover rate reflects the changes of stock market. The outbreak of the financial crisis in 2008 led to the rapid cooling of the stock market. The closeness centrality of stock exchange turnover rate declined, and its influence on financial risks of OFDI weakened. Then, with the recovery of the stock market, the position of stock exchange turnover rate in the network has become important again.

Betweenness Centrality
According to the results of UCINET network analysis, the betweenness centrality of financial risk network in 2008-2017 is shown in Appendix B. Betweenness centrality can reflect the degree of resource control of node C, that is, the extent to which information is transmitted from node A to node B depends on node C. The higher the value, the more obvious the mediation effect of the node, and the stronger the ability to control other nodes. The results in Appendix B show that the betweenness centrality of "M2/GDP" and "total stock transactions as a percentage of GDP" always ranks the top two, which is consistent with the results of degree centrality. It shows that these two risk indicators are not only closely related to other risk indicators, but also have a strong control effect on the entire financial risk network, but the control ability of "M2/GDP" is weakening.

Eigenvector Centrality
According to the results of UCINET network analysis, the eigenvector centrality of financial risk network in 2008-2017 is shown in Appendix B. The idea of eigenvector centrality is that if the centrality of a node's neighbors is greater, the centrality of that node will also be improved. According to the results in Appendix B, in the financial risk network in OFDI, the risk nodes with larger eigenvector centrality are: M2/GDP, foreign exchange reserve, stock exchange turnover rate, total government debt as a percentage of GDP. The results are basically consistent with the results of degree centrality, indicating that these risk indicators are not only key risks themselves, but the indicators adjacent to them are also of some importance.

Correlation of Risk Indicators
Based on the analysis of centrality, we can find out which indicators are critical to the financial risk environment. In order to further understand the correlation of risk indicators, we conduct a cohesive subgroup analysis of risk indicators. Cohesive subgroup refers to a small group structure formed by a closer relationship between risk indicators. Through cohesive subgroup analysis, the overseas investment financial risk network can be divided into several more concentrated risk subgroups, and the correlation between the risk subgroups and the risk subgroups can be analyzed, and the risk correlation characteristics of the overseas investment risk environment can be obtained.

Faction Analysis
First, UCINET was used to divide the risk indicators into three cliques by using Network→Subgroups→ faction path. Factions analysis is to find out the risk subgroups in the financial risk network. Risk indicators located in the same subgroup are more closely related.
It can be seen from Table 4 that the financial risk indicators are divided into three cliques, each of which contains specific risk indicators, and the correlation between indicators within the same clique is stronger. The members of cliques are in constant change, but there is no significant change, and there are some basic rules. The indicators X 2 , X 3 , and X 5 ; X 4 and X 7 ; X 6 and X 12 are always located in the same clique, indicating that these pairs of indicators have a high correlation. Although the members of the cliques do not change much, the density within each clique and between cliques has a certain change. The results are shown in Table 5. X 6 X 9 X 10 X 12 X 4 X 6 X 12 X 13

Density Analysis
We have just analyzed the internal relevance of risk subgroups. In order to further study the external relevance of the above risk subgroups, we need to analyze the density of cohesive subgroups (E-I index) to obtain the degree of closeness of risk subgroups in different years. It can be seen from Table 5 that among the three risk cliques, the connection density of the first clique is always the highest, and it is the riskclique with the closest internal connection. Among the associations between risk cliques, the communication between the first clique and the second clique was the closest before 2013. After 2013, the first clique and the third clique also began to be associated, increasing the overall relevance of risks.

The Overall Law of Risk Evolution
In the above research, we analyzed the importance and relevance of financial risk indicators from the perspective of network nodes. Next, we further calculate the overall parameters of the network from the perspective of the overall risk network, based on the two dimensions of time and space, and analyze the evolution characteristics of the financial risk environment. From the time dimension, we can analyze the dynamic fluctuation trend of financial risks over time. From the spatial dimension, we can measure the risk contagion probability and contagion speed of each host country.

