# Prediction of the Potential Trade Relationship of Lithium-Ion Battery’s Main Element Raw Material Minerals Combined with the Local Characteristics of the Trade Network

Authors: Yichi Zhang; Zhiliang Dong; Sen Liu; Qiaoran Yang; Yanjing Jia
Journal: International Journal of Energy Research
 (2023)

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## Abstract

In recent years, with the rapid development of the lithium-ion battery industry, the massive upstream consumption of mineral raw materials has led to great crises and challenges in balancing global supply and demand. A diversity of trading partners can effectively alleviate the pressure of supply and demand for raw materials; so, it is particularly important for trading countries to find suitable trading partners. This study takes nine important minerals contained in the main element raw materials of lithium-ion batteries as the research object, and the international trade data range from 2011 to 2020. The study combines complex networks and motifs and links prediction methods to predict the potential international trade relations of the nine minerals based on the actual network topology. We summarize three trade link rules as follows. (1) The predicted links have a timeliness requirement, and they generally turn into actual trade links within 3 years. (2) When looking for trading partners, trading countries tend to establish long-term and stable trade relations. (3) The existing trade relations will promote the establishment of predicted trade relations. In addition, we find that successfully predicted links will promote the formation of important motifs in the network. This study can provide a theoretical basis for trading countries to find suitable trading partners and can strengthen the safety of trading countries in the trade of the main element minerals for lithium-ion batteries.


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## Body

## 1. Introduction

Energy is the material basis for human survival and social development. However, with the rapid development of the global economy, problems, such as energy shortages, ecological deterioration, and environmental pollution, have gradually deepened in recent years. Energy issues have become an important factor that affects the international political and economic situation [1]. The concept of sustainable development has gradually penetrated countries and even enterprises [2]. At present, the world’s energy consumption is mainly based on fossil energy. Because of its nonrenewable nature, traditional fossil energy has been continuously extracted with the development of human society and has become increasingly exhausted. The energy crisis that faces humankind is becoming increasingly serious; thus, it is urgent to find alternative energy sources [3]. In this predicament, lithium-ion batteries have become the dawn of human society’s energy development, and their importance has become increasingly prominent.Lithium-ion batteries have many advantages, such as a high energy density, high output power, good safety performance, long cycle life, and clean and pollution-free operation, and occupy an important position in the development and utilization of new energy [4]. In recent years, the market for lithium-ion batteries has shown a rapid growth trend. Lithium-ion batteries have been on the market for less than 30 years but already account for 85% of the global rechargeable battery market (excluding lead-acid batteries) [5]. The rapid development of the lithium-ion battery industry has attracted the attention of global resource issues. The use of lithium, nickel, cobalt, graphite, and other mineral raw materials in lithium-ion batteries accounts for 50-70% of the total cost of lithium-ion batteries [6]. The massive consumption of raw mineral materials has put tremendous pressure on the global supply. However, the distribution of mineral resources in the world is extremely uneven [7], and few countries can rely only on their own reserves to meet the needs of industrial production. Therefore, countries export superior minerals and import scarce minerals through frequent import and export trade to achieve a balance between supply and demand.With the development of international trade theory, the application of mathematical model and physical model in international trade is increasing gradually. Examples include input-output analysis [8], regression clustering [9], trade gravity models [10], and complex networks [11]. Since the end of the 20th century, two pioneering research achievements have emerged in complex network research: small-world network models (WS models) [12, 13] and scale-free network models (BA models) [14, 15]. Since then, complex networks have become an important interdisciplinary research method and have been widely used in many research fields [16–20]. With the in-depth development of trade globalization, in recent years, complex networks have been widely used in the study of the international mineral trade. Through the analysis of network topology indicators, the overall pattern and evolution characteristics of international trade can be well reflected [21]. Some scholars have explored the trade network of a single mineral [22–24], and some studies have examined the trade network of multiple mineral resources [25]. These studies provide good ideas for the analysis of the international trade network of minerals, but there are still gaps in the current research on the multimineral trade network of the industrial chain.The current international trade situation is faced with the adverse effects of epidemics, war, geopolitics, etc. In this context, it is increasingly important to find new trading partners accurately. As emerging methods in the research of complex networks, link prediction provides a new direction for the study of international trade relations. Through information such as known network nodes and the network structure, link prediction predicts the possibility of a connection between two network nodes that have not yet formed an edge [26, 27]. Link prediction has important applications in network reconfiguration [28], network evolution model evaluation [29], recommendation system [30], etc. Initially, the research on link prediction mainly focused on improving the accuracy of the algorithm and the innovation of new algorithms [26, 31–35]. Gradually, link prediction is widely used in the exploration of citation networks [36], cooperation networks [37], traffic networks [38], and social networks [39]. In recent years, Guan et al. [40], Feng et al. [41], Liu and Dong [42, 43], Zhang et al. [44], and Yang et al.[45] applied link prediction algorithms to explore the rules for the formation of trade relations in international mineral trade networks. The studies of the above scholars indicate that these algorithms are effective in finding potential trade link relationships, but they are all concerned with undirected prediction and do not incorporate trade direction information into the prediction research. We consider that the link prediction method can well analyze the global characteristics of international trade, but its analysis results lack local trade structure information. In reality, for the international trade of a single product, a country often has fixed and few major trading partners; so, the analysis of the local trade structure is very important reference information for a country to find new trading partners. In order to make up for the limitations of link prediction method, we combined the motif method to study.The motif [46], as a basic structural unit that appears repeatedly and is statistically significant in the network, plays an important role in the evolution and optimization of the network [47, 48], and with the development of motif research, this concept has also been widely used in the study of empirical networks, including biological systems [49], transportation [50], business [51], virus transmission among societies [52], and international trade [53, 54]. These studies have proven that the application of motifs in different fields can provide effective research perspectives for the pattern characteristics of subjects in the network, but the analysis often focuses only on the mining of statistically significant structural units and the pattern features presented by the network neutron graphs, not enabling the combination of the motif analysis results with other analysis methods. The motif provides a good direction for the analysis of the local trade structure in international trade networks and makes up for the limitations of link prediction methods. Therefore, this article combines these two methods to jointly explore the formation of international trade relations in the main element minerals of lithium-ion batteries.Based on this, this article selects 9 important minerals contained in the main element raw materials of lithium-ion batteries as the research objects (Al, C, Co, Cu, Fe, Li2CO3, Mn, Ni, and Ti) to build complex networks of international trade [55]. We construct a new forecasting method that introduces the concept of motifs on the basis of link prediction to explore the characteristics of the successful prediction of trade relations. By introducing the motif, we can better explore the characteristics of trade relationship formation and compensate for the details lost by the overall average indicators to help trading countries find new partners on the basis of the existing trade topology and enhance their trade security.This paper is organized as follows. Section2 introduces the data and methods. In Section 3, we forecast the potential international trade relations of nine minerals. Finally, Section 4 contains the discussion and conclusion.


## 2. Data and Methods

### 2.1. Data Source and Processing

Song et al. [55] constructed a critical raw material (CRM) evaluation model that defined 9 critical mineral raw materials used upstream in the lithium-ion battery industry chain. This article takes these 9 critical minerals as the research object; the data come from the UN Comtrade Database (https://comtrade.un.org/data/) and include the import and export trade data of 9 mineral resources in 254 trading countries or regions around the world from 2011 to 2020. The specific mineral names and codes are shown in Table 1 below.Table 1
Resource classification and coding.
Critical mineralHS codeCode cited in the paperNickel2604NiCobalt2605CoGraphite250410CLithium carbonate283691LiCIron2601FeManganese2602MnCopper2603CuAluminum2606AlTitanium2614TiThe data downloaded by the UN Comtrade Database are two-way report data, including imports and exports, and there may be accidents, such as the duplication of data records and unequal records on both sides of the trade. In data processing, when the same trade stream is repeatedly recorded and the values are not equal, a smaller value is deleted, and a larger value is retained. The smaller value may be caused by statistical negligence. Regarding the trade flow with the international code “other areas,” since this trade flow accounts for a small proportion of the total global trade volume, this article considers only the global goal and retains only the countries and regions with the International Organization for Standardization (ISO) country code. Other unnamed trade flows are ignored.As many countries and regions as possible are involved in the analysis to present a concise and intuitive result to readers, the names of all countries/regions contained in the figures and tables in this paper are represented by the two letters of ISO2.


### 2.2. Methods

Figure1 shows the flow chart of this study. First, after preprocessing the international trade data of the nine critical minerals, nine complex networks were constructed. Then, the power law distribution characteristics of the nine networks were tested. Next, on the basis of complex network construction, a link prediction model analysis and motif recognition were carried out. Finally, the analysis results of the two methods were substituted into the model of potential links in international trade to find potential international trading partners. The concrete realization process and theoretical basis of each step in the flow chart are explained in detail in this section.Figure 1
Flow chart of experimental methods.


#### 2.2.1. Complex Network Construction

After processing the original data downloaded from the UN Comtrade Database, a complex directed weighted international trade network of nine minerals is constructed, with countries as the nodes, trade relations between countries as the edges, trade direction as the edge direction, and trade value (US$) as the edge weight. Trade value (US$) is chosen as the weight of an edge because trade value (US$) takes into account the dual attributes of the trade volume and mineral price, and at the same time, it is unified in dimension, which is conducive to a horizontal comparison between different minerals.From 2011 to 2020, a network is constructed every year. The main element raw materials of lithium-ion batteries comprise 9 types of minerals, which generate a total of 90 complex networks of international trade. Figure2 is a schematic diagram of the complex network of LiC international trade in 2020. Each node in Figure 2 corresponds to different countries in the trade, and the edges represent the trade relations between countries. The size of each node is distinguished by the weighting degree. When the weighting degree is larger, the node is larger, and the thickness of the edge represents the amount of trade. Figure 2 shows the top ten countries in terms of weighting in the international LiC trade in 2020. These countries are extremely active in trade, form a large number of trade relations and occupy most of the trade flow.Figure 2
Complex network of LiC international trade in 2020.


#### 2.2.2. Verification of the Power Law Distribution

To verify whether a network belongs to the category of complex networks, it is necessary to verify the power law of the network. The so-called power law of the network means that the connection status (degree value) between nodes is extremely uneven. A few hub nodes in the network have many connections, while most other nodes have only a few connections. This paper uses the constructed network model to calculate the degree value of each node in the mineral trade network and determines whether the network is a complex network by observing the fitting of the double logarithmic power law distribution between the node and the degree [21]. Figure 3 shows the fitting diagram of the power law distribution of the nine minerals in 2020, and Figure 4 shows the goodness of fit results of the nine minerals from 2011 to 2020. The power law of the 9 mineral trade networks is well fitted, and the goodness of fit is above 0.6. This shows that the 9 mineral international trade network models constructed in this paper conform to the definition of complex networks, and the subsequent analysis of their network evolution characteristics is reliable.Figure 3
Power law distribution fitting diagram of 9 minerals in 2020.Figure 4
Goodness-of-fit results of 9 minerals from 2011 to 2020.


#### 2.2.3. Link Prediction Model Construction

Link prediction refers to predicting through information, such as the known network nodes and network structure, the possibility of a connection between two network nodes that have not yet formed an edge [26, 27]; it enables the prediction of network links through an algorithm definition, test set division, finding unknown edges, and algorithm accuracy evaluation.At present, many scholars have applied the link prediction algorithm to the analysis of the international mineral trade network [40–44], which proves the feasibility of the method in the analysis of the international mineral trade. Based on the research of the above scholars, this paper expands the undirected link prediction model, adds direction information, and builds a directed link prediction model. The construction process is described as follows:(1) Step 1: Algorithm Selection. Common neighbors (CN), Adamic-Adar (AA), resource allocation (RA), and preferential attachment (PA) are the four mainstream algorithms in the current link prediction research. The following discussion briefly introduces these four algorithms in combination with international trade.(i) CN Algorithm. The basic assumption of the CN indicator is that if two unconnected nodes have more common neighbors, then they are more inclined to connect edges. Correspondingly, in international trade, if two countries have more common trading partners, then it is more likely that the two countries will establish a trade relationship. The calculation formulas are as follows. Formula (1) is an unweighted algorithm that does not consider the trade volume, and Formula (2) is a weighted algorithm that considers the trade volume.
(1)SxyCN=Γoutx∩Γiny.In Formula (1), x and y represent two countries that participate in international trade, Γoutx identifies the set of exporting countries of country x, Γiny indicates the set of importing countries of country y, and Γoutx∩Γiny denotes the number of all trading countries that import from country x and export to country y.
(2)SxyCN=∑z∈Γoutx∩Γinywxz+wzy2.In Formula (2), z is the trading country that imports from country x and exports to country y, and wxz and wzy represent the trade volume between country z and country x and between country z and country y, respectively.(ii) AA Algorithm. The idea of the AA indicator [33] is that the contribution of common neighbor nodes with a small degree value is greater than the contribution of common neighbor nodes with a large degree value. Formula (3) is used when weight is not considered, and Formula (4) is used when weight is considered.
(3)SxyAA=∑z∈Γoutx∩Γiny1logkz,(4)SxyAA=∑z∈Γoutx∩Γinywxz+wzylog1+sz.In Formula (3), kz is the number of countries that have trade relations with country z. In Formula (4), sz represents the strength of node vz, that is, the sum of the trade volume of country z in international trade. sz=∑i∈Γzwzi, where i is the country that trades with country z.(iii) RA Algorithm. Inspired by the process of network resource allocation [56], Zhou Tao and other scholars constructed an RA algorithm that is similar to the AA algorithm [26]. Considering two countries x and y that have no direct trade relationship in international trade, their common neighbors can be the medium of transmission that transfers the resources of country x to country y, and the number of resources accepted by country y can be defined as the similarity between country x and country y. Formula (5) is used when weight is not considered, and Formula (6) is used when weight is considered.
(5)SxyRA=∑z∈Γoutx∩Γiny1kz,(6)SxyRA=∑z∈Γoutx∩Γinywxz+wzysz.(iv) PA Algorithm. The idea here is that countries with more trading partners more easily establish new trade relations. Formula (7) is used when weight is not considered, and Formula (8) is used when weight is considered.
(7)SxyPA=Γoutx×Γiny,(8)SxyPA=∑j∈Γoutxwxj×∑q∈Γinywyq.In Formula (8), j represents the country that imports from country x; similarly, q represents the country that exports to country y.(2) Step 2: Divide the Training Set and Test Set. To further test the accuracy of the algorithm, we randomly select 10% of the existing trade links (E) as the test set and record it as ET; then, we use the remaining 90% of the trade links as the training set and record it as ER.
(9)E=ET+ER,ET=10%∗E.(3) Step 3: Find Links That Do Not Exist. To predict potential trade relations in international trade, we must first find links that have not yet existed in the trade network. Assume that there are n countries that participate in the international trade of a certain commodity; then, the set U that represents all possible trade links between these countries can be calculated by Formula (10); therefore, the set EI that identifies nonexistent links can be calculated by Formula (11).
(10)U=n∗n−12,(11)EI=U−E.(4) Step 4: Sort the Scores of the Links inEI. The four mainstream algorithms of CN, AA, RA, and PA are used to calculate the trade relations in EI, which are sorted according to the score. When the score is higher, the nonexistent trade relationship will more likely be transformed into a real trade relationship in the future.(5) Step 5: Evaluate Each Algorithm and Select the Best One. The area under the curve (AUC) is the most commonly used indicator to measure the accuracy of link prediction algorithms. The idea is that there is a greater probability of randomly selecting a higher score edge in ET than in EI. The calculation process randomly selects an edge from ET every time and then randomly selects an edge from EI. If the score of the edge in ET is higher than the score of the edge in EI, then 1 point is added, and if the score is equal, 0.5 point is added. Repeat the comparison n times, where n′ represents the number of times that the score of the edge in ET is higher than the score of the edge in EI, and n" represents the number of times that the scores of both sides are equal. Then, the AUC can be calculated by using Equation (12).
(12)AUC=n′+0.5n"n.According to Equation (12), if all the scores are generated randomly, then AUC≈0.5; therefore, an AUC greater than 0.5 measures the accuracy of the algorithm; that is, when the AUC score is higher, the corresponding algorithm is more accurate.


#### 2.2.4. Network Motifs

Network motifs are patterns of interconnections that occur in complex networks at numbers that are significantly higher than those in randomized networks [46]. Mining the motifs in the international trade network can better explore the characteristics of trade relationship formation and compensate for the details lost by the overall average indicators.(1) Definition of Motif. Motifs are network subgraphs that meet the following conditions:The probability is very small that the number of times that the subgraph appears in the random network that corresponds to the empirical network is greater than the number of times that it appears in the empirical network, and the probability is usually required to be less than a certain thresholdP, such as P=0.01(1)
The number of times that the subgraph appears in the empirical network (Nreal) is not less than a certain lower limit U, such as U=4(2)
The number of times that the subgraph appears in the empirical network (Nreal) is significantly higher than the number of times that it appears in the random network (Nrand), and the general requirement is that Nreal−Nrand>0.1Nrand(2) Basic Form of a Motif. The three-motif form is the most commonly used subgraph in the mining of various network structures. Although the number of subjects can be gradually increased, the number of motifs that exist between subjects will increase exponentially, which greatly increases the complexity of motif recognition and the difficulty of analyzing the related information between subjects. Moreover, existing studies have shown that the motif patterns of more than four subjects can be formed by combining the various motif patterns of three subjects [57]. Therefore, the recognition of three motifs can satisfy the mining of local structural features in the international trade network of the main element raw materials of lithium-ion batteries.The number of three-motif forms in different network types is different. For example, there are only 2 forms of three motifs in undirected and unweighted networks, 7 forms in undirected and weighted networks, and 13 forms in directed and unweighted networks. Because the international trade networks constructed by this study are directed networks and as the focus of this paper is to explore the local trade links between countries in the trade network while not focusing on the transmission of the local trade volume between countries, this study chooses the directed and unweighted motif form for mining. The 13 forms of directed and unweighted motifs are numbered here, as shown in Figure5 below.Figure 5
Directed and unweighted three motifs.(3) Statistical Significance of Motifs. The statistical significance of motifs refers to whether the motif is a local structure unique to empirical networks rather than randomly generated and is often used to describe its importance to the formation and evolution of the network structure [47, 48]. In this paper, the Z score is used to measure the statistical significance of the motif, and the specific calculation formula is Equation (13).For motif (Mi), the number of times that it appears in the empirical network is recorded as Nreali, the number of times that it appears in the random network is recorded as Nrandi, and the average value of Nrandi is recorded as <Nrandi>. The standard deviation is σrandi. Then, the Z score of Mi in the empirical network is
(13)Zi=Nreali−<Nrandi>σrandi.