Time Law of Risk Evolution
We used the Ucinet software to calculate the network density and network clustering coefficient of complex networks in each year. The results are shown in Figure 4. As can be seen from the figure, the fluctuations of network density and clustering coefficient are relatively large. From 2008 to 2011, affected by financial crisis, the financial market was increasingly depressed, OFDI reduced, and the network density and clustering coefficient reached the bottom. After 2011, the impact of the financial crisis gradually receded and the financial market began to flourish. OFDI became more frequent, the network density and clustering coefficient ushered in a substantial increase, and then tended to be stable. Since 2016, the network density and clustering coefficient have tended to grow, indicating that under the trend of globalization, the financial risk environment has become increasingly complex, and the correlation between risks has increased. The change of a risk factor will lead to the rapid spread of risks and eventually lead to the outbreak of financial risks.

Analysis of Risk Characteristics
We used the Ucinet software to calculate the network density and network clustering coefficient of complex networks in different countries. The results are shown in Table 6. Network density indicates the tightness of the whole network connection. In terms of the network density of financial risk network, Pakistan, the United States, Israel have higher network density. It means that the financial risk environment of these countries is more complex and the risk is more closely related, that is, the risk has strong correlation; Clustering coefficient represents the degree of node clustering in the network. According to the results of clustering coefficient, the financial risk network in Pakistan, the United States, Israel have a high clustering coefficient, and both are greater than 0.5. This is consistent with the results of network density, indicating that the financial risk indicators in these countries are not only closely related, but also have a centralized trend, that is, the risk has a strong transitivity; The global efficiency of the network reflects the speed of risk evolution. From the results of the global efficiency of the network, Pakistan, the United States, Poland and other countries get higher rankings, indicating that when the host country has the same hidden risks, the risk spreads fastest in these countries.The analysis results based on network density, clustering coefficient and global efficiency show that under the same fluctuation of risk factors, the financial risk correlation in Australia, the United States, Israel, Poland and other countries is more complicated, the risk transitivity is stronger, and the investment in these countries is more likely to suffer financial risks.

Risk Transmission Path
After finding the important countries, in order to further analyze the relationship between financial risks among different countries, this paper constructs the MST to find the most possible transmission path of risk among countries. The basic principle of MST is based on greedy algorithm (a greedy algorithm means that when solving a problem, it always makes the best choice at the moment. That is to say, instead of considering the overall optimality, what it does is a local optimal solution in a certain sense). MST is a tree structure with n-1 edges formed by n nodes in a system. The edge set is the edge combination with the smallest weight and guarantees that no loop is formed, so MST has good robustness. In this paper, MST represents the strongest connection in the network. When MST is unique, it means it is the most possible risk transmission path in the financial network. That is, when a country's financial environment is exposed to external shocks and risks occur, risk may spread to other countries along this risk transmission path at the fastest speed.
Before generating the MST, pearson correlation coefficient between country i and country j needs to be calculated. The calculation method is as follows: where cov denotes covariance, σ i and σ j denote the standard deviation. Because the correlation coefficient does not satisfy the condition of metric space, this paper uses the practice of Mantegna [55] as a reference to convert the correlation coefficient into the distance between countries. The formulas is as follows: Then Kruskal's algorithm is used to calculate the distance matrix, and the MST is obtained (the critical codes to generate MST are listed in Appendix A). The MST for 2017 is shown in Figure 5. By analyzing the most possible transmission path of financial risk, we conclude the following characteristics: Firstly, the minimum spanning tree consists of 20 sample countries. According to the meaning of MST, we believe that the countries with more countries connected are the crucial countries for risk transmission. Therefore, Australia and Bulgaria are crucial countries for risk transmission among the 20 countries. Secondly, the MST of 20 countries can be roughly divided into four modules, For example, Bulgaria, Pakistan, Ukraine, and Zambia are combined to form a module, indicating that the financial risks of these four countries are closely related.
In addition, the length of the MST changes with time as shown in Figure 6. Generally, the shorter the length of the tree, the closer the relationship between countries. Figure 6 shows that after the 2008 financial crisis, the length of the tree was gradually decreasing, reaching a minimum in 2012. This shows that after the financial crisis, the financial market began to adjust. With the gradual recovery of the market, the links between countries became closer and closer, and the risk transmission was faster. After 2014, the length of the tree began to rise, indicating that the relationship between countries began to decline, and the path of financial risk transmission was longer, which was a good signal for OFDI enterprises.