#### 2.2.5. Analysis Model of Potential Links in International Trade

Directed link prediction and motifs can be used to mine the network structure information from the overall and local aspects, respectively. Therefore, this article combines these two methods to construct an analysis model for the international trade of the main element minerals of lithium-ion batteries, explore the formation rules of international trade relations, and determine the potential trade links that are most likely to be transformed into real trade relations. The specific steps are as follows.(1) Step 1: Identify the Key Motif. To explore the characteristics of the formation of trade relations from a local perspective, this paper identifies the key motifs in the complex network of the international trade of the nine minerals and analyzes the local trade structures with statistical significance in the trade network.(2) Step 2: Verify the Validity of the Link Prediction Model. Based on the link prediction model, the predicted potential trade relationship is compared with the actual trade relationship. By counting the number of potential trade relations successfully transformed into actual trade relations, the success rate of prediction is calculated to verify the validity of the link prediction model.(3) Step 3: Explore the Rules of the Successful Prediction of Trade Links. The potential trade links that were successfully predicted in the nine mineral trade networks are individually selected, and the rules of their successful predictions are explored from the overall and local perspectives. In general, this paper analyzes three aspects, namely, the timeliness of forecasting, the stability of trade relations, and the influence of past trade relations. At the local level, the motif method is used to explore the influence of successfully predicted links on the local structure of the trade network.(4) Step 4: Look for High-Quality Potential Trade Relations. According to the trade rules summarized in step 3, screen the potential links predicted and demarcate the potential trade relations with a high possibility of establishing real trade relations.


## 2.1. Data Source and Processing

Song et al. [55] constructed a critical raw material (CRM) evaluation model that defined 9 critical mineral raw materials used upstream in the lithium-ion battery industry chain. This article takes these 9 critical minerals as the research object; the data come from the UN Comtrade Database (https://comtrade.un.org/data/) and include the import and export trade data of 9 mineral resources in 254 trading countries or regions around the world from 2011 to 2020. The specific mineral names and codes are shown in Table 1 below.Table 1
Resource classification and coding.
Critical mineralHS codeCode cited in the paperNickel2604NiCobalt2605CoGraphite250410CLithium carbonate283691LiCIron2601FeManganese2602MnCopper2603CuAluminum2606AlTitanium2614TiThe data downloaded by the UN Comtrade Database are two-way report data, including imports and exports, and there may be accidents, such as the duplication of data records and unequal records on both sides of the trade. In data processing, when the same trade stream is repeatedly recorded and the values are not equal, a smaller value is deleted, and a larger value is retained. The smaller value may be caused by statistical negligence. Regarding the trade flow with the international code “other areas,” since this trade flow accounts for a small proportion of the total global trade volume, this article considers only the global goal and retains only the countries and regions with the International Organization for Standardization (ISO) country code. Other unnamed trade flows are ignored.As many countries and regions as possible are involved in the analysis to present a concise and intuitive result to readers, the names of all countries/regions contained in the figures and tables in this paper are represented by the two letters of ISO2.


## 2.2. Methods

Figure1 shows the flow chart of this study. First, after preprocessing the international trade data of the nine critical minerals, nine complex networks were constructed. Then, the power law distribution characteristics of the nine networks were tested. Next, on the basis of complex network construction, a link prediction model analysis and motif recognition were carried out. Finally, the analysis results of the two methods were substituted into the model of potential links in international trade to find potential international trading partners. The concrete realization process and theoretical basis of each step in the flow chart are explained in detail in this section.Figure 1
Flow chart of experimental methods.


### 2.2.1. Complex Network Construction

After processing the original data downloaded from the UN Comtrade Database, a complex directed weighted international trade network of nine minerals is constructed, with countries as the nodes, trade relations between countries as the edges, trade direction as the edge direction, and trade value (US$) as the edge weight. Trade value (US$) is chosen as the weight of an edge because trade value (US$) takes into account the dual attributes of the trade volume and mineral price, and at the same time, it is unified in dimension, which is conducive to a horizontal comparison between different minerals.From 2011 to 2020, a network is constructed every year. The main element raw materials of lithium-ion batteries comprise 9 types of minerals, which generate a total of 90 complex networks of international trade. Figure2 is a schematic diagram of the complex network of LiC international trade in 2020. Each node in Figure 2 corresponds to different countries in the trade, and the edges represent the trade relations between countries. The size of each node is distinguished by the weighting degree. When the weighting degree is larger, the node is larger, and the thickness of the edge represents the amount of trade. Figure 2 shows the top ten countries in terms of weighting in the international LiC trade in 2020. These countries are extremely active in trade, form a large number of trade relations and occupy most of the trade flow.Figure 2
Complex network of LiC international trade in 2020.


### 2.2.2. Verification of the Power Law Distribution

To verify whether a network belongs to the category of complex networks, it is necessary to verify the power law of the network. The so-called power law of the network means that the connection status (degree value) between nodes is extremely uneven. A few hub nodes in the network have many connections, while most other nodes have only a few connections. This paper uses the constructed network model to calculate the degree value of each node in the mineral trade network and determines whether the network is a complex network by observing the fitting of the double logarithmic power law distribution between the node and the degree [21]. Figure 3 shows the fitting diagram of the power law distribution of the nine minerals in 2020, and Figure 4 shows the goodness of fit results of the nine minerals from 2011 to 2020. The power law of the 9 mineral trade networks is well fitted, and the goodness of fit is above 0.6. This shows that the 9 mineral international trade network models constructed in this paper conform to the definition of complex networks, and the subsequent analysis of their network evolution characteristics is reliable.Figure 3
Power law distribution fitting diagram of 9 minerals in 2020.Figure 4
Goodness-of-fit results of 9 minerals from 2011 to 2020.


### 2.2.3. Link Prediction Model Construction

Link prediction refers to predicting through information, such as the known network nodes and network structure, the possibility of a connection between two network nodes that have not yet formed an edge [26, 27]; it enables the prediction of network links through an algorithm definition, test set division, finding unknown edges, and algorithm accuracy evaluation.At present, many scholars have applied the link prediction algorithm to the analysis of the international mineral trade network [40–44], which proves the feasibility of the method in the analysis of the international mineral trade. Based on the research of the above scholars, this paper expands the undirected link prediction model, adds direction information, and builds a directed link prediction model. The construction process is described as follows:(1) Step 1: Algorithm Selection. Common neighbors (CN), Adamic-Adar (AA), resource allocation (RA), and preferential attachment (PA) are the four mainstream algorithms in the current link prediction research. The following discussion briefly introduces these four algorithms in combination with international trade.(i) CN Algorithm. The basic assumption of the CN indicator is that if two unconnected nodes have more common neighbors, then they are more inclined to connect edges. Correspondingly, in international trade, if two countries have more common trading partners, then it is more likely that the two countries will establish a trade relationship. The calculation formulas are as follows. Formula (1) is an unweighted algorithm that does not consider the trade volume, and Formula (2) is a weighted algorithm that considers the trade volume.
(1)SxyCN=Γoutx∩Γiny.In Formula (1), x and y represent two countries that participate in international trade, Γoutx identifies the set of exporting countries of country x, Γiny indicates the set of importing countries of country y, and Γoutx∩Γiny denotes the number of all trading countries that import from country x and export to country y.
(2)SxyCN=∑z∈Γoutx∩Γinywxz+wzy2.In Formula (2), z is the trading country that imports from country x and exports to country y, and wxz and wzy represent the trade volume between country z and country x and between country z and country y, respectively.(ii) AA Algorithm. The idea of the AA indicator [33] is that the contribution of common neighbor nodes with a small degree value is greater than the contribution of common neighbor nodes with a large degree value. Formula (3) is used when weight is not considered, and Formula (4) is used when weight is considered.
(3)SxyAA=∑z∈Γoutx∩Γiny1logkz,(4)SxyAA=∑z∈Γoutx∩Γinywxz+wzylog1+sz.In Formula (3), kz is the number of countries that have trade relations with country z. In Formula (4), sz represents the strength of node vz, that is, the sum of the trade volume of country z in international trade. sz=∑i∈Γzwzi, where i is the country that trades with country z.(iii) RA Algorithm. Inspired by the process of network resource allocation [56], Zhou Tao and other scholars constructed an RA algorithm that is similar to the AA algorithm [26]. Considering two countries x and y that have no direct trade relationship in international trade, their common neighbors can be the medium of transmission that transfers the resources of country x to country y, and the number of resources accepted by country y can be defined as the similarity between country x and country y. Formula (5) is used when weight is not considered, and Formula (6) is used when weight is considered.
(5)SxyRA=∑z∈Γoutx∩Γiny1kz,(6)SxyRA=∑z∈Γoutx∩Γinywxz+wzysz.(iv) PA Algorithm. The idea here is that countries with more trading partners more easily establish new trade relations. Formula (7) is used when weight is not considered, and Formula (8) is used when weight is considered.
(7)SxyPA=Γoutx×Γiny,(8)SxyPA=∑j∈Γoutxwxj×∑q∈Γinywyq.In Formula (8), j represents the country that imports from country x; similarly, q represents the country that exports to country y.(2) Step 2: Divide the Training Set and Test Set. To further test the accuracy of the algorithm, we randomly select 10% of the existing trade links (E) as the test set and record it as ET; then, we use the remaining 90% of the trade links as the training set and record it as ER.
(9)E=ET+ER,ET=10%∗E.(3) Step 3: Find Links That Do Not Exist. To predict potential trade relations in international trade, we must first find links that have not yet existed in the trade network. Assume that there are n countries that participate in the international trade of a certain commodity; then, the set U that represents all possible trade links between these countries can be calculated by Formula (10); therefore, the set EI that identifies nonexistent links can be calculated by Formula (11).
(10)U=n∗n−12,(11)EI=U−E.(4) Step 4: Sort the Scores of the Links inEI. The four mainstream algorithms of CN, AA, RA, and PA are used to calculate the trade relations in EI, which are sorted according to the score. When the score is higher, the nonexistent trade relationship will more likely be transformed into a real trade relationship in the future.(5) Step 5: Evaluate Each Algorithm and Select the Best One. The area under the curve (AUC) is the most commonly used indicator to measure the accuracy of link prediction algorithms. The idea is that there is a greater probability of randomly selecting a higher score edge in ET than in EI. The calculation process randomly selects an edge from ET every time and then randomly selects an edge from EI. If the score of the edge in ET is higher than the score of the edge in EI, then 1 point is added, and if the score is equal, 0.5 point is added. Repeat the comparison n times, where n′ represents the number of times that the score of the edge in ET is higher than the score of the edge in EI, and n" represents the number of times that the scores of both sides are equal. Then, the AUC can be calculated by using Equation (12).
(12)AUC=n′+0.5n"n.According to Equation (12), if all the scores are generated randomly, then AUC≈0.5; therefore, an AUC greater than 0.5 measures the accuracy of the algorithm; that is, when the AUC score is higher, the corresponding algorithm is more accurate.


### 2.2.4. Network Motifs

Network motifs are patterns of interconnections that occur in complex networks at numbers that are significantly higher than those in randomized networks [46]. Mining the motifs in the international trade network can better explore the characteristics of trade relationship formation and compensate for the details lost by the overall average indicators.(1) Definition of Motif. Motifs are network subgraphs that meet the following conditions:The probability is very small that the number of times that the subgraph appears in the random network that corresponds to the empirical network is greater than the number of times that it appears in the empirical network, and the probability is usually required to be less than a certain thresholdP, such as P=0.01(1)
The number of times that the subgraph appears in the empirical network (Nreal) is not less than a certain lower limit U, such as U=4(2)
The number of times that the subgraph appears in the empirical network (Nreal) is significantly higher than the number of times that it appears in the random network (Nrand), and the general requirement is that Nreal−Nrand>0.1Nrand(2) Basic Form of a Motif. The three-motif form is the most commonly used subgraph in the mining of various network structures. Although the number of subjects can be gradually increased, the number of motifs that exist between subjects will increase exponentially, which greatly increases the complexity of motif recognition and the difficulty of analyzing the related information between subjects. Moreover, existing studies have shown that the motif patterns of more than four subjects can be formed by combining the various motif patterns of three subjects [57]. Therefore, the recognition of three motifs can satisfy the mining of local structural features in the international trade network of the main element raw materials of lithium-ion batteries.The number of three-motif forms in different network types is different. For example, there are only 2 forms of three motifs in undirected and unweighted networks, 7 forms in undirected and weighted networks, and 13 forms in directed and unweighted networks. Because the international trade networks constructed by this study are directed networks and as the focus of this paper is to explore the local trade links between countries in the trade network while not focusing on the transmission of the local trade volume between countries, this study chooses the directed and unweighted motif form for mining. The 13 forms of directed and unweighted motifs are numbered here, as shown in Figure5 below.Figure 5
Directed and unweighted three motifs.(3) Statistical Significance of Motifs. The statistical significance of motifs refers to whether the motif is a local structure unique to empirical networks rather than randomly generated and is often used to describe its importance to the formation and evolution of the network structure [47, 48]. In this paper, the Z score is used to measure the statistical significance of the motif, and the specific calculation formula is Equation (13).For motif (Mi), the number of times that it appears in the empirical network is recorded as Nreali, the number of times that it appears in the random network is recorded as Nrandi, and the average value of Nrandi is recorded as <Nrandi>. The standard deviation is σrandi. Then, the Z score of Mi in the empirical network is
(13)Zi=Nreali−<Nrandi>σrandi.


### 2.2.5. Analysis Model of Potential Links in International Trade

Directed link prediction and motifs can be used to mine the network structure information from the overall and local aspects, respectively. Therefore, this article combines these two methods to construct an analysis model for the international trade of the main element minerals of lithium-ion batteries, explore the formation rules of international trade relations, and determine the potential trade links that are most likely to be transformed into real trade relations. The specific steps are as follows.(1) Step 1: Identify the Key Motif. To explore the characteristics of the formation of trade relations from a local perspective, this paper identifies the key motifs in the complex network of the international trade of the nine minerals and analyzes the local trade structures with statistical significance in the trade network.(2) Step 2: Verify the Validity of the Link Prediction Model. Based on the link prediction model, the predicted potential trade relationship is compared with the actual trade relationship. By counting the number of potential trade relations successfully transformed into actual trade relations, the success rate of prediction is calculated to verify the validity of the link prediction model.(3) Step 3: Explore the Rules of the Successful Prediction of Trade Links. The potential trade links that were successfully predicted in the nine mineral trade networks are individually selected, and the rules of their successful predictions are explored from the overall and local perspectives. In general, this paper analyzes three aspects, namely, the timeliness of forecasting, the stability of trade relations, and the influence of past trade relations. At the local level, the motif method is used to explore the influence of successfully predicted links on the local structure of the trade network.(4) Step 4: Look for High-Quality Potential Trade Relations. According to the trade rules summarized in step 3, screen the potential links predicted and demarcate the potential trade relations with a high possibility of establishing real trade relations.


## 2.2.1. Complex Network Construction

After processing the original data downloaded from the UN Comtrade Database, a complex directed weighted international trade network of nine minerals is constructed, with countries as the nodes, trade relations between countries as the edges, trade direction as the edge direction, and trade value (US$) as the edge weight. Trade value (US$) is chosen as the weight of an edge because trade value (US$) takes into account the dual attributes of the trade volume and mineral price, and at the same time, it is unified in dimension, which is conducive to a horizontal comparison between different minerals.From 2011 to 2020, a network is constructed every year. The main element raw materials of lithium-ion batteries comprise 9 types of minerals, which generate a total of 90 complex networks of international trade. Figure2 is a schematic diagram of the complex network of LiC international trade in 2020. Each node in Figure 2 corresponds to different countries in the trade, and the edges represent the trade relations between countries. The size of each node is distinguished by the weighting degree. When the weighting degree is larger, the node is larger, and the thickness of the edge represents the amount of trade. Figure 2 shows the top ten countries in terms of weighting in the international LiC trade in 2020. These countries are extremely active in trade, form a large number of trade relations and occupy most of the trade flow.Figure 2
Complex network of LiC international trade in 2020.


## 2.2.2. Verification of the Power Law Distribution

To verify whether a network belongs to the category of complex networks, it is necessary to verify the power law of the network. The so-called power law of the network means that the connection status (degree value) between nodes is extremely uneven. A few hub nodes in the network have many connections, while most other nodes have only a few connections. This paper uses the constructed network model to calculate the degree value of each node in the mineral trade network and determines whether the network is a complex network by observing the fitting of the double logarithmic power law distribution between the node and the degree [21]. Figure 3 shows the fitting diagram of the power law distribution of the nine minerals in 2020, and Figure 4 shows the goodness of fit results of the nine minerals from 2011 to 2020. The power law of the 9 mineral trade networks is well fitted, and the goodness of fit is above 0.6. This shows that the 9 mineral international trade network models constructed in this paper conform to the definition of complex networks, and the subsequent analysis of their network evolution characteristics is reliable.Figure 3
Power law distribution fitting diagram of 9 minerals in 2020.Figure 4
Goodness-of-fit results of 9 minerals from 2011 to 2020.