Conclusions
Through theoretical study of complex network model, based on the empirical analysis framework of "theoretical analysis-model construction-variable selection-network parameters analysis", this paper first constructs the the risk monitoring model of financial ecological environment. Through identifying the financial risk factors of OFDI, a risk indicator system including exchange rate risk, interest rate risk, capital market risk and financing risk is constructed. The financial risk data of 20 OFDI countries from 2008 to 2017 are selected as sample data for empirical analysis. By analyzing the characteristic parameters of the network model, the general laws of financial ecological environment risk in Chinese OFDI are obtained. The main conclusions of this paper are as follows: The first is the importance of financial risk indicators of OFDI. M2/GDP, foreign exchange reserve, stock exchange turnover rate and total government debt as a percentage of GDP rank high in the degree centrality, indicating that these four risk indicators play an important role in the risk network and are the key nodes of risk evolution; At the same time, the result of closeness centrality is consistent with that of degree centrality, which means that these risk indicators are located at the core of the network and have strong independence. In addition, the betweenness centrality of the percentage of M2/GDP always ranks first, which is consistent with the result of degree centrality. It means that this indicator is not only closely related to other risk indicators, but also has a strong control effect on the whole financial risk network. However, the control ability of this indicator tends to weaken. Enterprises should focus on monitoring the fluctuations of the above indicators when conducting risk warnings.
The second is the relevance of financial risk indicators of OFDI. The following pairs of indicators are strongly correlated: Foreign exchange reserves, M2/GDP, and total government debt as a percentage of GDP (%); M2 growth and economic growth; inflation rates and non-performing loan ratio. These indicators should be monitored simultaneously. Usually, the abnormal fluctuation of one indicator will cause the change of another indicator, which will spread to the whole financial risk network and lead to the outbreak of financial risks.
The third is the overall evolution of financial risks on OFDI. In the time dimension, since 2016, network density and clustering coefficient have tended to grow, indicating that under the trend of globalization, the financial risk environment has become increasingly complex, the correlation between risks has increased. The change of a risk factor will lead to the rapid spread of risks and eventually lead to the outbreak of financial risks. In the spatial dimension, among the 20 sample countries, countries such as Pakistan, the United States and Israel have higher network density and clustering coefficient, which indicates that the financial risk within these countries is more complicated, risk transitivity is stronger, and the investment in these countries is more likely to suffer financial risks. Enterprises should avoid or be more cautious in choosing these countries as destination countries for OFDI, and the Chinese government should also increase its review of investment projects invested in these countries. The risk transmission path based on MST shows that Australia and Bulgaria are important countries for risk transmission. Since 2014, the length of risk transmission path has increased, that is, the path of financial risk transmission has been longer, which is a good signal for OFDI enterprises.
The contribution of this paper lies in introducing the method of complex network analysis into the study of OFDI financial risk, constructing the the monitoring model of financial risk evolution in an innovative manner, describing the general laws of inancial ecological environment risk in OFDI. The conclusions of this study have guiding significance for overseas investment companies to prevent investment risks and ensure their sustainable development overseas. Meanwhile, it can provide references for relevant departments to make policies. We acknowledge some limitations to our study. Due to the lack of complete data, we have to exclude some countries and only select 20 countries as samples. We believe that we could further extend the present study to enhance the credibility of the conclusion when the data becomes available.