## 2.2.3. Link Prediction Model Construction

Link prediction refers to predicting through information, such as the known network nodes and network structure, the possibility of a connection between two network nodes that have not yet formed an edge [26, 27]; it enables the prediction of network links through an algorithm definition, test set division, finding unknown edges, and algorithm accuracy evaluation.At present, many scholars have applied the link prediction algorithm to the analysis of the international mineral trade network [40–44], which proves the feasibility of the method in the analysis of the international mineral trade. Based on the research of the above scholars, this paper expands the undirected link prediction model, adds direction information, and builds a directed link prediction model. The construction process is described as follows:(1) Step 1: Algorithm Selection. Common neighbors (CN), Adamic-Adar (AA), resource allocation (RA), and preferential attachment (PA) are the four mainstream algorithms in the current link prediction research. The following discussion briefly introduces these four algorithms in combination with international trade.(i) CN Algorithm. The basic assumption of the CN indicator is that if two unconnected nodes have more common neighbors, then they are more inclined to connect edges. Correspondingly, in international trade, if two countries have more common trading partners, then it is more likely that the two countries will establish a trade relationship. The calculation formulas are as follows. Formula (1) is an unweighted algorithm that does not consider the trade volume, and Formula (2) is a weighted algorithm that considers the trade volume.
(1)SxyCN=Γoutx∩Γiny.In Formula (1), x and y represent two countries that participate in international trade, Γoutx identifies the set of exporting countries of country x, Γiny indicates the set of importing countries of country y, and Γoutx∩Γiny denotes the number of all trading countries that import from country x and export to country y.
(2)SxyCN=∑z∈Γoutx∩Γinywxz+wzy2.In Formula (2), z is the trading country that imports from country x and exports to country y, and wxz and wzy represent the trade volume between country z and country x and between country z and country y, respectively.(ii) AA Algorithm. The idea of the AA indicator [33] is that the contribution of common neighbor nodes with a small degree value is greater than the contribution of common neighbor nodes with a large degree value. Formula (3) is used when weight is not considered, and Formula (4) is used when weight is considered.
(3)SxyAA=∑z∈Γoutx∩Γiny1logkz,(4)SxyAA=∑z∈Γoutx∩Γinywxz+wzylog1+sz.In Formula (3), kz is the number of countries that have trade relations with country z. In Formula (4), sz represents the strength of node vz, that is, the sum of the trade volume of country z in international trade. sz=∑i∈Γzwzi, where i is the country that trades with country z.(iii) RA Algorithm. Inspired by the process of network resource allocation [56], Zhou Tao and other scholars constructed an RA algorithm that is similar to the AA algorithm [26]. Considering two countries x and y that have no direct trade relationship in international trade, their common neighbors can be the medium of transmission that transfers the resources of country x to country y, and the number of resources accepted by country y can be defined as the similarity between country x and country y. Formula (5) is used when weight is not considered, and Formula (6) is used when weight is considered.
(5)SxyRA=∑z∈Γoutx∩Γiny1kz,(6)SxyRA=∑z∈Γoutx∩Γinywxz+wzysz.(iv) PA Algorithm. The idea here is that countries with more trading partners more easily establish new trade relations. Formula (7) is used when weight is not considered, and Formula (8) is used when weight is considered.
(7)SxyPA=Γoutx×Γiny,(8)SxyPA=∑j∈Γoutxwxj×∑q∈Γinywyq.In Formula (8), j represents the country that imports from country x; similarly, q represents the country that exports to country y.(2) Step 2: Divide the Training Set and Test Set. To further test the accuracy of the algorithm, we randomly select 10% of the existing trade links (E) as the test set and record it as ET; then, we use the remaining 90% of the trade links as the training set and record it as ER.
(9)E=ET+ER,ET=10%∗E.(3) Step 3: Find Links That Do Not Exist. To predict potential trade relations in international trade, we must first find links that have not yet existed in the trade network. Assume that there are n countries that participate in the international trade of a certain commodity; then, the set U that represents all possible trade links between these countries can be calculated by Formula (10); therefore, the set EI that identifies nonexistent links can be calculated by Formula (11).
(10)U=n∗n−12,(11)EI=U−E.(4) Step 4: Sort the Scores of the Links inEI. The four mainstream algorithms of CN, AA, RA, and PA are used to calculate the trade relations in EI, which are sorted according to the score. When the score is higher, the nonexistent trade relationship will more likely be transformed into a real trade relationship in the future.(5) Step 5: Evaluate Each Algorithm and Select the Best One. The area under the curve (AUC) is the most commonly used indicator to measure the accuracy of link prediction algorithms. The idea is that there is a greater probability of randomly selecting a higher score edge in ET than in EI. The calculation process randomly selects an edge from ET every time and then randomly selects an edge from EI. If the score of the edge in ET is higher than the score of the edge in EI, then 1 point is added, and if the score is equal, 0.5 point is added. Repeat the comparison n times, where n′ represents the number of times that the score of the edge in ET is higher than the score of the edge in EI, and n" represents the number of times that the scores of both sides are equal. Then, the AUC can be calculated by using Equation (12).
(12)AUC=n′+0.5n"n.According to Equation (12), if all the scores are generated randomly, then AUC≈0.5; therefore, an AUC greater than 0.5 measures the accuracy of the algorithm; that is, when the AUC score is higher, the corresponding algorithm is more accurate.


## 2.2.4. Network Motifs

Network motifs are patterns of interconnections that occur in complex networks at numbers that are significantly higher than those in randomized networks [46]. Mining the motifs in the international trade network can better explore the characteristics of trade relationship formation and compensate for the details lost by the overall average indicators.(1) Definition of Motif. Motifs are network subgraphs that meet the following conditions:The probability is very small that the number of times that the subgraph appears in the random network that corresponds to the empirical network is greater than the number of times that it appears in the empirical network, and the probability is usually required to be less than a certain thresholdP, such as P=0.01(1)
The number of times that the subgraph appears in the empirical network (Nreal) is not less than a certain lower limit U, such as U=4(2)
The number of times that the subgraph appears in the empirical network (Nreal) is significantly higher than the number of times that it appears in the random network (Nrand), and the general requirement is that Nreal−Nrand>0.1Nrand(2) Basic Form of a Motif. The three-motif form is the most commonly used subgraph in the mining of various network structures. Although the number of subjects can be gradually increased, the number of motifs that exist between subjects will increase exponentially, which greatly increases the complexity of motif recognition and the difficulty of analyzing the related information between subjects. Moreover, existing studies have shown that the motif patterns of more than four subjects can be formed by combining the various motif patterns of three subjects [57]. Therefore, the recognition of three motifs can satisfy the mining of local structural features in the international trade network of the main element raw materials of lithium-ion batteries.The number of three-motif forms in different network types is different. For example, there are only 2 forms of three motifs in undirected and unweighted networks, 7 forms in undirected and weighted networks, and 13 forms in directed and unweighted networks. Because the international trade networks constructed by this study are directed networks and as the focus of this paper is to explore the local trade links between countries in the trade network while not focusing on the transmission of the local trade volume between countries, this study chooses the directed and unweighted motif form for mining. The 13 forms of directed and unweighted motifs are numbered here, as shown in Figure5 below.Figure 5
Directed and unweighted three motifs.(3) Statistical Significance of Motifs. The statistical significance of motifs refers to whether the motif is a local structure unique to empirical networks rather than randomly generated and is often used to describe its importance to the formation and evolution of the network structure [47, 48]. In this paper, the Z score is used to measure the statistical significance of the motif, and the specific calculation formula is Equation (13).For motif (Mi), the number of times that it appears in the empirical network is recorded as Nreali, the number of times that it appears in the random network is recorded as Nrandi, and the average value of Nrandi is recorded as <Nrandi>. The standard deviation is σrandi. Then, the Z score of Mi in the empirical network is
(13)Zi=Nreali−<Nrandi>σrandi.


## 2.2.5. Analysis Model of Potential Links in International Trade

Directed link prediction and motifs can be used to mine the network structure information from the overall and local aspects, respectively. Therefore, this article combines these two methods to construct an analysis model for the international trade of the main element minerals of lithium-ion batteries, explore the formation rules of international trade relations, and determine the potential trade links that are most likely to be transformed into real trade relations. The specific steps are as follows.(1) Step 1: Identify the Key Motif. To explore the characteristics of the formation of trade relations from a local perspective, this paper identifies the key motifs in the complex network of the international trade of the nine minerals and analyzes the local trade structures with statistical significance in the trade network.(2) Step 2: Verify the Validity of the Link Prediction Model. Based on the link prediction model, the predicted potential trade relationship is compared with the actual trade relationship. By counting the number of potential trade relations successfully transformed into actual trade relations, the success rate of prediction is calculated to verify the validity of the link prediction model.(3) Step 3: Explore the Rules of the Successful Prediction of Trade Links. The potential trade links that were successfully predicted in the nine mineral trade networks are individually selected, and the rules of their successful predictions are explored from the overall and local perspectives. In general, this paper analyzes three aspects, namely, the timeliness of forecasting, the stability of trade relations, and the influence of past trade relations. At the local level, the motif method is used to explore the influence of successfully predicted links on the local structure of the trade network.(4) Step 4: Look for High-Quality Potential Trade Relations. According to the trade rules summarized in step 3, screen the potential links predicted and demarcate the potential trade relations with a high possibility of establishing real trade relations.


## 3. Results and Discussion

### 3.1. Key Motif Recognition

The FANMOOD tool was used to mine the key motifs in the international trade network of the nine minerals, and theZ score indicator (Equation (13)) was chosen in the selection of the statistical significance indicator of the motif. The Z score is a common indicator to measure the statistical significance of motifs, and the Z score has been widely used in motif recognition in different types of empirical network research [50, 51].Taking LiC as an example, Figure6 shows the evolution of the key motifs in the LiC international trade network. The Z scores of the six key identified motifs fluctuate sharply every year, which indicates that the local trade relations among countries in the LiC international trade network also evolved greatly every year. From the perspective of the evolution trend of the key LiC motifs, the Z scores of M4 and M7 were in the top two for ten years. Both motifs have bilateral trade relations, which shows that countries in the LiC trade mostly adopt the reciprocal trade mode to meet the balance of supply and demand of their own resources. The Z scores of M9 have been on an upward trend over the past decade; this suggests that an increasing number of countries as “transit countries” in the LiC trade have played a considerable role in promoting the global flow of LiC resources. The Z scores of M8 fluctuate the most, which implies that the country’s unilateral export or import trade model is unstable and brings trade risks.Figure 6
The evolution of key motifs of the LiC international trade network.The key motifs identified in the international trade network of the nine important minerals are summarized in Table2.Table 2
Identification of key motifs of the nine important minerals.
MineralKey motifs identifiedAlM4, M6, M7, M8, M9, M12CM4, M6, M7, M8, M9, M12CoM1, M5, M6, M11CuM4, M6, M7, M9, M11, M12FeM4, M6, M7, M9, M11, M12LiCM4, M6, M7, M8, M9, M12MnM4, M5, M6, M7, M9, M11, M12NiM4, M5, M6, M9, M11TiM4, M5, M6, M7, M9


### 3.2. Verification of the Validity of the Link Prediction Model

In this section, the accuracy of the four mainstream algorithms is tested to select the optimal algorithm, and then, the optimal algorithm is used to predict the potential trade relations of the nine mineral trades by comparing the prediction success proportion of the potential links in the actual trade to test the validity of the link prediction model and to prove the reliability of the algorithm applied in empirical networks.


#### 3.2.1. Select the Optimal Algorithm

Four mainstream algorithms, specifically, CN, AA, RA, and PA, are used to calculateET and EI, and these links are ranked according to the score of the algorithm. A higher score means that the nonexistent link is more likely to be converted into an existing link in the future; that is, the country/region pair that corresponds to this link is more likely to have trade relations in the future. By comparing the accuracy indicators, the AUCs of the four algorithms are used to find the optimal algorithm. When the AUC score is higher, the accuracy of the corresponding algorithm is higher.In the choice of network type, the directed and unweighted network is selected for prediction based on two considerations. First, the choice of the directed network structure means that the direction of trade between countries is considered, which can provide at the import and export ends accurate trading partners for the trading countries such that the research results have more practical significance. In addition, in the undirected network structure, there are fewer motifs, the analysis of the local network structure is less meticulous, and the degree of discrimination in statistical significance is low. Second, choosing the unweighted network structure can eliminate the agglomeration effect of large import and export countries in the trade network. Only by considering the network structure, that is, the connectivity of trade channels, can the analysis and prediction be performed such that the possibility of the predictive links between small import and export countries emerge, which is conducive to discovering more trade links that are more likely to be realized.From using the four mainstream algorithms, the AUC scores of the nine important minerals are shown in Figure7. The x-axis represents the four algorithms of CN, AA, RA, and PA, the y-axis represents the years from 2011 to 2020, and the z-axis represents the AUC score results under the corresponding algorithm in the corresponding year. To reduce random errors and make the scoring result more scientific, the AUC score here is the average result of 10 experiments, and the data are randomly divided into 10% ET and 90% ER for all 10 experiments. By comparing the AUC scores, it can be concluded that the AUC scores are all greater than 0.5 and close to 1, which indicates that these four algorithms are applicable to the analysis of the international trade data of the nine important minerals. In addition, by comparing the scores of the four algorithms in the figure, it can be found that the optimal algorithms for the nine important minerals are all PA algorithms, which shows that the PA algorithm (countries with more trading partners more easily establish new trade relations) has universal applicability in the international trade network of minerals. Therefore, it can be concluded that the PA algorithm is the optimal algorithm to be applied in this study.Figure 7
AUC scores of nine important minerals.Based on the analysis of the accuracy indicator of the AUC scoring results, this paper chooses the directed and unweighted PA algorithm to find potential trade links. First, the links inET and EI are ranked according to the value of PA. According to the definition of the PA algorithm, countries with more trading partners more easily establish new trade relations. Therefore, countries with high PA values are more likely to have new trade relations than countries with lower PA values. Therefore, this study selects in EI the top potential country pairs that will be more conducive to the establishment of real trade relations in the future.


#### 3.2.2. Pick Potential Links

In the process of link prediction, the total dataset is divided into 10%ET and 90% ER; therefore, the result of the link prediction algorithm includes both test links and potential links. Potential links are predictions of unknown links and future links. This section selects the potential links in the network topology of the nine minerals that comprise the main element raw materials of lithium-ion batteries and observes whether they have actually established real trade relations after they are predicted to have trade relations.Taking LiC as an example, this study selects the top ten nonexistent links from 2011 to 2020. Table3 shows the top ten trading countries or regions of LiC in the PA algorithm score in 2020, including the test links and nonexistent links. The first column in Table 3 represents the PA value ranking of the nonexistent links, the second and third columns represent the two countries or regions included in the trade link, the fourth column represents the PA algorithm score of the trade link, and the fifth column represents the types of links: P is the link that does not exist at present, which is a potential trade link, and T is the link in the test set, which is the actual link. Among the 14 pairs of trading countries or regions, 4 pairs of trade relationships come from the test set, and the remaining 10 pairs of trade relationships represent nonexistent link relationships, which are the top 10 potential trade links that require further analysis. We follow the above steps to select and organize the top ten potential links of the nine minerals every year to observe whether they actually have trade relations in subsequent years.Table 3
The top 14 trade links of LiC’s PA value in 2020.
RankCountry or regionCountry or regionPA valueLink typeNLCH405TCANL378T1FINL297P2KRNL297P3NLZA270P4ITNL243P5CADE224P6JPNL216P7INES208PCNCH195TEENL189T8ILNL189P9MYNL189P10NLRS189P


#### 3.2.3. Comparison of the Potential Links and Actual Links

We select and organize the top ten potential links of the nine minerals each year. The summary results of LiC are shown in Figure8, and the summary results of the other minerals are shown in Figures 9–16.Figure 8
Comparison of potential trade links and actual trade links of LiC.Figure 9
Comparison of potential trade links and actual trade links of Al.Figure 10
Comparison of potential trade links and actual trade links of C.Figure 11
Comparison of potential trade links and actual trade links of Co.Figure 12
Comparison of potential trade links and actual trade links of Cu.Figure 13
Comparison of potential trade links and actual trade links of Fe.Figure 14
Comparison of potential trade links and actual trade links of Mn.Figure 15
Comparison of potential trade links and actual trade links of Ni.Figure 16
Comparison of potential trade links and actual trade links of Ti.Figures8 and 9–16 show the results of the aggregation of the top ten potential trading country/region pairs of the nine important minerals from 2010 to 2020. Since there are trading country pairs that repeatedly appear in the top ten PA value rankings in each year, the number of country pairs summarized by different minerals is different. The first column in the figure represents the labels of the trading country/region pairs, the second column represents the two countries/regions of the trade link, and the arrows between the countries/regions identify the trade direction. The third to the 12th columns represent the years from 2011 to 2020, and the 13th column indicates the cumulative number of predicted successful links. For each row, the green color block indicates that the country pair has not traded minerals for the corresponding year in this column, but because they are in the top ten rankings of the PA value, they are potential trade links. The white color block indicates that the country pair not only has not traded minerals for the corresponding year in this column but also is not in the top ten ranking of the PA values. The orange color block indicates that the country pair has actual trade relations for the corresponding year in this column. By observing the potential and actual trade links, it is possible to analyze the trend of the international mineral trade in the past decade and provide theoretical support for the next prediction.Next, we introduce the prediction rules, which are used to calculate the prediction success rate for the results shown in Figure8 (the prediction rules are the same for the other critical minerals). For the corresponding country pair in each row, if at least one orange color block appears after the green color block, then this means that the potential trade link did indeed have a trade relationship afterward, and that the country pair is a predicted successful country pair. Take the first country pair in Figure 8, France and India, as an example. The green color block appeared in 2011, which shows that the potential trade relationship of this country pair was predicted in 2011, and then, the orange color block appeared in 2012, which indicates that the country pair had an actual trade relationship in 2012; thus, the potential trade relationship of the country pair was predicted to be successful. In contrast, if the country pair has no orange color block after the green color block appears for the first time, then this means that the potential trade link did not have any actual trade relationship in the next few years, and it is defined as an invalid prediction. Take the 44th country pair in Figure 8, Japan and the Netherlands, as an example. For this country pair, orange color blocks appeared in 2013 and 2015, which suggests that a trade relationship has occurred. The green color block appeared for the first time in 2016, which demonstrates that a trade relationship is predicted to occur. However, no orange color blocks appeared in other years after 2016, and this signifies that the country pair did not have a trade relationship in other years; therefore, the country pair prediction failed.The effectiveness of the algorithm can be verified by counting the total proportion of the country pairs that are predicted to be successful. For the country pairs that showed green color blocks for the first time in 2020, as there are no actual trade data in 2021 to test whether the country pairs are predicted to be successful, they are not classified as prediction failures, and these country pairs are eliminated when the success rate is calculated.Table4 shows the statistical results of the prediction success rates of the nine minerals. Their success rates are all above 50%, which shows that it is effective to use the directed and unweighted PA algorithm to predict the potential relationships in the international trade of the nine minerals.Table 4
Statistics on the forecast success rate of the main element raw material minerals for lithium-ion batteries.
MineralAlCCoCuFeLiCMnNiTiNumber of potential country pairs345654323656384657The number after elimination315152313352364055Number of successful predictions203428202333242139Success rate64.5%66.7%53.8%64.5%69.7%63.5%66.7%52.5%70.9%


### 3.3. Explore the Rules of the Successful Prediction of Trade Links

In the previous section, this article predicted the potential link relationships in the international trade of the nine minerals and obtained a high prediction success rate. Most of the predicted potential trade relations were successfully realized in the next few years, but there are still some predicted potential links. Although they are in the top ten potential links, they do not produce actual trade relations after being predicted. This section analyzes the inherent characteristics of successfully predicted links to explore the rules of the successful prediction of trade links and to provide a theoretical basis for trading countries to find suitable trading partners.We take the successfully predicted trade links of LiC in Figure17 as an example to analyze their inherent characteristics. The results of the other minerals are shown in Figures 18–25. The potential links of LiC that were successfully predicted include 33 pairs of trading countries/regions. By observing the process from being predicted to successfully establishing trade relations, it is found that 20 pairs (61%) of trading countries/regions successfully established trade relations within 3 years after being first predicted, and these pairs are marked in column “A” in the figure. Therefore, this study sets the forecast time limit as 3 years; that is, a pair of potential trade relations can successfully establish a trade relationship with a high probability within 3 years after being predicted. If it exceeds 3 years, then the possibility of establishing a relationship is low. Column “B” lists the cumulative number of the country/region pairs that have established two or more trade relations in a decade. According to the statistics, a total of 27 (82%) out of 33 pairs successfully predicted that the country pairs fit this feature, which indicates that countries tend to establish long-term and stable trade relations in international trade. Column “C” lists the cumulative number of the country/region pairs that had actual trade relations before the trade relations were predicted for the first time. The country/region pairs that were predicted to have trade relations in 2011 are excluded from the statistics because there are no data before 2011 for verification. According to the statistics, among 25 country/region pairs, a total of 15 (60%) had actual trade relations before they were successfully predicted. Therefore, in the potential trade links of LiC, the existing trade relations promote the establishment of the predicted trade relations.Figure 17
Successfully predicted trade links of LiC.Figure 18
Successfully predicted trade links of Al.Figure 19
Successfully predicted trade links of C.Figure 20
Successfully predicted trade links of Co.Figure 21
Successfully predicted trade links of Cu.Figure 22
Successfully predicted trade links of Fe.Figure 23
Successfully predicted trade links of Mn.Figure 24
Successfully predicted trade links of Ni.Figure 25
Successfully predicted trade links of Ti.Based on the analysis of the potential links of the successful prediction of LiC, the prediction rules of the nine important minerals are summarized, and the following three trade link rules are obtained.(1)
The link prediction of the nine minerals, the main element raw materials of lithium-ion batteries, has a timeliness requirement, and it generally takes 3 years for the potential trade relationship to be predicted until the real trade relationship is establishedFrom the results in Table5, among the potential links that are successfully predicted for the nine important minerals, the percentages of links that meet the 3-year timeliness requirement are more than 60%, which shows that the establishment of trade relations for the main element minerals of lithium-ion batteries does not happen overnight but requires a certain time scale to complete. This paper sets the prediction timeliness requirement of the nine minerals as 3 years; that is, a pair of potential trade relations is highly likely to be successfully established within 3 years after being predicted, and the possibility of establishing a relationship is low if it exceeds 3 years.
(2)
The trading countries of the nine minerals tend to establish long-term and stable trade relations when looking for trading partnersTable 5
Statistics of the trade links of nine important minerals in line with rule 1.
MineralAlCCoCuFeLiCMnNiTiPredict the number of successful links203428202333242139Establish trade relations within 3 years183017172020191825Percentage90.0%88.2%60.7%85.0%87.0%60.6%79.2%85.7%64.1%From the results in Table6, among the potential links that are successfully predicted for the nine important minerals, the percentages of the links that have established two or more trade relations within ten years are more than 75%, which indicates that in international trade, countries tend to trade minerals with partners who can establish long-term and stable trade relations to meet their own balance of supply and demand, and long-term stable trade relations also help reduce trade risks and enhance trade security.
(3)
Among the international trade links of the nine minerals, the existing trade relations will promote the establishment of the predicted trade relationsTable 6
Statistics of the trade links of nine important minerals in line with rule 2.
MineralAlCCoCuFeLiCMnNiTiPredict the number of successful links203428202333242139Two or more trades173321201927221932Percentage85.0%97.1%75.0%100.0%82.6%81.8%91.7%90.5%82.1%Table7 shows the statistical results of the successfully predicted links of the nine important minerals in line with rule 3. The country pairs that were predicted to have trade relations in 2011 are excluded from the statistics because there are no actual trade data before 2011 for verification. According to the statistical results in Table 7, among the potential links that are successfully predicted for the nine important minerals, more than 60% of the links had trade relations before they were predicted for the first time. Therefore, in the prediction of the international trade links of the nine minerals, if there is an existing trade relation on the potential link before it is predicted, then the possibility that it will be converted to a real trade relation increases.Table 7
Statistics of the trade links of nine important minerals in line with rule 3.
MineralAlCCoCuFeLiCMnNiTiPredict the number of successful links152819141725151431Trade relations existed before being predicted10191312111591120Percentage66.7%67.9%68.4%85.7%64.7%60.0%60.0%78.6%64.5%


### 3.4. Explore the Impact of the Formation of Predicted Trade Links on the Structure of Local Mineral Trade Networks

In the previous section, from the global perspective, this paper analyzes the internal characteristics of the successfully predicted links in the link prediction of the nine mineral resources and summarizes three rules that help to find successfully predicted links. This section discusses the use of the motif analysis method to analyze in the nine mineral link predictions the formation of successfully predicted trade links from a local perspective, which changes the local structure of the international trade network of mineral resources and explores the influence of the formation of potential trade links on the local trade mode of mineral resources. From the perspective of network motifs, we can deeply study the reasons why potential trade links are successfully predicted and provide a more comprehensive theoretical basis for the follow-up search for high-quality potential trade links in the international trade of the nine minerals.According to the trade link rule 1 summarized in Section3.3, the link prediction of the nine minerals, the main element raw materials of lithium-ion batteries, has a timeliness requirement, and it generally takes 3 years for the potential trade relationship to be predicted until the real trade relationship is established. Therefore, based on the 3-year forecasting timeliness rule, this article selects the country/region pairs of the nine minerals that are predicted in each year from 2011 to 2017 and that successfully establish trade relations within 3 years. Then, it adds their trade relations to the international trade network of the predicted years, conducts a motif analysis, and compares the network structure before joining to determine the increase in its important motifs to analyze and study the impact of the formation of potential trade links on the local trade structure of minerals.Taking LiC as an example, it can be seen from Figure17 that the country pairs predicted in 2011, and that successfully established trade relations within 3 years were France → India and France → Korea. Therefore, these two pairs of trade relations were added to the LiC trade network in 2011. Compared with the network structure before joining, the network after joining is examined to determine the important motifs that were newly formed due to the increase in network information; in addition, the increase in the number was counted to analyze how the formation of potential trade links affects LiC’s local trade structure in this year and to explore the reasons for its predicted success. Since the forecast timeliness requirement is 3 years, the potential trade links after 2017 cannot be verified by actual trade data after 2020; thus, only 2011 to 2017 are analyzed on the time scale. Table 8 shows the motif statistics of the potential trade relations of LiC from 2011 to 2017. For the other important minerals, see Tables 9–16.Table 8
Statistics for the motifs in the process of realizing potential trade relations of LiC from 2011 to 2017.
YearSuccessfully predicted trading country pairsIncreased number of motifsM4M6M7M8M9M1220112390031220420127971010116362420134615111923122014245003113012015281660006920163740017213242017719514348744610Total27592352093133187124Table 9
Statistics for the motifs in the process of realizing potential trade relations of Al from 2011 to 2017.
YearSuccessfully predicted trading country pairsIncreased number of motifsM4M6M7M8M9M122011341626072020125158710132062462013463671117312014512678511593620153103178241854201647943031356201739633374733Total2766650413046223276Table 10
Statistics for the motifs in the process of realizing potential trade relations of C from 2011 to 2017.
YearSuccessfully predicted trading country pairsIncreased number of motifsM4M6M7M8M9M12201151231462615372520127110231072155320135809220142114201461302152714481520155356199217225320166104215101732192017410315717142921Total3810061224410977254400Table 11
Statistics for the motifs in the process of realizing potential trade relations of Co from 2011 to 2017.
YearSuccessfully predicted trading country pairsIncreased number of motifsM1M5M6M1120113171411120124400273120134280532020143100424201561515182016416031122017251211Total261313251687Table 12
Statistics for the motifs in the process of realizing potential trade relations of Cu from 2011 to 2017.
YearSuccessfully predicted trading country pairsIncreased number of motifsM4M6M7M9M11M122011417322194032962012940716242010395149201352411632832481052014736612252681151442015422616271424694201662551629174735111201742099162385490Total39187710717254330425789Table 13
Statistics for the motifs in the process of realizing potential trade relations of Fe from 2011 to 2017.
YearSuccessfully predicted trading country pairsIncreased number of motifsM4M6M7M9M11M12201153241814188980105201273491010201248410120133172612079501620143176114104148622015633318131728177802016313614680476120175253189176210443Total3217439557110423590468Table 14
Statistics for the motifs in the process of realizing potential trade relations of Mn from 2011 to 2017.
YearSuccessfully predicted trading country pairsIncreased number of motifsM4M5M6M7M9M11M12201193739341422105116732012292364327262320136244611121148985820147323726112610111735201551920215145393620167269510171346100782017628131411178611832Total4217743312274106466668305Table 15
Statistics for the motifs in the process of realizing potential trade relations of Ni from 2011 to 2017.
YearSuccessfully predicted trading country pairsIncreased number of motifsM4M5M6M9M1120115535016032201243553101072013710975125728201435250424192015251010320165959211353820174754162935Total30424361160155162Table 16
Statistics for the motifs in the process of realizing potential trade relations of Ti from 2011 to 2017.
YearSuccessfully predicted trading country pairsIncreased number of motifsM4M5M6M7M9201168613131315322012458126131017201337101117522014463378936201556647121132201671029171675320178149329131589Total3759544907674311Table8 shows the statistics for the motifs in the process of realizing the potential trade relations of LiC from 2011 to 2017. From 2011 to 2017, the cumulative number of successful predictions of potential trading country/region pairs was 27, and the total number of newly added important motifs was 592. Among them, the newly added numbers M9, M8, and M12 motifs were more prominent than other important motifs, which indicates that the formation of potential links mainly promotes the international trade of LiC: as a transit country, country A imports LiC from country B and exports it to country C, country A exports LiC to countries B and C at the same time, and country A imports LiC from countries B and C and exports LiC to country B. Thus, three local trade models are formed.A horizontal comparison of the statistics for the motifs involved in the process of realizing the potential trade relations of the nine minerals from 2011 to 2017 shows that the number of newly added motifs of Cu, Fe, and Mn far exceeds that of the other minerals, which indicates that the establishment of potential trade relations has the greatest impact on the local trade structure of these three minerals. The number of newly added motifs for C is calculated at the upstream level, the number of newly added motifs for Al, Ti, LiC, and Ni is calculated at the midstream level, the number of newly added motifs for Co is the lowest, and there is a large gap with other minerals. In terms of the motif form, in addition to Co, the number of newly added M9 motifs for the other 8 minerals is relatively large (especially reflected in the motif statistics of Ti), which suggests that the establishment of potential trade relations has played a major role in promoting the local trade mode of the “transit” form of the eight types of international mineral trade. Except for Ti, many motif forms with a “bilateral” structure have been added to the other 8 minerals, which shows that the establishment of potential trade relations has played a major role in promoting the “reciprocal” local trade model in the international trade of the 8 minerals. In addition, M8 appeared more frequently in the statistics of the LiC motif; this demonstrates that the formation of potential trade relations in the LiC international trade tends to establish a unilateral export form of the local trade model. In the statistics of the newly added motifs of the nine minerals, Al and C have similarities, M9 and M12 have more new additions, Cu, Fe, and Mn have similarities, and M9, M11, and M12 have more new additions.


### 3.5. International Trade Relation Forecast

In the previous section, this paper uses the motif analysis method to study the impact of successfully predicted links on the local mineral trade structure, and statistics are presented on the addition of important motifs in the realization of the potential trade relations of the nine minerals from 2011 to 2017. It is found that the successfully predicted links promote the formation of important motifs in the network. Therefore, based on the results of this study, we can compare the impact of the potential trade links on the increase in the important motifs in the network and screen out the country/region pairs that are most likely to transform into actual trade relations.This section preliminarily screens the potential trade links with predictive significance based on the criteria that these links had actual trade relations before but did not have actual trade in the last 3 years (2018-2020). We apply the motif analysis method to compare from a local perspective how the formation of these potential trade links will affect the local trade structure in the mineral international trade. Based on this analysis, combined with the three prediction rules, the country/region pairs that are most likely to establish trade relations among the nine international mineral trades are further screened out.


#### 3.5.1. Preliminary Screening of Potential Trade Links

The research purpose of this article is to find new and suitable trading partners for the countries/regions involved in the trade of the nine types of minerals to enhance their trade security, meet the supply and demand balance of minerals, and reduce the risks in their international trade. In consideration of the research purpose of this article, if a pair of trading countries/regions already has had a trade relationship in recent years, then the trade relationship is likely to continue on the basis of this “familiarity”; therefore, its actual forecast is of little significance. The second prediction rule in Section3.3 of this article states the following: the trading countries of the nine minerals, the main element raw materials of lithium-ion batteries, tend to establish long-term and stable trade relations when looking for trading partners. This rule also reflects a related reality. For the countries/regions that may have never tried to establish diplomatic relations historically or have not conducted actual trade transactions in a long time due to changes in international situations or trade policies, the new creation or the restoration of their trade relations will have a great positive effect on the expansion of their trade channels, thereby providing more mineral sources or export points, increasing their ability to guarantee their trade security, and satisfying supply and demand. In combination with the third rule of prediction in Section 3.3 of this article, among the international trade links of the nine minerals, the existing trade relations will promote the establishment of the predicted trade relations. Therefore, this study preliminarily screens the potential trade links with predictive significance based on the criteria that the trade links have supported actual trade relations before but have not been involved in actual trade in the last 3 years (2018-2020).Table17 shows the preliminary screening results of the potential trade links of the nine important minerals.Table 17
Preliminary screening of potential trade links of the nine important minerals.
CountAlCCoCuFeLiCMnNiTi1AE → EUID→EUBE→INCN → INCN → ATFR → KRMX → INCN → BECN → RU2DK → USDK → DECN → FRCN → THCN → HUCA → DEIN→USDE → ZAMY→NL3CZ → FRIN→THIN→GBCN → JPCN → HKCA → BEIT→INCN → FRCN → PL4FR → INID→INBE→GBCN → CHCN → QACA → RUCN → UACN → HKIN→US5DK → ININ→CHCN → GBCA → NLJP → NLNL → AECN → SKCN → INKR → US6DK → ESIN→BRCN → CHKH → CNCN → ESNL → RSCN → ESCA → AUKR → EU7HK → NLFR → ATBE→USKR → ESKR → NLCN → NLCA → DEKR → NL8NL → THIN→ESCN → NLCN → NAAU → NLID→NLCA → SGCN → MA9SA → EUNL → BRDE → NLID→NLCN → BECA → GBCN → FI10DE → KRNL → THNL → USJP → NLCN → DKMK → EUCN → HU11FR → USTH → USNL → INMY→NLCZ → INCL → EUJP → US12KR → NLHK → ESIL → NLCA → NLJP → NL13KR → RUES → USCA → IN14CN → DKCA → CH


#### 3.5.2. Motif Analysis of the Potential Trade Links

Section3.4 of this article shows that successfully predicted links promote the formation of important motifs in the network. Therefore, after a preliminary screening of the potential trade links, the motif analysis method is applied to add the screened potential trade links one-by-one to the mineral international trade network to check the formation of their important motifs. If the potential links form more important motifs, then when their similarity with the successfully predicted link is stronger, the possibility of turning it into an actual link is higher. Because it predicts the future trade links of the mineral international trade, the potential trade links initially screened out are added to the 2020 mineral international trade network one-by-one. By checking a link’s contribution to the formation of important motifs in the 2020 trade network, we can compare and analyze the possibility of its transformation into a real trade relationship.Table18 shows the contribution to important motifs of the potential links preliminarily screened for LiC, and the results of the other important minerals are shown in Tables 19–26.Table 18
The contribution to important motifs of potential links preliminarily screened for LiC.
Preliminary screening of potential linksThe number of newly added motifsM4M5M6M7M8M9M12FR → KR150304503CA → DE1300003100CA → BE72031001CA → RU170403361NL → AE150202920NL → RS1801051110KR → NL2800000919AU → NL32001011020ID→NL35000001223JP → NL37014041117MY→NL31000001021IL → NL30000003Table 19
The contribution to important motifs of potential links preliminarily screened for Al.
Preliminary screening of potential linksThe number of newly added motifsM4M6M7M8M9M12AE → EU10100009DK → US131100011CZ → FR12001173FR → IN11112007DK → IN9011007DK → ES210002145HK → NL4101011821NL → TH240011931SA → EU10001009DE → KR1000010FR → US230013163Table 20
The contribution to important motifs of potential links preliminarily screened for C.
Preliminary screening of potential linksThe number of newly added motifsM4M6M7M8M9M12ID→EU9000009DK → DE10000280IN→TH4100323150ID→IN170400013IN→CH16450007IN→BR14311009FR → AT120002100IN→ES3700223111NL → BR7403000NL → TH220051520TH → US7000007KR → NL3901011522KR → RU8000260CN → DK7401002Table 21
The contribution to important motifs of potential links preliminarily screened for Co.
Preliminary screening of potential linksThe number of newly added motifsM1M5M6M11BE→IN20200CN → FR30102IN→GB1300013BE→GB1000010CN → GB90009CN → CH40103BE→US60024CN → NL40103DE → NL00000NL → US20200NL → IN10100HK → ES10001ES → US21100Table 22
The contribution to important motifs of potential links preliminarily screened for Cu.
Preliminary screening of potential linksThe number of newly added motifsM4M6M7M9M11M12CN → IN503700436CN → TH510100545CN → JP470043760CN → CH510124080CA → NL190131140KH → CN160005011KR → ES12000813CN → NA530620342Table 23
The contribution to important motifs of potential links preliminarily screened for Fe.
Preliminary screening of potential linksThe number of newly added motifsM4M6M7M9M11M12CN → AT5701336170CN → HU5601434170CN → HK5700437160CN → QA5110101435JP → NL281330129CN → ES5367201028Table 24
The contribution to important motifs of potential links preliminarily screened for Mn.
Preliminary screening of potential linksThe number of newly added motifsM4M5M6M7M9M11M12MX → IN180211905IN→US40105101419IT→IN260703835CN → UA50000002327CN → SK40020124121CN → ES51083125122CN → NL57202302921ID→NL2610000214CN → BE57002602722CN → DK47050229110CZ → IN2605111225Table 25
The contribution to important motifs of potential links preliminarily screened for Ni.
Preliminary screening of potential linksThe number of newly added motifsM4M5M6M9M11CN → BE600141DE → ZA000000CN → FR700061CN → HK500041CN → IN401030CA → AU710204CA → DE18000153CA → SG17010142CA → GB400004MK → EU600060CL → EU400040CA → NL23040163CA → IN18020142CA → CH500203Table 26
The contribution to important motifs of potential links preliminarily screened for Ti.
Preliminary screening of potential linksThe number of newly added motifsM4M5M6M7M9CN → RU20000416MY→NL33020031CN → PL20040313IN→US1120630KR → US310200KR → EU210100KR → NL34020032CN → MA17000215CN → FI18010116CN → HU17020114JP → US610500JP → NL39031035


#### 3.5.3. Select the Best Potential Link

In Section3.5.1, we preliminarily screen the potential trade relations of the 9 critical minerals. Next, we further filter these potential links to obtain the best potential links. There are two principles for this step. The first principle is to check whether the potential link follows the three rules summarized in Section 3.3. If the potential link follows one or more of the three rules, then we think that the quality of the potential link is high. The second principle is to check how much the potential link increases the number of key motifs in the network. When there is a greater increase in this number, we think that the quality of the potential link is higher. The results are shown in Table 27, and the specific analysis process is also described.Table 27
The best potential links of the international trade relations of 9 critical minerals.
Best potential linksThe number of newly added motifsRule 1Rule 2Rule 3AlHK → NL41√FR → US23√√√CKR → NL39√√IN→ES37√√NL → TH22√√CoIN→GB13√BE→GB10√√CN → GB9√√CuCN → IN50√√CN → TH51√√CN → JP47√√CN → CH51√√CN → NA53√√√FeCN → HU56√√CN → ES53√√√LiCKR → NL28√√AU → NL32√√JP → NL37√√MY→NL31√√MnCN → UA50√√CN → ES51√√CN → NL57√√√CN → BE57√√CN → DK47√√NiCA → DE18√√√CA → NL23√√CA → IN18√√TiCN → RU20√√√MY→NL33√√KR → NL34√√JP → NL39√√For Al, Hong Kong → the Netherlands and France → the United States are most likely to transform into real trade relationships in the future. Hong Kong → the Netherlands established trade contacts in 2011 and 2014, which complies with the trade link rule 3, and the potential of this link to promote the formation of important motifs in the network is the highest among the 11 pairs of potential trade links initially screened for Al. France → the United States had continuous trade exchanges from 2011 to 2017, and this trade link was predicted from 2018 to 2019, which complies with trade link rules 1, 2, and 3, and the potential of the link to promote the formation of important motifs in the network is the highest among the 11 pairs of potential trade links initially screened for Al.For C, South Korea → the Netherlands, India → Spain, and the Netherlands → Thailand are most likely to transform into real trade relationships in the future. All of these potential trade links have a high facilitating effect on the formation of important motifs. South Korea → the Netherlands had actual trade relations in 2015 and 2016, and this link was continuously predicted from 2017 to 2019, which is in line with trade link rules 1 and 3. India → Spain had actual trade relations in 2011, and trade was predicted in 2020, which is consistent with trade link rules 1 and 3. The Netherlands → Thailand had actual trade relations in 2011, 2012, and 2015, and trade was continuously predicted from 2016 to 2019, which is in line with trade link rules 1 and 3.For Co, India → the United Kingdom, Belgium → the United Kingdom, and China → the United Kingdom are most likely to transform into real trade relationships in the future. All of these potential trade links have a high facilitating effect on the formation of important motifs, and they are the top 3 among the 13 pairs of potential trade links initially screened for Co. India → the United Kingdom had actual trade relations in 2016 and 2017, which is consistent with trade link rule 3. Belgium → the United Kingdom continued to conduct trade transactions from 2012 to 2016, which is in line with trade link rules 2 and 3. China → the United Kingdom had actual trade relations in 2011 and 2014, and trade was predicted in 2020, which is consistent with trade link rules 1 and 3.For Cu, China → India, China → Thailand, China → Japan, China → Switzerland, and China → Namibia are most likely to transform into real trade relationships in the future. All of these potential trade links have a high facilitating effect on the formation of important motifs, and they far exceed the other three pairs of potential links. China → India had actual trade relations in 2011 and 2017, and the trade link was predicted in other years, which is in line with trade link rules 1 and 3. China → Thailand had actual trade relations in 2011, 2013, 2014, 2015, and 2017, which is consistent with trade link rules 2 and 3. China → Japan had actual trade relations in 2011 and 2014, and trade was predicted in other years, which is in line with trade link rules 1 and 3. China → Switzerland had actual trade relations in 2011 and 2013, and trade was continuously predicted from 2017 to 2020, which is consistent with trade link rules 1 and 3. China → Namibia had actual trade relations in 2014, 2015, and 2017, and trade was predicted in 2020, which is in line with trade link rules 1, 2, and 3.For Fe, China → Hungary and China → Spain are most likely to transform into real trade relationships in the future. All of these potential trade links have a high facilitating effect on the formation of important motifs. China → Hungary had an actual trade relation in 2015, and it was predicted in 2020, which is in line with trade link rules 1 and 3. China → Spain continued to conduct trade exchanges from 2011 to 2015, and they were continuously predicted from 2016 to 2020, which is consistent with trade link rules 1, 2, and 3.For LiC, South Korea → the Netherlands, Australia → the Netherlands, Japan → the Netherlands, and Malaysia → the Netherlands are most likely to transform into real trade relationships in the future. All of these potential trade links have a high facilitating effect on the formation of important motifs. South Korea → the Netherlands had actual trade relations in 2012 and 2015, and trade was continuously predicted from 2016 to 2020, which is in line with trade link rules 1 and 3. Australia → the Netherlands had actual trade relations in 2015, and they were predicted in 2016 and 2018, which is consistent with trade link rules 1 and 3. Japan → the Netherlands had actual trade relations in 2013 and 2015, and relations were predicted in 2016, 2018, and 2020, which is in line with trade link rules 1 and 3. Malaysia → the Netherlands had actual trade relations in 2015, and trade was predicted in 2016, 2018, and 2020, which is consistent with trade link rules 1 and 3.For Mn, China → Ukraine, China → Spain, China → the Netherlands, China → Belgium, and China → Denmark are most likely to transform into real trade relationships in the future. All of these potential trade links have a high facilitating effect on the formation of important motifs, and they are the top 5 of the 11 pairs of potential trade links initially screened for Mn. China → Ukraine had actual trade relations in 2016, and trade was continuously predicted from 2017 to 2018, which is in line with trade link rules 1 and 3. China → Spain had actual trade relations in 2011 and 2013, and trade was continuously predicted from 2016 to 2020, which is consistent with trade link rules 1 and 3. China → the Netherlands continued to conduct trade exchanges from 2011 to 2014, and they were continuously predicted from 2015 to 2020, which is in line with trade link rules 1, 2, and 3. China → Belgium had actual trade relations in 2014, and trade was continuously predicted from 2017 to 2020, which is consistent with trade link rules 1 and 3. China → Denmark had actual trade relations in 2014, and trade was continuously predicted from 2018 to 2019, which is in line with trade link rules 1 and 3.For Ni, Canada → Germany, Canada → the Netherlands, and Canada → the India are most likely to transform into real trade relationships in the future. All of these potential trade links have a high facilitating effect on the formation of important motifs, and they are the top 3 of the 14 pairs of potential trade links initially screened for Ni. Canada → Germany continued to conduct trade exchanges from 2011 to 2015, and trade was predicted in 2016 and 2018, which is in line with trade link rules 1, 2, and 3. Canada → the Netherlands had actual trade relations in 2014 and 2017, and trade was predicted in 2020, which is consistent with trade link rules 1 and 3. Canada → India had actual trade relations in 2011, and trade was predicted in 2020, which is in line with trade link rules 1 and 3.For Ti, China → Russia, Malaysia → the Netherlands, South Korea → the Netherlands, and Japan → The Netherlands are most likely to transform into real trade relationships in the future. All of these potential trade links have a high facilitating effect on the formation of important motifs, and they are the top 4 of the 12 pairs of potential trade links initially screened for Ti. China → Russia continued to conduct trade exchanges from 2012 to 2014, and trade was continuously predicted from 2017 to 2019, which is consistent with trade link rules 1, 2, and 3. Malaysia → the Netherlands had actual trade relations in 2015, and trade was predicted in 2019, which is in line with trade link rules 1 and 3. South Korea → the Netherlands had actual trade relations in 2015, and trade was continuously predicted from 2018 to 2019, which is consistent with trade link rules 1 and 3. Finally, Japan → the Netherlands had actual trade relations in 2014 and 2015, and trade was continuously predicted from 2018 to 2020, which is in line with trade link rules 1 and 3.


### 3.6. Forecast of the International Trade Relations of the Raw Materials Required for Lithium-Ion Battery Midstream Products

The frequent replacement and upgrading of small electronic products and the rapid development of the electric vehicle industry have increased the pressure on the supply of raw materials for the manufacturing end of lithium-ion batteries. However, because of the impact of the international political situation, national trade policies, natural disasters, and unexpected disasters such as COVID-19, the supply of raw materials for lithium-ion batteries is unstable. For example, in response to the rapid increase in new coronavirus infection cases, Chile announced that it would close its borders on April 5, 2021, which had a strong impact on the world’s lithium resource supply situation and led to a rapid increase in the price of battery-grade lithium carbonate worldwide. China, Japan, and South Korea, as the main export sources for Chile, have been the most directly affected. The sudden riot in South Africa on July 18, 2021 caused considerable economic losses and hindered the export of various mineral raw materials for lithium-ion batteries. In 2018, the DRC government substantially increased the mining tax rate of cobalt metal. In March of the same year, the DRC President signed a new mining law that increased the mining tax rate of cobalt from 2% to 3.5%, which was implemented in June of the same year. On December 3, 2018, the DRC government announced that cobalt was a strategic metal and further increased the mining tax rate on cobalt from 3.5% to 10%, which resulted in an increase in the global price of cobalt minerals. These unexpected factors in international trade directly affect the manufacturing of midstream lithium-ion battery products, especially for countries with developed lithium-ion battery manufacturing industries. The growth of trading partners in a country makes shortages recede, just as the growth of wealth in a society makes corruption recede [58]. Therefore, this article selects midstream products that require larger mineral raw materials, such as electrolytes, cathode materials, and anode materials. Countries with developed manufacturing industries for midstream products of lithium-ion batteries and the main mineral raw materials needed to produce midstream products of lithium-ion batteries should be identified. Based on the results of this study, the potential import trade of mineral raw materials required by these countries is predicted. The results are summarized in Table 28. Based on the predicted results, these countries should appropriately increase the diversity of their trading partners, expand their import channels, and enhance the supply security of raw materials in the manufacturing of products in the middle reaches of the lithium-ion battery industry chain.Table 28
Trade forecast of the imported raw material end of the developed countries in mid-stream product manufacturing of the lithium-ion battery industry chain.
Midstream productsElectrolyteAnode materialCathode materialIndustrially developed countriesCN, KRCN, KR, BE, JPUS, JPMain mineral raw materialsLiCLiCCoNiMnCPotential trade relationsFR → KRFR → KRCN → KRCN → JPCN → BEFR → JPCA → CNCA → CNCN → BECA → JPCZ → USFR → BEFR → BECA → KRKR → USCA → BECN → JPDE → KRPL → USCN → BEDE → KRCN → KRTR → USKR → BECN → BEIN→USCA → CNES → USRU → USTH → USIT→US


## 3.1. Key Motif Recognition

The FANMOOD tool was used to mine the key motifs in the international trade network of the nine minerals, and theZ score indicator (Equation (13)) was chosen in the selection of the statistical significance indicator of the motif. The Z score is a common indicator to measure the statistical significance of motifs, and the Z score has been widely used in motif recognition in different types of empirical network research [50, 51].Taking LiC as an example, Figure6 shows the evolution of the key motifs in the LiC international trade network. The Z scores of the six key identified motifs fluctuate sharply every year, which indicates that the local trade relations among countries in the LiC international trade network also evolved greatly every year. From the perspective of the evolution trend of the key LiC motifs, the Z scores of M4 and M7 were in the top two for ten years. Both motifs have bilateral trade relations, which shows that countries in the LiC trade mostly adopt the reciprocal trade mode to meet the balance of supply and demand of their own resources. The Z scores of M9 have been on an upward trend over the past decade; this suggests that an increasing number of countries as “transit countries” in the LiC trade have played a considerable role in promoting the global flow of LiC resources. The Z scores of M8 fluctuate the most, which implies that the country’s unilateral export or import trade model is unstable and brings trade risks.Figure 6
The evolution of key motifs of the LiC international trade network.The key motifs identified in the international trade network of the nine important minerals are summarized in Table2.Table 2
Identification of key motifs of the nine important minerals.
MineralKey motifs identifiedAlM4, M6, M7, M8, M9, M12CM4, M6, M7, M8, M9, M12CoM1, M5, M6, M11CuM4, M6, M7, M9, M11, M12FeM4, M6, M7, M9, M11, M12LiCM4, M6, M7, M8, M9, M12MnM4, M5, M6, M7, M9, M11, M12NiM4, M5, M6, M9, M11TiM4, M5, M6, M7, M9


## 3.2. Verification of the Validity of the Link Prediction Model

In this section, the accuracy of the four mainstream algorithms is tested to select the optimal algorithm, and then, the optimal algorithm is used to predict the potential trade relations of the nine mineral trades by comparing the prediction success proportion of the potential links in the actual trade to test the validity of the link prediction model and to prove the reliability of the algorithm applied in empirical networks.


### 3.2.1. Select the Optimal Algorithm

Four mainstream algorithms, specifically, CN, AA, RA, and PA, are used to calculateET and EI, and these links are ranked according to the score of the algorithm. A higher score means that the nonexistent link is more likely to be converted into an existing link in the future; that is, the country/region pair that corresponds to this link is more likely to have trade relations in the future. By comparing the accuracy indicators, the AUCs of the four algorithms are used to find the optimal algorithm. When the AUC score is higher, the accuracy of the corresponding algorithm is higher.In the choice of network type, the directed and unweighted network is selected for prediction based on two considerations. First, the choice of the directed network structure means that the direction of trade between countries is considered, which can provide at the import and export ends accurate trading partners for the trading countries such that the research results have more practical significance. In addition, in the undirected network structure, there are fewer motifs, the analysis of the local network structure is less meticulous, and the degree of discrimination in statistical significance is low. Second, choosing the unweighted network structure can eliminate the agglomeration effect of large import and export countries in the trade network. Only by considering the network structure, that is, the connectivity of trade channels, can the analysis and prediction be performed such that the possibility of the predictive links between small import and export countries emerge, which is conducive to discovering more trade links that are more likely to be realized.From using the four mainstream algorithms, the AUC scores of the nine important minerals are shown in Figure7. The x-axis represents the four algorithms of CN, AA, RA, and PA, the y-axis represents the years from 2011 to 2020, and the z-axis represents the AUC score results under the corresponding algorithm in the corresponding year. To reduce random errors and make the scoring result more scientific, the AUC score here is the average result of 10 experiments, and the data are randomly divided into 10% ET and 90% ER for all 10 experiments. By comparing the AUC scores, it can be concluded that the AUC scores are all greater than 0.5 and close to 1, which indicates that these four algorithms are applicable to the analysis of the international trade data of the nine important minerals. In addition, by comparing the scores of the four algorithms in the figure, it can be found that the optimal algorithms for the nine important minerals are all PA algorithms, which shows that the PA algorithm (countries with more trading partners more easily establish new trade relations) has universal applicability in the international trade network of minerals. Therefore, it can be concluded that the PA algorithm is the optimal algorithm to be applied in this study.Figure 7
AUC scores of nine important minerals.Based on the analysis of the accuracy indicator of the AUC scoring results, this paper chooses the directed and unweighted PA algorithm to find potential trade links. First, the links inET and EI are ranked according to the value of PA. According to the definition of the PA algorithm, countries with more trading partners more easily establish new trade relations. Therefore, countries with high PA values are more likely to have new trade relations than countries with lower PA values. Therefore, this study selects in EI the top potential country pairs that will be more conducive to the establishment of real trade relations in the future.


### 3.2.2. Pick Potential Links

In the process of link prediction, the total dataset is divided into 10%ET and 90% ER; therefore, the result of the link prediction algorithm includes both test links and potential links. Potential links are predictions of unknown links and future links. This section selects the potential links in the network topology of the nine minerals that comprise the main element raw materials of lithium-ion batteries and observes whether they have actually established real trade relations after they are predicted to have trade relations.Taking LiC as an example, this study selects the top ten nonexistent links from 2011 to 2020. Table3 shows the top ten trading countries or regions of LiC in the PA algorithm score in 2020, including the test links and nonexistent links. The first column in Table 3 represents the PA value ranking of the nonexistent links, the second and third columns represent the two countries or regions included in the trade link, the fourth column represents the PA algorithm score of the trade link, and the fifth column represents the types of links: P is the link that does not exist at present, which is a potential trade link, and T is the link in the test set, which is the actual link. Among the 14 pairs of trading countries or regions, 4 pairs of trade relationships come from the test set, and the remaining 10 pairs of trade relationships represent nonexistent link relationships, which are the top 10 potential trade links that require further analysis. We follow the above steps to select and organize the top ten potential links of the nine minerals every year to observe whether they actually have trade relations in subsequent years.Table 3
The top 14 trade links of LiC’s PA value in 2020.
RankCountry or regionCountry or regionPA valueLink typeNLCH405TCANL378T1FINL297P2KRNL297P3NLZA270P4ITNL243P5CADE224P6JPNL216P7INES208PCNCH195TEENL189T8ILNL189P9MYNL189P10NLRS189P


### 3.2.3. Comparison of the Potential Links and Actual Links

We select and organize the top ten potential links of the nine minerals each year. The summary results of LiC are shown in Figure8, and the summary results of the other minerals are shown in Figures 9–16.Figure 8
Comparison of potential trade links and actual trade links of LiC.Figure 9
Comparison of potential trade links and actual trade links of Al.Figure 10
Comparison of potential trade links and actual trade links of C.Figure 11
Comparison of potential trade links and actual trade links of Co.Figure 12
Comparison of potential trade links and actual trade links of Cu.Figure 13
Comparison of potential trade links and actual trade links of Fe.Figure 14
Comparison of potential trade links and actual trade links of Mn.Figure 15
Comparison of potential trade links and actual trade links of Ni.Figure 16
Comparison of potential trade links and actual trade links of Ti.Figures8 and 9–16 show the results of the aggregation of the top ten potential trading country/region pairs of the nine important minerals from 2010 to 2020. Since there are trading country pairs that repeatedly appear in the top ten PA value rankings in each year, the number of country pairs summarized by different minerals is different. The first column in the figure represents the labels of the trading country/region pairs, the second column represents the two countries/regions of the trade link, and the arrows between the countries/regions identify the trade direction. The third to the 12th columns represent the years from 2011 to 2020, and the 13th column indicates the cumulative number of predicted successful links. For each row, the green color block indicates that the country pair has not traded minerals for the corresponding year in this column, but because they are in the top ten rankings of the PA value, they are potential trade links. The white color block indicates that the country pair not only has not traded minerals for the corresponding year in this column but also is not in the top ten ranking of the PA values. The orange color block indicates that the country pair has actual trade relations for the corresponding year in this column. By observing the potential and actual trade links, it is possible to analyze the trend of the international mineral trade in the past decade and provide theoretical support for the next prediction.Next, we introduce the prediction rules, which are used to calculate the prediction success rate for the results shown in Figure8 (the prediction rules are the same for the other critical minerals). For the corresponding country pair in each row, if at least one orange color block appears after the green color block, then this means that the potential trade link did indeed have a trade relationship afterward, and that the country pair is a predicted successful country pair. Take the first country pair in Figure 8, France and India, as an example. The green color block appeared in 2011, which shows that the potential trade relationship of this country pair was predicted in 2011, and then, the orange color block appeared in 2012, which indicates that the country pair had an actual trade relationship in 2012; thus, the potential trade relationship of the country pair was predicted to be successful. In contrast, if the country pair has no orange color block after the green color block appears for the first time, then this means that the potential trade link did not have any actual trade relationship in the next few years, and it is defined as an invalid prediction. Take the 44th country pair in Figure 8, Japan and the Netherlands, as an example. For this country pair, orange color blocks appeared in 2013 and 2015, which suggests that a trade relationship has occurred. The green color block appeared for the first time in 2016, which demonstrates that a trade relationship is predicted to occur. However, no orange color blocks appeared in other years after 2016, and this signifies that the country pair did not have a trade relationship in other years; therefore, the country pair prediction failed.The effectiveness of the algorithm can be verified by counting the total proportion of the country pairs that are predicted to be successful. For the country pairs that showed green color blocks for the first time in 2020, as there are no actual trade data in 2021 to test whether the country pairs are predicted to be successful, they are not classified as prediction failures, and these country pairs are eliminated when the success rate is calculated.Table4 shows the statistical results of the prediction success rates of the nine minerals. Their success rates are all above 50%, which shows that it is effective to use the directed and unweighted PA algorithm to predict the potential relationships in the international trade of the nine minerals.Table 4
Statistics on the forecast success rate of the main element raw material minerals for lithium-ion batteries.
MineralAlCCoCuFeLiCMnNiTiNumber of potential country pairs345654323656384657The number after elimination315152313352364055Number of successful predictions203428202333242139Success rate64.5%66.7%53.8%64.5%69.7%63.5%66.7%52.5%70.9%


## 3.2.1. Select the Optimal Algorithm

Four mainstream algorithms, specifically, CN, AA, RA, and PA, are used to calculateET and EI, and these links are ranked according to the score of the algorithm. A higher score means that the nonexistent link is more likely to be converted into an existing link in the future; that is, the country/region pair that corresponds to this link is more likely to have trade relations in the future. By comparing the accuracy indicators, the AUCs of the four algorithms are used to find the optimal algorithm. When the AUC score is higher, the accuracy of the corresponding algorithm is higher.In the choice of network type, the directed and unweighted network is selected for prediction based on two considerations. First, the choice of the directed network structure means that the direction of trade between countries is considered, which can provide at the import and export ends accurate trading partners for the trading countries such that the research results have more practical significance. In addition, in the undirected network structure, there are fewer motifs, the analysis of the local network structure is less meticulous, and the degree of discrimination in statistical significance is low. Second, choosing the unweighted network structure can eliminate the agglomeration effect of large import and export countries in the trade network. Only by considering the network structure, that is, the connectivity of trade channels, can the analysis and prediction be performed such that the possibility of the predictive links between small import and export countries emerge, which is conducive to discovering more trade links that are more likely to be realized.From using the four mainstream algorithms, the AUC scores of the nine important minerals are shown in Figure7. The x-axis represents the four algorithms of CN, AA, RA, and PA, the y-axis represents the years from 2011 to 2020, and the z-axis represents the AUC score results under the corresponding algorithm in the corresponding year. To reduce random errors and make the scoring result more scientific, the AUC score here is the average result of 10 experiments, and the data are randomly divided into 10% ET and 90% ER for all 10 experiments. By comparing the AUC scores, it can be concluded that the AUC scores are all greater than 0.5 and close to 1, which indicates that these four algorithms are applicable to the analysis of the international trade data of the nine important minerals. In addition, by comparing the scores of the four algorithms in the figure, it can be found that the optimal algorithms for the nine important minerals are all PA algorithms, which shows that the PA algorithm (countries with more trading partners more easily establish new trade relations) has universal applicability in the international trade network of minerals. Therefore, it can be concluded that the PA algorithm is the optimal algorithm to be applied in this study.Figure 7
AUC scores of nine important minerals.Based on the analysis of the accuracy indicator of the AUC scoring results, this paper chooses the directed and unweighted PA algorithm to find potential trade links. First, the links inET and EI are ranked according to the value of PA. According to the definition of the PA algorithm, countries with more trading partners more easily establish new trade relations. Therefore, countries with high PA values are more likely to have new trade relations than countries with lower PA values. Therefore, this study selects in EI the top potential country pairs that will be more conducive to the establishment of real trade relations in the future.


## 3.2.2. Pick Potential Links

In the process of link prediction, the total dataset is divided into 10%ET and 90% ER; therefore, the result of the link prediction algorithm includes both test links and potential links. Potential links are predictions of unknown links and future links. This section selects the potential links in the network topology of the nine minerals that comprise the main element raw materials of lithium-ion batteries and observes whether they have actually established real trade relations after they are predicted to have trade relations.Taking LiC as an example, this study selects the top ten nonexistent links from 2011 to 2020. Table3 shows the top ten trading countries or regions of LiC in the PA algorithm score in 2020, including the test links and nonexistent links. The first column in Table 3 represents the PA value ranking of the nonexistent links, the second and third columns represent the two countries or regions included in the trade link, the fourth column represents the PA algorithm score of the trade link, and the fifth column represents the types of links: P is the link that does not exist at present, which is a potential trade link, and T is the link in the test set, which is the actual link. Among the 14 pairs of trading countries or regions, 4 pairs of trade relationships come from the test set, and the remaining 10 pairs of trade relationships represent nonexistent link relationships, which are the top 10 potential trade links that require further analysis. We follow the above steps to select and organize the top ten potential links of the nine minerals every year to observe whether they actually have trade relations in subsequent years.Table 3
The top 14 trade links of LiC’s PA value in 2020.
RankCountry or regionCountry or regionPA valueLink typeNLCH405TCANL378T1FINL297P2KRNL297P3NLZA270P4ITNL243P5CADE224P6JPNL216P7INES208PCNCH195TEENL189T8ILNL189P9MYNL189P10NLRS189P


## 3.2.3. Comparison of the Potential Links and Actual Links

We select and organize the top ten potential links of the nine minerals each year. The summary results of LiC are shown in Figure8, and the summary results of the other minerals are shown in Figures 9–16.Figure 8
Comparison of potential trade links and actual trade links of LiC.Figure 9
Comparison of potential trade links and actual trade links of Al.Figure 10
Comparison of potential trade links and actual trade links of C.Figure 11
Comparison of potential trade links and actual trade links of Co.Figure 12
Comparison of potential trade links and actual trade links of Cu.Figure 13
Comparison of potential trade links and actual trade links of Fe.Figure 14
Comparison of potential trade links and actual trade links of Mn.Figure 15
Comparison of potential trade links and actual trade links of Ni.Figure 16
Comparison of potential trade links and actual trade links of Ti.Figures8 and 9–16 show the results of the aggregation of the top ten potential trading country/region pairs of the nine important minerals from 2010 to 2020. Since there are trading country pairs that repeatedly appear in the top ten PA value rankings in each year, the number of country pairs summarized by different minerals is different. The first column in the figure represents the labels of the trading country/region pairs, the second column represents the two countries/regions of the trade link, and the arrows between the countries/regions identify the trade direction. The third to the 12th columns represent the years from 2011 to 2020, and the 13th column indicates the cumulative number of predicted successful links. For each row, the green color block indicates that the country pair has not traded minerals for the corresponding year in this column, but because they are in the top ten rankings of the PA value, they are potential trade links. The white color block indicates that the country pair not only has not traded minerals for the corresponding year in this column but also is not in the top ten ranking of the PA values. The orange color block indicates that the country pair has actual trade relations for the corresponding year in this column. By observing the potential and actual trade links, it is possible to analyze the trend of the international mineral trade in the past decade and provide theoretical support for the next prediction.Next, we introduce the prediction rules, which are used to calculate the prediction success rate for the results shown in Figure8 (the prediction rules are the same for the other critical minerals). For the corresponding country pair in each row, if at least one orange color block appears after the green color block, then this means that the potential trade link did indeed have a trade relationship afterward, and that the country pair is a predicted successful country pair. Take the first country pair in Figure 8, France and India, as an example. The green color block appeared in 2011, which shows that the potential trade relationship of this country pair was predicted in 2011, and then, the orange color block appeared in 2012, which indicates that the country pair had an actual trade relationship in 2012; thus, the potential trade relationship of the country pair was predicted to be successful. In contrast, if the country pair has no orange color block after the green color block appears for the first time, then this means that the potential trade link did not have any actual trade relationship in the next few years, and it is defined as an invalid prediction. Take the 44th country pair in Figure 8, Japan and the Netherlands, as an example. For this country pair, orange color blocks appeared in 2013 and 2015, which suggests that a trade relationship has occurred. The green color block appeared for the first time in 2016, which demonstrates that a trade relationship is predicted to occur. However, no orange color blocks appeared in other years after 2016, and this signifies that the country pair did not have a trade relationship in other years; therefore, the country pair prediction failed.The effectiveness of the algorithm can be verified by counting the total proportion of the country pairs that are predicted to be successful. For the country pairs that showed green color blocks for the first time in 2020, as there are no actual trade data in 2021 to test whether the country pairs are predicted to be successful, they are not classified as prediction failures, and these country pairs are eliminated when the success rate is calculated.Table4 shows the statistical results of the prediction success rates of the nine minerals. Their success rates are all above 50%, which shows that it is effective to use the directed and unweighted PA algorithm to predict the potential relationships in the international trade of the nine minerals.Table 4
Statistics on the forecast success rate of the main element raw material minerals for lithium-ion batteries.
MineralAlCCoCuFeLiCMnNiTiNumber of potential country pairs345654323656384657The number after elimination315152313352364055Number of successful predictions203428202333242139Success rate64.5%66.7%53.8%64.5%69.7%63.5%66.7%52.5%70.9%


## 3.3. Explore the Rules of the Successful Prediction of Trade Links

In the previous section, this article predicted the potential link relationships in the international trade of the nine minerals and obtained a high prediction success rate. Most of the predicted potential trade relations were successfully realized in the next few years, but there are still some predicted potential links. Although they are in the top ten potential links, they do not produce actual trade relations after being predicted. This section analyzes the inherent characteristics of successfully predicted links to explore the rules of the successful prediction of trade links and to provide a theoretical basis for trading countries to find suitable trading partners.We take the successfully predicted trade links of LiC in Figure17 as an example to analyze their inherent characteristics. The results of the other minerals are shown in Figures 18–25. The potential links of LiC that were successfully predicted include 33 pairs of trading countries/regions. By observing the process from being predicted to successfully establishing trade relations, it is found that 20 pairs (61%) of trading countries/regions successfully established trade relations within 3 years after being first predicted, and these pairs are marked in column “A” in the figure. Therefore, this study sets the forecast time limit as 3 years; that is, a pair of potential trade relations can successfully establish a trade relationship with a high probability within 3 years after being predicted. If it exceeds 3 years, then the possibility of establishing a relationship is low. Column “B” lists the cumulative number of the country/region pairs that have established two or more trade relations in a decade. According to the statistics, a total of 27 (82%) out of 33 pairs successfully predicted that the country pairs fit this feature, which indicates that countries tend to establish long-term and stable trade relations in international trade. Column “C” lists the cumulative number of the country/region pairs that had actual trade relations before the trade relations were predicted for the first time. The country/region pairs that were predicted to have trade relations in 2011 are excluded from the statistics because there are no data before 2011 for verification. According to the statistics, among 25 country/region pairs, a total of 15 (60%) had actual trade relations before they were successfully predicted. Therefore, in the potential trade links of LiC, the existing trade relations promote the establishment of the predicted trade relations.Figure 17
Successfully predicted trade links of LiC.Figure 18
Successfully predicted trade links of Al.Figure 19
Successfully predicted trade links of C.Figure 20
Successfully predicted trade links of Co.Figure 21
Successfully predicted trade links of Cu.Figure 22
Successfully predicted trade links of Fe.Figure 23
Successfully predicted trade links of Mn.Figure 24
Successfully predicted trade links of Ni.Figure 25
Successfully predicted trade links of Ti.Based on the analysis of the potential links of the successful prediction of LiC, the prediction rules of the nine important minerals are summarized, and the following three trade link rules are obtained.(1)
The link prediction of the nine minerals, the main element raw materials of lithium-ion batteries, has a timeliness requirement, and it generally takes 3 years for the potential trade relationship to be predicted until the real trade relationship is establishedFrom the results in Table5, among the potential links that are successfully predicted for the nine important minerals, the percentages of links that meet the 3-year timeliness requirement are more than 60%, which shows that the establishment of trade relations for the main element minerals of lithium-ion batteries does not happen overnight but requires a certain time scale to complete. This paper sets the prediction timeliness requirement of the nine minerals as 3 years; that is, a pair of potential trade relations is highly likely to be successfully established within 3 years after being predicted, and the possibility of establishing a relationship is low if it exceeds 3 years.
(2)
The trading countries of the nine minerals tend to establish long-term and stable trade relations when looking for trading partnersTable 5
Statistics of the trade links of nine important minerals in line with rule 1.
MineralAlCCoCuFeLiCMnNiTiPredict the number of successful links203428202333242139Establish trade relations within 3 years183017172020191825Percentage90.0%88.2%60.7%85.0%87.0%60.6%79.2%85.7%64.1%From the results in Table6, among the potential links that are successfully predicted for the nine important minerals, the percentages of the links that have established two or more trade relations within ten years are more than 75%, which indicates that in international trade, countries tend to trade minerals with partners who can establish long-term and stable trade relations to meet their own balance of supply and demand, and long-term stable trade relations also help reduce trade risks and enhance trade security.
(3)
Among the international trade links of the nine minerals, the existing trade relations will promote the establishment of the predicted trade relationsTable 6
Statistics of the trade links of nine important minerals in line with rule 2.
MineralAlCCoCuFeLiCMnNiTiPredict the number of successful links203428202333242139Two or more trades173321201927221932Percentage85.0%97.1%75.0%100.0%82.6%81.8%91.7%90.5%82.1%Table7 shows the statistical results of the successfully predicted links of the nine important minerals in line with rule 3. The country pairs that were predicted to have trade relations in 2011 are excluded from the statistics because there are no actual trade data before 2011 for verification. According to the statistical results in Table 7, among the potential links that are successfully predicted for the nine important minerals, more than 60% of the links had trade relations before they were predicted for the first time. Therefore, in the prediction of the international trade links of the nine minerals, if there is an existing trade relation on the potential link before it is predicted, then the possibility that it will be converted to a real trade relation increases.Table 7
Statistics of the trade links of nine important minerals in line with rule 3.
MineralAlCCoCuFeLiCMnNiTiPredict the number of successful links152819141725151431Trade relations existed before being predicted10191312111591120Percentage66.7%67.9%68.4%85.7%64.7%60.0%60.0%78.6%64.5%


## 3.4. Explore the Impact of the Formation of Predicted Trade Links on the Structure of Local Mineral Trade Networks

In the previous section, from the global perspective, this paper analyzes the internal characteristics of the successfully predicted links in the link prediction of the nine mineral resources and summarizes three rules that help to find successfully predicted links. This section discusses the use of the motif analysis method to analyze in the nine mineral link predictions the formation of successfully predicted trade links from a local perspective, which changes the local structure of the international trade network of mineral resources and explores the influence of the formation of potential trade links on the local trade mode of mineral resources. From the perspective of network motifs, we can deeply study the reasons why potential trade links are successfully predicted and provide a more comprehensive theoretical basis for the follow-up search for high-quality potential trade links in the international trade of the nine minerals.According to the trade link rule 1 summarized in Section3.3, the link prediction of the nine minerals, the main element raw materials of lithium-ion batteries, has a timeliness requirement, and it generally takes 3 years for the potential trade relationship to be predicted until the real trade relationship is established. Therefore, based on the 3-year forecasting timeliness rule, this article selects the country/region pairs of the nine minerals that are predicted in each year from 2011 to 2017 and that successfully establish trade relations within 3 years. Then, it adds their trade relations to the international trade network of the predicted years, conducts a motif analysis, and compares the network structure before joining to determine the increase in its important motifs to analyze and study the impact of the formation of potential trade links on the local trade structure of minerals.Taking LiC as an example, it can be seen from Figure17 that the country pairs predicted in 2011, and that successfully established trade relations within 3 years were France → India and France → Korea. Therefore, these two pairs of trade relations were added to the LiC trade network in 2011. Compared with the network structure before joining, the network after joining is examined to determine the important motifs that were newly formed due to the increase in network information; in addition, the increase in the number was counted to analyze how the formation of potential trade links affects LiC’s local trade structure in this year and to explore the reasons for its predicted success. Since the forecast timeliness requirement is 3 years, the potential trade links after 2017 cannot be verified by actual trade data after 2020; thus, only 2011 to 2017 are analyzed on the time scale. Table 8 shows the motif statistics of the potential trade relations of LiC from 2011 to 2017. For the other important minerals, see Tables 9–16.Table 8
Statistics for the motifs in the process of realizing potential trade relations of LiC from 2011 to 2017.
YearSuccessfully predicted trading country pairsIncreased number of motifsM4M6M7M8M9M1220112390031220420127971010116362420134615111923122014245003113012015281660006920163740017213242017719514348744610Total27592352093133187124Table 9
Statistics for the motifs in the process of realizing potential trade relations of Al from 2011 to 2017.
YearSuccessfully predicted trading country pairsIncreased number of motifsM4M6M7M8M9M122011341626072020125158710132062462013463671117312014512678511593620153103178241854201647943031356201739633374733Total2766650413046223276Table 10
Statistics for the motifs in the process of realizing potential trade relations of C from 2011 to 2017.
YearSuccessfully predicted trading country pairsIncreased number of motifsM4M6M7M8M9M12201151231462615372520127110231072155320135809220142114201461302152714481520155356199217225320166104215101732192017410315717142921Total3810061224410977254400Table 11
Statistics for the motifs in the process of realizing potential trade relations of Co from 2011 to 2017.
YearSuccessfully predicted trading country pairsIncreased number of motifsM1M5M6M1120113171411120124400273120134280532020143100424201561515182016416031122017251211Total261313251687Table 12
Statistics for the motifs in the process of realizing potential trade relations of Cu from 2011 to 2017.
YearSuccessfully predicted trading country pairsIncreased number of motifsM4M6M7M9M11M122011417322194032962012940716242010395149201352411632832481052014736612252681151442015422616271424694201662551629174735111201742099162385490Total39187710717254330425789Table 13
Statistics for the motifs in the process of realizing potential trade relations of Fe from 2011 to 2017.
YearSuccessfully predicted trading country pairsIncreased number of motifsM4M6M7M9M11M12201153241814188980105201273491010201248410120133172612079501620143176114104148622015633318131728177802016313614680476120175253189176210443Total3217439557110423590468Table 14
Statistics for the motifs in the process of realizing potential trade relations of Mn from 2011 to 2017.
YearSuccessfully predicted trading country pairsIncreased number of motifsM4M5M6M7M9M11M12201193739341422105116732012292364327262320136244611121148985820147323726112610111735201551920215145393620167269510171346100782017628131411178611832Total4217743312274106466668305Table 15
Statistics for the motifs in the process of realizing potential trade relations of Ni from 2011 to 2017.
YearSuccessfully predicted trading country pairsIncreased number of motifsM4M5M6M9M1120115535016032201243553101072013710975125728201435250424192015251010320165959211353820174754162935Total30424361160155162Table 16
Statistics for the motifs in the process of realizing potential trade relations of Ti from 2011 to 2017.
YearSuccessfully predicted trading country pairsIncreased number of motifsM4M5M6M7M9201168613131315322012458126131017201337101117522014463378936201556647121132201671029171675320178149329131589Total3759544907674311Table8 shows the statistics for the motifs in the process of realizing the potential trade relations of LiC from 2011 to 2017. From 2011 to 2017, the cumulative number of successful predictions of potential trading country/region pairs was 27, and the total number of newly added important motifs was 592. Among them, the newly added numbers M9, M8, and M12 motifs were more prominent than other important motifs, which indicates that the formation of potential links mainly promotes the international trade of LiC: as a transit country, country A imports LiC from country B and exports it to country C, country A exports LiC to countries B and C at the same time, and country A imports LiC from countries B and C and exports LiC to country B. Thus, three local trade models are formed.A horizontal comparison of the statistics for the motifs involved in the process of realizing the potential trade relations of the nine minerals from 2011 to 2017 shows that the number of newly added motifs of Cu, Fe, and Mn far exceeds that of the other minerals, which indicates that the establishment of potential trade relations has the greatest impact on the local trade structure of these three minerals. The number of newly added motifs for C is calculated at the upstream level, the number of newly added motifs for Al, Ti, LiC, and Ni is calculated at the midstream level, the number of newly added motifs for Co is the lowest, and there is a large gap with other minerals. In terms of the motif form, in addition to Co, the number of newly added M9 motifs for the other 8 minerals is relatively large (especially reflected in the motif statistics of Ti), which suggests that the establishment of potential trade relations has played a major role in promoting the local trade mode of the “transit” form of the eight types of international mineral trade. Except for Ti, many motif forms with a “bilateral” structure have been added to the other 8 minerals, which shows that the establishment of potential trade relations has played a major role in promoting the “reciprocal” local trade model in the international trade of the 8 minerals. In addition, M8 appeared more frequently in the statistics of the LiC motif; this demonstrates that the formation of potential trade relations in the LiC international trade tends to establish a unilateral export form of the local trade model. In the statistics of the newly added motifs of the nine minerals, Al and C have similarities, M9 and M12 have more new additions, Cu, Fe, and Mn have similarities, and M9, M11, and M12 have more new additions.


## 3.5. International Trade Relation Forecast

In the previous section, this paper uses the motif analysis method to study the impact of successfully predicted links on the local mineral trade structure, and statistics are presented on the addition of important motifs in the realization of the potential trade relations of the nine minerals from 2011 to 2017. It is found that the successfully predicted links promote the formation of important motifs in the network. Therefore, based on the results of this study, we can compare the impact of the potential trade links on the increase in the important motifs in the network and screen out the country/region pairs that are most likely to transform into actual trade relations.This section preliminarily screens the potential trade links with predictive significance based on the criteria that these links had actual trade relations before but did not have actual trade in the last 3 years (2018-2020). We apply the motif analysis method to compare from a local perspective how the formation of these potential trade links will affect the local trade structure in the mineral international trade. Based on this analysis, combined with the three prediction rules, the country/region pairs that are most likely to establish trade relations among the nine international mineral trades are further screened out.


### 3.5.1. Preliminary Screening of Potential Trade Links

The research purpose of this article is to find new and suitable trading partners for the countries/regions involved in the trade of the nine types of minerals to enhance their trade security, meet the supply and demand balance of minerals, and reduce the risks in their international trade. In consideration of the research purpose of this article, if a pair of trading countries/regions already has had a trade relationship in recent years, then the trade relationship is likely to continue on the basis of this “familiarity”; therefore, its actual forecast is of little significance. The second prediction rule in Section3.3 of this article states the following: the trading countries of the nine minerals, the main element raw materials of lithium-ion batteries, tend to establish long-term and stable trade relations when looking for trading partners. This rule also reflects a related reality. For the countries/regions that may have never tried to establish diplomatic relations historically or have not conducted actual trade transactions in a long time due to changes in international situations or trade policies, the new creation or the restoration of their trade relations will have a great positive effect on the expansion of their trade channels, thereby providing more mineral sources or export points, increasing their ability to guarantee their trade security, and satisfying supply and demand. In combination with the third rule of prediction in Section 3.3 of this article, among the international trade links of the nine minerals, the existing trade relations will promote the establishment of the predicted trade relations. Therefore, this study preliminarily screens the potential trade links with predictive significance based on the criteria that the trade links have supported actual trade relations before but have not been involved in actual trade in the last 3 years (2018-2020).Table17 shows the preliminary screening results of the potential trade links of the nine important minerals.Table 17
Preliminary screening of potential trade links of the nine important minerals.
CountAlCCoCuFeLiCMnNiTi1AE → EUID→EUBE→INCN → INCN → ATFR → KRMX → INCN → BECN → RU2DK → USDK → DECN → FRCN → THCN → HUCA → DEIN→USDE → ZAMY→NL3CZ → FRIN→THIN→GBCN → JPCN → HKCA → BEIT→INCN → FRCN → PL4FR → INID→INBE→GBCN → CHCN → QACA → RUCN → UACN → HKIN→US5DK → ININ→CHCN → GBCA → NLJP → NLNL → AECN → SKCN → INKR → US6DK → ESIN→BRCN → CHKH → CNCN → ESNL → RSCN → ESCA → AUKR → EU7HK → NLFR → ATBE→USKR → ESKR → NLCN → NLCA → DEKR → NL8NL → THIN→ESCN → NLCN → NAAU → NLID→NLCA → SGCN → MA9SA → EUNL → BRDE → NLID→NLCN → BECA → GBCN → FI10DE → KRNL → THNL → USJP → NLCN → DKMK → EUCN → HU11FR → USTH → USNL → INMY→NLCZ → INCL → EUJP → US12KR → NLHK → ESIL → NLCA → NLJP → NL13KR → RUES → USCA → IN14CN → DKCA → CH


### 3.5.2. Motif Analysis of the Potential Trade Links

Section3.4 of this article shows that successfully predicted links promote the formation of important motifs in the network. Therefore, after a preliminary screening of the potential trade links, the motif analysis method is applied to add the screened potential trade links one-by-one to the mineral international trade network to check the formation of their important motifs. If the potential links form more important motifs, then when their similarity with the successfully predicted link is stronger, the possibility of turning it into an actual link is higher. Because it predicts the future trade links of the mineral international trade, the potential trade links initially screened out are added to the 2020 mineral international trade network one-by-one. By checking a link’s contribution to the formation of important motifs in the 2020 trade network, we can compare and analyze the possibility of its transformation into a real trade relationship.Table18 shows the contribution to important motifs of the potential links preliminarily screened for LiC, and the results of the other important minerals are shown in Tables 19–26.Table 18
The contribution to important motifs of potential links preliminarily screened for LiC.
Preliminary screening of potential linksThe number of newly added motifsM4M5M6M7M8M9M12FR → KR150304503CA → DE1300003100CA → BE72031001CA → RU170403361NL → AE150202920NL → RS1801051110KR → NL2800000919AU → NL32001011020ID→NL35000001223JP → NL37014041117MY→NL31000001021IL → NL30000003Table 19
The contribution to important motifs of potential links preliminarily screened for Al.
Preliminary screening of potential linksThe number of newly added motifsM4M6M7M8M9M12AE → EU10100009DK → US131100011CZ → FR12001173FR → IN11112007DK → IN9011007DK → ES210002145HK → NL4101011821NL → TH240011931SA → EU10001009DE → KR1000010FR → US230013163Table 20
The contribution to important motifs of potential links preliminarily screened for C.
Preliminary screening of potential linksThe number of newly added motifsM4M6M7M8M9M12ID→EU9000009DK → DE10000280IN→TH4100323150ID→IN170400013IN→CH16450007IN→BR14311009FR → AT120002100IN→ES3700223111NL → BR7403000NL → TH220051520TH → US7000007KR → NL3901011522KR → RU8000260CN → DK7401002Table 21
The contribution to important motifs of potential links preliminarily screened for Co.
Preliminary screening of potential linksThe number of newly added motifsM1M5M6M11BE→IN20200CN → FR30102IN→GB1300013BE→GB1000010CN → GB90009CN → CH40103BE→US60024CN → NL40103DE → NL00000NL → US20200NL → IN10100HK → ES10001ES → US21100Table 22
The contribution to important motifs of potential links preliminarily screened for Cu.
Preliminary screening of potential linksThe number of newly added motifsM4M6M7M9M11M12CN → IN503700436CN → TH510100545CN → JP470043760CN → CH510124080CA → NL190131140KH → CN160005011KR → ES12000813CN → NA530620342Table 23
The contribution to important motifs of potential links preliminarily screened for Fe.
Preliminary screening of potential linksThe number of newly added motifsM4M6M7M9M11M12CN → AT5701336170CN → HU5601434170CN → HK5700437160CN → QA5110101435JP → NL281330129CN → ES5367201028Table 24
The contribution to important motifs of potential links preliminarily screened for Mn.
Preliminary screening of potential linksThe number of newly added motifsM4M5M6M7M9M11M12MX → IN180211905IN→US40105101419IT→IN260703835CN → UA50000002327CN → SK40020124121CN → ES51083125122CN → NL57202302921ID→NL2610000214CN → BE57002602722CN → DK47050229110CZ → IN2605111225Table 25
The contribution to important motifs of potential links preliminarily screened for Ni.
Preliminary screening of potential linksThe number of newly added motifsM4M5M6M9M11CN → BE600141DE → ZA000000CN → FR700061CN → HK500041CN → IN401030CA → AU710204CA → DE18000153CA → SG17010142CA → GB400004MK → EU600060CL → EU400040CA → NL23040163CA → IN18020142CA → CH500203Table 26
The contribution to important motifs of potential links preliminarily screened for Ti.
Preliminary screening of potential linksThe number of newly added motifsM4M5M6M7M9CN → RU20000416MY→NL33020031CN → PL20040313IN→US1120630KR → US310200KR → EU210100KR → NL34020032CN → MA17000215CN → FI18010116CN → HU17020114JP → US610500JP → NL39031035


### 3.5.3. Select the Best Potential Link

In Section3.5.1, we preliminarily screen the potential trade relations of the 9 critical minerals. Next, we further filter these potential links to obtain the best potential links. There are two principles for this step. The first principle is to check whether the potential link follows the three rules summarized in Section 3.3. If the potential link follows one or more of the three rules, then we think that the quality of the potential link is high. The second principle is to check how much the potential link increases the number of key motifs in the network. When there is a greater increase in this number, we think that the quality of the potential link is higher. The results are shown in Table 27, and the specific analysis process is also described.Table 27
The best potential links of the international trade relations of 9 critical minerals.
Best potential linksThe number of newly added motifsRule 1Rule 2Rule 3AlHK → NL41√FR → US23√√√CKR → NL39√√IN→ES37√√NL → TH22√√CoIN→GB13√BE→GB10√√CN → GB9√√CuCN → IN50√√CN → TH51√√CN → JP47√√CN → CH51√√CN → NA53√√√FeCN → HU56√√CN → ES53√√√LiCKR → NL28√√AU → NL32√√JP → NL37√√MY→NL31√√MnCN → UA50√√CN → ES51√√CN → NL57√√√CN → BE57√√CN → DK47√√NiCA → DE18√√√CA → NL23√√CA → IN18√√TiCN → RU20√√√MY→NL33√√KR → NL34√√JP → NL39√√For Al, Hong Kong → the Netherlands and France → the United States are most likely to transform into real trade relationships in the future. Hong Kong → the Netherlands established trade contacts in 2011 and 2014, which complies with the trade link rule 3, and the potential of this link to promote the formation of important motifs in the network is the highest among the 11 pairs of potential trade links initially screened for Al. France → the United States had continuous trade exchanges from 2011 to 2017, and this trade link was predicted from 2018 to 2019, which complies with trade link rules 1, 2, and 3, and the potential of the link to promote the formation of important motifs in the network is the highest among the 11 pairs of potential trade links initially screened for Al.For C, South Korea → the Netherlands, India → Spain, and the Netherlands → Thailand are most likely to transform into real trade relationships in the future. All of these potential trade links have a high facilitating effect on the formation of important motifs. South Korea → the Netherlands had actual trade relations in 2015 and 2016, and this link was continuously predicted from 2017 to 2019, which is in line with trade link rules 1 and 3. India → Spain had actual trade relations in 2011, and trade was predicted in 2020, which is consistent with trade link rules 1 and 3. The Netherlands → Thailand had actual trade relations in 2011, 2012, and 2015, and trade was continuously predicted from 2016 to 2019, which is in line with trade link rules 1 and 3.For Co, India → the United Kingdom, Belgium → the United Kingdom, and China → the United Kingdom are most likely to transform into real trade relationships in the future. All of these potential trade links have a high facilitating effect on the formation of important motifs, and they are the top 3 among the 13 pairs of potential trade links initially screened for Co. India → the United Kingdom had actual trade relations in 2016 and 2017, which is consistent with trade link rule 3. Belgium → the United Kingdom continued to conduct trade transactions from 2012 to 2016, which is in line with trade link rules 2 and 3. China → the United Kingdom had actual trade relations in 2011 and 2014, and trade was predicted in 2020, which is consistent with trade link rules 1 and 3.For Cu, China → India, China → Thailand, China → Japan, China → Switzerland, and China → Namibia are most likely to transform into real trade relationships in the future. All of these potential trade links have a high facilitating effect on the formation of important motifs, and they far exceed the other three pairs of potential links. China → India had actual trade relations in 2011 and 2017, and the trade link was predicted in other years, which is in line with trade link rules 1 and 3. China → Thailand had actual trade relations in 2011, 2013, 2014, 2015, and 2017, which is consistent with trade link rules 2 and 3. China → Japan had actual trade relations in 2011 and 2014, and trade was predicted in other years, which is in line with trade link rules 1 and 3. China → Switzerland had actual trade relations in 2011 and 2013, and trade was continuously predicted from 2017 to 2020, which is consistent with trade link rules 1 and 3. China → Namibia had actual trade relations in 2014, 2015, and 2017, and trade was predicted in 2020, which is in line with trade link rules 1, 2, and 3.For Fe, China → Hungary and China → Spain are most likely to transform into real trade relationships in the future. All of these potential trade links have a high facilitating effect on the formation of important motifs. China → Hungary had an actual trade relation in 2015, and it was predicted in 2020, which is in line with trade link rules 1 and 3. China → Spain continued to conduct trade exchanges from 2011 to 2015, and they were continuously predicted from 2016 to 2020, which is consistent with trade link rules 1, 2, and 3.For LiC, South Korea → the Netherlands, Australia → the Netherlands, Japan → the Netherlands, and Malaysia → the Netherlands are most likely to transform into real trade relationships in the future. All of these potential trade links have a high facilitating effect on the formation of important motifs. South Korea → the Netherlands had actual trade relations in 2012 and 2015, and trade was continuously predicted from 2016 to 2020, which is in line with trade link rules 1 and 3. Australia → the Netherlands had actual trade relations in 2015, and they were predicted in 2016 and 2018, which is consistent with trade link rules 1 and 3. Japan → the Netherlands had actual trade relations in 2013 and 2015, and relations were predicted in 2016, 2018, and 2020, which is in line with trade link rules 1 and 3. Malaysia → the Netherlands had actual trade relations in 2015, and trade was predicted in 2016, 2018, and 2020, which is consistent with trade link rules 1 and 3.For Mn, China → Ukraine, China → Spain, China → the Netherlands, China → Belgium, and China → Denmark are most likely to transform into real trade relationships in the future. All of these potential trade links have a high facilitating effect on the formation of important motifs, and they are the top 5 of the 11 pairs of potential trade links initially screened for Mn. China → Ukraine had actual trade relations in 2016, and trade was continuously predicted from 2017 to 2018, which is in line with trade link rules 1 and 3. China → Spain had actual trade relations in 2011 and 2013, and trade was continuously predicted from 2016 to 2020, which is consistent with trade link rules 1 and 3. China → the Netherlands continued to conduct trade exchanges from 2011 to 2014, and they were continuously predicted from 2015 to 2020, which is in line with trade link rules 1, 2, and 3. China → Belgium had actual trade relations in 2014, and trade was continuously predicted from 2017 to 2020, which is consistent with trade link rules 1 and 3. China → Denmark had actual trade relations in 2014, and trade was continuously predicted from 2018 to 2019, which is in line with trade link rules 1 and 3.For Ni, Canada → Germany, Canada → the Netherlands, and Canada → the India are most likely to transform into real trade relationships in the future. All of these potential trade links have a high facilitating effect on the formation of important motifs, and they are the top 3 of the 14 pairs of potential trade links initially screened for Ni. Canada → Germany continued to conduct trade exchanges from 2011 to 2015, and trade was predicted in 2016 and 2018, which is in line with trade link rules 1, 2, and 3. Canada → the Netherlands had actual trade relations in 2014 and 2017, and trade was predicted in 2020, which is consistent with trade link rules 1 and 3. Canada → India had actual trade relations in 2011, and trade was predicted in 2020, which is in line with trade link rules 1 and 3.For Ti, China → Russia, Malaysia → the Netherlands, South Korea → the Netherlands, and Japan → The Netherlands are most likely to transform into real trade relationships in the future. All of these potential trade links have a high facilitating effect on the formation of important motifs, and they are the top 4 of the 12 pairs of potential trade links initially screened for Ti. China → Russia continued to conduct trade exchanges from 2012 to 2014, and trade was continuously predicted from 2017 to 2019, which is consistent with trade link rules 1, 2, and 3. Malaysia → the Netherlands had actual trade relations in 2015, and trade was predicted in 2019, which is in line with trade link rules 1 and 3. South Korea → the Netherlands had actual trade relations in 2015, and trade was continuously predicted from 2018 to 2019, which is consistent with trade link rules 1 and 3. Finally, Japan → the Netherlands had actual trade relations in 2014 and 2015, and trade was continuously predicted from 2018 to 2020, which is in line with trade link rules 1 and 3.


## 3.5.1. Preliminary Screening of Potential Trade Links

The research purpose of this article is to find new and suitable trading partners for the countries/regions involved in the trade of the nine types of minerals to enhance their trade security, meet the supply and demand balance of minerals, and reduce the risks in their international trade. In consideration of the research purpose of this article, if a pair of trading countries/regions already has had a trade relationship in recent years, then the trade relationship is likely to continue on the basis of this “familiarity”; therefore, its actual forecast is of little significance. The second prediction rule in Section3.3 of this article states the following: the trading countries of the nine minerals, the main element raw materials of lithium-ion batteries, tend to establish long-term and stable trade relations when looking for trading partners. This rule also reflects a related reality. For the countries/regions that may have never tried to establish diplomatic relations historically or have not conducted actual trade transactions in a long time due to changes in international situations or trade policies, the new creation or the restoration of their trade relations will have a great positive effect on the expansion of their trade channels, thereby providing more mineral sources or export points, increasing their ability to guarantee their trade security, and satisfying supply and demand. In combination with the third rule of prediction in Section 3.3 of this article, among the international trade links of the nine minerals, the existing trade relations will promote the establishment of the predicted trade relations. Therefore, this study preliminarily screens the potential trade links with predictive significance based on the criteria that the trade links have supported actual trade relations before but have not been involved in actual trade in the last 3 years (2018-2020).Table17 shows the preliminary screening results of the potential trade links of the nine important minerals.Table 17
Preliminary screening of potential trade links of the nine important minerals.
CountAlCCoCuFeLiCMnNiTi1AE → EUID→EUBE→INCN → INCN → ATFR → KRMX → INCN → BECN → RU2DK → USDK → DECN → FRCN → THCN → HUCA → DEIN→USDE → ZAMY→NL3CZ → FRIN→THIN→GBCN → JPCN → HKCA → BEIT→INCN → FRCN → PL4FR → INID→INBE→GBCN → CHCN → QACA → RUCN → UACN → HKIN→US5DK → ININ→CHCN → GBCA → NLJP → NLNL → AECN → SKCN → INKR → US6DK → ESIN→BRCN → CHKH → CNCN → ESNL → RSCN → ESCA → AUKR → EU7HK → NLFR → ATBE→USKR → ESKR → NLCN → NLCA → DEKR → NL8NL → THIN→ESCN → NLCN → NAAU → NLID→NLCA → SGCN → MA9SA → EUNL → BRDE → NLID→NLCN → BECA → GBCN → FI10DE → KRNL → THNL → USJP → NLCN → DKMK → EUCN → HU11FR → USTH → USNL → INMY→NLCZ → INCL → EUJP → US12KR → NLHK → ESIL → NLCA → NLJP → NL13KR → RUES → USCA → IN14CN → DKCA → CH


## 3.5.2. Motif Analysis of the Potential Trade Links

Section3.4 of this article shows that successfully predicted links promote the formation of important motifs in the network. Therefore, after a preliminary screening of the potential trade links, the motif analysis method is applied to add the screened potential trade links one-by-one to the mineral international trade network to check the formation of their important motifs. If the potential links form more important motifs, then when their similarity with the successfully predicted link is stronger, the possibility of turning it into an actual link is higher. Because it predicts the future trade links of the mineral international trade, the potential trade links initially screened out are added to the 2020 mineral international trade network one-by-one. By checking a link’s contribution to the formation of important motifs in the 2020 trade network, we can compare and analyze the possibility of its transformation into a real trade relationship.Table18 shows the contribution to important motifs of the potential links preliminarily screened for LiC, and the results of the other important minerals are shown in Tables 19–26.Table 18
The contribution to important motifs of potential links preliminarily screened for LiC.
Preliminary screening of potential linksThe number of newly added motifsM4M5M6M7M8M9M12FR → KR150304503CA → DE1300003100CA → BE72031001CA → RU170403361NL → AE150202920NL → RS1801051110KR → NL2800000919AU → NL32001011020ID→NL35000001223JP → NL37014041117MY→NL31000001021IL → NL30000003Table 19
The contribution to important motifs of potential links preliminarily screened for Al.
Preliminary screening of potential linksThe number of newly added motifsM4M6M7M8M9M12AE → EU10100009DK → US131100011CZ → FR12001173FR → IN11112007DK → IN9011007DK → ES210002145HK → NL4101011821NL → TH240011931SA → EU10001009DE → KR1000010FR → US230013163Table 20
The contribution to important motifs of potential links preliminarily screened for C.
Preliminary screening of potential linksThe number of newly added motifsM4M6M7M8M9M12ID→EU9000009DK → DE10000280IN→TH4100323150ID→IN170400013IN→CH16450007IN→BR14311009FR → AT120002100IN→ES3700223111NL → BR7403000NL → TH220051520TH → US7000007KR → NL3901011522KR → RU8000260CN → DK7401002Table 21
The contribution to important motifs of potential links preliminarily screened for Co.
Preliminary screening of potential linksThe number of newly added motifsM1M5M6M11BE→IN20200CN → FR30102IN→GB1300013BE→GB1000010CN → GB90009CN → CH40103BE→US60024CN → NL40103DE → NL00000NL → US20200NL → IN10100HK → ES10001ES → US21100Table 22
The contribution to important motifs of potential links preliminarily screened for Cu.
Preliminary screening of potential linksThe number of newly added motifsM4M6M7M9M11M12CN → IN503700436CN → TH510100545CN → JP470043760CN → CH510124080CA → NL190131140KH → CN160005011KR → ES12000813CN → NA530620342Table 23
The contribution to important motifs of potential links preliminarily screened for Fe.
Preliminary screening of potential linksThe number of newly added motifsM4M6M7M9M11M12CN → AT5701336170CN → HU5601434170CN → HK5700437160CN → QA5110101435JP → NL281330129CN → ES5367201028Table 24
The contribution to important motifs of potential links preliminarily screened for Mn.
Preliminary screening of potential linksThe number of newly added motifsM4M5M6M7M9M11M12MX → IN180211905IN→US40105101419IT→IN260703835CN → UA50000002327CN → SK40020124121CN → ES51083125122CN → NL57202302921ID→NL2610000214CN → BE57002602722CN → DK47050229110CZ → IN2605111225Table 25
The contribution to important motifs of potential links preliminarily screened for Ni.
Preliminary screening of potential linksThe number of newly added motifsM4M5M6M9M11CN → BE600141DE → ZA000000CN → FR700061CN → HK500041CN → IN401030CA → AU710204CA → DE18000153CA → SG17010142CA → GB400004MK → EU600060CL → EU400040CA → NL23040163CA → IN18020142CA → CH500203Table 26
The contribution to important motifs of potential links preliminarily screened for Ti.
Preliminary screening of potential linksThe number of newly added motifsM4M5M6M7M9CN → RU20000416MY→NL33020031CN → PL20040313IN→US1120630KR → US310200KR → EU210100KR → NL34020032CN → MA17000215CN → FI18010116CN → HU17020114JP → US610500JP → NL39031035


## 3.5.3. Select the Best Potential Link

In Section3.5.1, we preliminarily screen the potential trade relations of the 9 critical minerals. Next, we further filter these potential links to obtain the best potential links. There are two principles for this step. The first principle is to check whether the potential link follows the three rules summarized in Section 3.3. If the potential link follows one or more of the three rules, then we think that the quality of the potential link is high. The second principle is to check how much the potential link increases the number of key motifs in the network. When there is a greater increase in this number, we think that the quality of the potential link is higher. The results are shown in Table 27, and the specific analysis process is also described.Table 27
The best potential links of the international trade relations of 9 critical minerals.
Best potential linksThe number of newly added motifsRule 1Rule 2Rule 3AlHK → NL41√FR → US23√√√CKR → NL39√√IN→ES37√√NL → TH22√√CoIN→GB13√BE→GB10√√CN → GB9√√CuCN → IN50√√CN → TH51√√CN → JP47√√CN → CH51√√CN → NA53√√√FeCN → HU56√√CN → ES53√√√LiCKR → NL28√√AU → NL32√√JP → NL37√√MY→NL31√√MnCN → UA50√√CN → ES51√√CN → NL57√√√CN → BE57√√CN → DK47√√NiCA → DE18√√√CA → NL23√√CA → IN18√√TiCN → RU20√√√MY→NL33√√KR → NL34√√JP → NL39√√For Al, Hong Kong → the Netherlands and France → the United States are most likely to transform into real trade relationships in the future. Hong Kong → the Netherlands established trade contacts in 2011 and 2014, which complies with the trade link rule 3, and the potential of this link to promote the formation of important motifs in the network is the highest among the 11 pairs of potential trade links initially screened for Al. France → the United States had continuous trade exchanges from 2011 to 2017, and this trade link was predicted from 2018 to 2019, which complies with trade link rules 1, 2, and 3, and the potential of the link to promote the formation of important motifs in the network is the highest among the 11 pairs of potential trade links initially screened for Al.For C, South Korea → the Netherlands, India → Spain, and the Netherlands → Thailand are most likely to transform into real trade relationships in the future. All of these potential trade links have a high facilitating effect on the formation of important motifs. South Korea → the Netherlands had actual trade relations in 2015 and 2016, and this link was continuously predicted from 2017 to 2019, which is in line with trade link rules 1 and 3. India → Spain had actual trade relations in 2011, and trade was predicted in 2020, which is consistent with trade link rules 1 and 3. The Netherlands → Thailand had actual trade relations in 2011, 2012, and 2015, and trade was continuously predicted from 2016 to 2019, which is in line with trade link rules 1 and 3.For Co, India → the United Kingdom, Belgium → the United Kingdom, and China → the United Kingdom are most likely to transform into real trade relationships in the future. All of these potential trade links have a high facilitating effect on the formation of important motifs, and they are the top 3 among the 13 pairs of potential trade links initially screened for Co. India → the United Kingdom had actual trade relations in 2016 and 2017, which is consistent with trade link rule 3. Belgium → the United Kingdom continued to conduct trade transactions from 2012 to 2016, which is in line with trade link rules 2 and 3. China → the United Kingdom had actual trade relations in 2011 and 2014, and trade was predicted in 2020, which is consistent with trade link rules 1 and 3.For Cu, China → India, China → Thailand, China → Japan, China → Switzerland, and China → Namibia are most likely to transform into real trade relationships in the future. All of these potential trade links have a high facilitating effect on the formation of important motifs, and they far exceed the other three pairs of potential links. China → India had actual trade relations in 2011 and 2017, and the trade link was predicted in other years, which is in line with trade link rules 1 and 3. China → Thailand had actual trade relations in 2011, 2013, 2014, 2015, and 2017, which is consistent with trade link rules 2 and 3. China → Japan had actual trade relations in 2011 and 2014, and trade was predicted in other years, which is in line with trade link rules 1 and 3. China → Switzerland had actual trade relations in 2011 and 2013, and trade was continuously predicted from 2017 to 2020, which is consistent with trade link rules 1 and 3. China → Namibia had actual trade relations in 2014, 2015, and 2017, and trade was predicted in 2020, which is in line with trade link rules 1, 2, and 3.For Fe, China → Hungary and China → Spain are most likely to transform into real trade relationships in the future. All of these potential trade links have a high facilitating effect on the formation of important motifs. China → Hungary had an actual trade relation in 2015, and it was predicted in 2020, which is in line with trade link rules 1 and 3. China → Spain continued to conduct trade exchanges from 2011 to 2015, and they were continuously predicted from 2016 to 2020, which is consistent with trade link rules 1, 2, and 3.For LiC, South Korea → the Netherlands, Australia → the Netherlands, Japan → the Netherlands, and Malaysia → the Netherlands are most likely to transform into real trade relationships in the future. All of these potential trade links have a high facilitating effect on the formation of important motifs. South Korea → the Netherlands had actual trade relations in 2012 and 2015, and trade was continuously predicted from 2016 to 2020, which is in line with trade link rules 1 and 3. Australia → the Netherlands had actual trade relations in 2015, and they were predicted in 2016 and 2018, which is consistent with trade link rules 1 and 3. Japan → the Netherlands had actual trade relations in 2013 and 2015, and relations were predicted in 2016, 2018, and 2020, which is in line with trade link rules 1 and 3. Malaysia → the Netherlands had actual trade relations in 2015, and trade was predicted in 2016, 2018, and 2020, which is consistent with trade link rules 1 and 3.For Mn, China → Ukraine, China → Spain, China → the Netherlands, China → Belgium, and China → Denmark are most likely to transform into real trade relationships in the future. All of these potential trade links have a high facilitating effect on the formation of important motifs, and they are the top 5 of the 11 pairs of potential trade links initially screened for Mn. China → Ukraine had actual trade relations in 2016, and trade was continuously predicted from 2017 to 2018, which is in line with trade link rules 1 and 3. China → Spain had actual trade relations in 2011 and 2013, and trade was continuously predicted from 2016 to 2020, which is consistent with trade link rules 1 and 3. China → the Netherlands continued to conduct trade exchanges from 2011 to 2014, and they were continuously predicted from 2015 to 2020, which is in line with trade link rules 1, 2, and 3. China → Belgium had actual trade relations in 2014, and trade was continuously predicted from 2017 to 2020, which is consistent with trade link rules 1 and 3. China → Denmark had actual trade relations in 2014, and trade was continuously predicted from 2018 to 2019, which is in line with trade link rules 1 and 3.For Ni, Canada → Germany, Canada → the Netherlands, and Canada → the India are most likely to transform into real trade relationships in the future. All of these potential trade links have a high facilitating effect on the formation of important motifs, and they are the top 3 of the 14 pairs of potential trade links initially screened for Ni. Canada → Germany continued to conduct trade exchanges from 2011 to 2015, and trade was predicted in 2016 and 2018, which is in line with trade link rules 1, 2, and 3. Canada → the Netherlands had actual trade relations in 2014 and 2017, and trade was predicted in 2020, which is consistent with trade link rules 1 and 3. Canada → India had actual trade relations in 2011, and trade was predicted in 2020, which is in line with trade link rules 1 and 3.For Ti, China → Russia, Malaysia → the Netherlands, South Korea → the Netherlands, and Japan → The Netherlands are most likely to transform into real trade relationships in the future. All of these potential trade links have a high facilitating effect on the formation of important motifs, and they are the top 4 of the 12 pairs of potential trade links initially screened for Ti. China → Russia continued to conduct trade exchanges from 2012 to 2014, and trade was continuously predicted from 2017 to 2019, which is consistent with trade link rules 1, 2, and 3. Malaysia → the Netherlands had actual trade relations in 2015, and trade was predicted in 2019, which is in line with trade link rules 1 and 3. South Korea → the Netherlands had actual trade relations in 2015, and trade was continuously predicted from 2018 to 2019, which is consistent with trade link rules 1 and 3. Finally, Japan → the Netherlands had actual trade relations in 2014 and 2015, and trade was continuously predicted from 2018 to 2020, which is in line with trade link rules 1 and 3.


## 3.6. Forecast of the International Trade Relations of the Raw Materials Required for Lithium-Ion Battery Midstream Products

The frequent replacement and upgrading of small electronic products and the rapid development of the electric vehicle industry have increased the pressure on the supply of raw materials for the manufacturing end of lithium-ion batteries. However, because of the impact of the international political situation, national trade policies, natural disasters, and unexpected disasters such as COVID-19, the supply of raw materials for lithium-ion batteries is unstable. For example, in response to the rapid increase in new coronavirus infection cases, Chile announced that it would close its borders on April 5, 2021, which had a strong impact on the world’s lithium resource supply situation and led to a rapid increase in the price of battery-grade lithium carbonate worldwide. China, Japan, and South Korea, as the main export sources for Chile, have been the most directly affected. The sudden riot in South Africa on July 18, 2021 caused considerable economic losses and hindered the export of various mineral raw materials for lithium-ion batteries. In 2018, the DRC government substantially increased the mining tax rate of cobalt metal. In March of the same year, the DRC President signed a new mining law that increased the mining tax rate of cobalt from 2% to 3.5%, which was implemented in June of the same year. On December 3, 2018, the DRC government announced that cobalt was a strategic metal and further increased the mining tax rate on cobalt from 3.5% to 10%, which resulted in an increase in the global price of cobalt minerals. These unexpected factors in international trade directly affect the manufacturing of midstream lithium-ion battery products, especially for countries with developed lithium-ion battery manufacturing industries. The growth of trading partners in a country makes shortages recede, just as the growth of wealth in a society makes corruption recede [58]. Therefore, this article selects midstream products that require larger mineral raw materials, such as electrolytes, cathode materials, and anode materials. Countries with developed manufacturing industries for midstream products of lithium-ion batteries and the main mineral raw materials needed to produce midstream products of lithium-ion batteries should be identified. Based on the results of this study, the potential import trade of mineral raw materials required by these countries is predicted. The results are summarized in Table 28. Based on the predicted results, these countries should appropriately increase the diversity of their trading partners, expand their import channels, and enhance the supply security of raw materials in the manufacturing of products in the middle reaches of the lithium-ion battery industry chain.Table 28
Trade forecast of the imported raw material end of the developed countries in mid-stream product manufacturing of the lithium-ion battery industry chain.
Midstream productsElectrolyteAnode materialCathode materialIndustrially developed countriesCN, KRCN, KR, BE, JPUS, JPMain mineral raw materialsLiCLiCCoNiMnCPotential trade relationsFR → KRFR → KRCN → KRCN → JPCN → BEFR → JPCA → CNCA → CNCN → BECA → JPCZ → USFR → BEFR → BECA → KRKR → USCA → BECN → JPDE → KRPL → USCN → BEDE → KRCN → KRTR → USKR → BECN → BEIN→USCA → CNES → USRU → USTH → USIT→US


## 4. Conclusion and Recommendations

In recent years, the rapid increase in the consumption of lithium-ion batteries has created crises and challenges to the global supply of raw materials. Various countries are actively establishing new diplomatic relations and looking for more trading partners to broaden import and export channels and reduce trade risks. In this context, how to choose a suitable trading partner has become the primary issue. To provide a reference method to solve this practical problem, this paper constructs an international trade network for the main element minerals of lithium-ion batteries and combines the link prediction method with the motif method. From a more comprehensive perspective, the international trade relations of nine raw mineral materials are specifically predicted. According to the analysis results of this article, the following conclusions and policy inspirations are obtained.(1)
Look for Countries with Diversified Import and Export Channels as Trading Partners. In the accuracy calculation of the four mainstream algorithms for link prediction, the PA algorithm is the best for all nine minerals, which indicates that the possibility of establishing a trade relationship between two countries is proportional to the product of the number of import trading partners and the number of export trading partners. Therefore, when looking for trading partners, a country should first clarify its demand for imports and exports and then look for countries with diversified channels in the corresponding ports as trading partners, which makes it easier to establish trade relations.(2)
When Looking for Trading Partners, Local Trade Structures Should Be Considered. In the analysis in Section3.4 of this article, it is found that the establishment of potential trade relations will have a certain degree of impact on the local trade structure of minerals, among which Cu, Fe, and Mn have the greatest impact. Therefore, when looking for trading partners, trading countries should consider the perspective of the local trade structure. For example, we found that in the impact of the potential links on the local trade structure of minerals, in addition to Co, the number of newly added M9 motifs for the other 8 minerals is relatively large (especially reflected in the motif statistics of Ti). Therefore, for these 8 minerals, the country can consider a form of “transit” to realize the circulation of minerals in the country when looking for trading partners. Except for Ti, many motif forms with a “bilateral” structure have been added to the other 8 minerals. Therefore, for these 8 minerals, a country should consider the establishment of a “reciprocal” trade mode when looking for trading partners. In addition, M8 appears more frequently in the statistics of the LiC motif. Therefore, for LiC, a country should consider the establishment of a “unilateral export form” trade mode when looking for trading partners.(3)
This study provides a new approach to trading partner prediction by adding an analysis of the local trade structure to the overall network structure index. For the high-quality potential trading partnership results predicted in this paper, countries/regions can take this result as a reference to consider actively trying to establish diplomatic relations, thereby increasing the diversity of trade channels, better satisfying their own supply and demand needs, and enhancing their trade security. For countries/regions not involved, the research in this paper can be used as a theoretical basis to find suitable trading partners and serve as a reference for decision making in establishing new trade relations(4)
Developed countries with manufacturing industries for midstream products in the lithium-ion battery industry chain should strengthen their ties with the upstream mineral supply countries in the industry chain and should establish new supply channels based on the potential trade relationships predicted in this article to ensure the safety of the supply of raw materials required for the manufacturing of midstream products



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*Source: 2280027-2023-02-08.xml*