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Research on the evolution of lithium trade communities based on the complex network
Physica A 540 (2020) 123002
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Research on the evolution of lithium trade communities based on the complex network ∗
Guang Chen, Rui Kong , Yixin Wang School of Economics and Management, China University of Geosciences, Beijing, 100083, China Key Laboratory of Carrying Capacity Assessment for Resource and Environment, Ministry of Land and Resources, Beijing, 100083, China
article
info
Article history: Received 27 December 2018 Received in revised form 10 July 2019 Available online 11 October 2019 Keywords: Lithium Evolution of communities Complex network
a b s t r a c t In recent years, electric vehicles, a new type of cleaner vehicles, are attracting widespread attention around the world. Therefore, as one of the most important raw materials of lithium battery, which is the main power of electric vehicles, lithium has won considerable concern. Countries engaged in the development of electric vehicles are concerned about steadily importing lithium and resource-rich countries seek to maximize their exporting interests. In this paper, complex network model is introduced to construct the global trade networks for lithium between 1990 and 2017 to analysis the evolution of lithium trade communities. Some conclusions can be drawn from the result, first, the division of communities varies a lot from year to year; second, there are two to four major trading communities in the trade network over the years; besides, the changes of major trade countries in communities are obvious. © 2019 Elsevier B.V. All rights reserved.
1. Introduction Recently, with the prompt development of new energy vehicle, lithium battery, which is the main power of new energy vehicle, has become one of the most rapidly developing areas [1]. The global demand for electric vehicles is increasing [2,3], which means that there is a greater global demand for lithium in the coming decades [4]. The increasing demand will change the price of non-renewable resources [5]. Thus, understanding the international trade pattern of lithium is crucial to the social and economic development of this period [6]. In addition, lithium is a very active metal which mainly exists in the form of compounds, such as lithium carbonate and lithium hydroxide. According to the USGS, almost all of the trade products of lithium resources are lithium carbonate and lithium hydroxide. Especially, the largest lithium consumption in the world is lithium carbonate, and lithium consumption is measured by lithium carbonate equivalent [7]. Therefore, studying the international trade situation of lithium carbonate and lithium hydroxide could help analyze the international trade pattern of lithium minerals. Previous studies on lithium were mostly about the characteristic of lithium battery-related [8], recycling technology [9], etc. Few scholars have studied the material flow of lithium [10,11]and global lithium supply [12]. As for the studies about trade, they are mainly based on traditional international trade theories and models [13–18]. Thus, a systematic model to reflect the global pattern of lithium international trade is needed. Complex Network Method is an effective way to modeling complicated systems, its main idea is to regard the relationship between the various parts of the real system as a complex network and describe the relationship between ∗ Corresponding author at: School of Economics and Management, China University of Geosciences, Beijing, 100083, China. E-mail addresses: [email protected] (G. Chen), [email protected] (R. Kong), [email protected] (Y. Wang). https://doi.org/10.1016/j.physa.2019.123002 0378-4371/© 2019 Elsevier B.V. All rights reserved.
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the various parts of the real system in the form of network, so that it could help us better understand the essential characteristics of the real system [19]. Serrano et al. [20] firstly applied the complex network method to the study of international trade network. Complex network theory plays a significant role in the study of world trade networks [21– 23]. Hao et al. [24] studied the distribution of fossil energy international trade network. Chen et al. [25] studied the international trade pattern of liquid natural gas by using complex network, and analyzed the competitiveness of each trading country. Sun et al. [26] studied the stability of the international oil trade network. Tokito et al. [27] took Japan as an example to study the complexity of platinum’s international trade network. Hao et al. [28] analyzed the relationship between importing countries of the iron trade network from the perspective of competition. Community analysis of complex networks can be used to reveal the global pattern of international trade, it has the advantages of discovering clusters and interactive links on multiple nodes [20]. There are only very few scholars have studied the evolution of the community in the trade network. For example, Zhong et al. [29] studied the evolution of communities in international oil trade by complex network models; Dong et al. (2018) analyzed copper international trade network associations based on complex networks and resource dependence; Zhong et al. [30] studied the evolution of the fossil fuel international trade network community. From the existing literatures, it is easy to see that the evolution of communities in the trade network belongs to a relatively new research field. The normalized mutual information (NMI) in the network is used to measure the global pattern of the trading community. NMI indicates the similarity of two results of partitions obtained in the network [31]. In this study, two types of NMI innovatively designed to further quantify the evolution of the global lithium resource trading community. International trade is of vital importance to the global economy, its researches cover a wide range of fields with many perspectives. International trade is a dynamic system of multinational; it is necessary to study not only the trade relations between two or more but also the trade relations between each country from the overall perspective. In this paper, a complex network approach is used to study the international trade communities of lithium resources from 1990 to 2017. This study is divided into 3 parts, international trade networks, the analysis of trade communities and the changes of major trade countries in communities. Through the analysis of the above contents, this study finds the process of trade communities’ evolution. Besides, by analyzing many trade countries in the communities, it helps those countries who engaged in the development of electric vehicles realize more about how to import lithium steadily with their partner countries in the community, and helps some resource-rich countries seek to maximize their exporting interests. 2. Data and methodology 2.1. Data The data of international trade of lithium carbonate (the HS code is 2836910000) and lithium hydroxide (the HS code is 2825201000) are from the website of UN Comtrade, which contains all export and import flows more than 200 countries or regions in the world. The annual trade data of all the available countries from 1990 to 2017 are included in this study. It defined each country or region as a node, trade relations between countries as an edge and trade volume was used to define the weight of edges. 2.2. Methodology 2.2.1. Construction of the trade network In this study, the international trade network can be abstracted as a connected network (i, j) by node i and node j (i and j represent different countries or regions). If country i imports from country j, the direction of the edge is from j to i. Conversely, if country i exports to country j, the direction of the edge is from i to j. If country j import from country i in year t, then aij (t) = 1, otherwise aij (t) = 0. Besides, the trade volume was considered as the weight of the edge, and ωij (t) was used to define the weight of country j import from country i in year t. 2.2.2. The betweenness centrality Betweenness centrality is used to analyze which countries are intermediaries in the lithium carbonate network. We assume that there are n shortcuts between node j and node k. A node i’s betweenness centrality relative to node j and node k refers to the ability of this node in the shortcut between these two nodes. The betweenness centrality measures the intermediary of a country in the network, and it is calculated by Eq. (1) [32]: CRBi = CABi =
2CABi
(1)
CPax n n ∑ ∑ j
bjk(i), j ̸ = k ̸ = i, j < k, bjk(i) =
k
CPax = (n2 − 3Q + 2)/2
gjk(i) gjk
(2) (3)
where gjk denotes the number of shortcuts between node j and node k, and gjk(i) represents the number of shortcuts node i had in the two nodes.
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Fig. 1. Three types of NMI.
2.2.3. The eigenvector centrality Eigenvector centrality comes from calculating the normalized eigenvectors corresponding to the maximum eigenvalues of adjacent matrices. In many cases, the importance of nodes in the network is increased by connecting with other vital nodes, it is calculated by Eq. (4) [33]: Ei = λ−1
N ∑
Aij ej
(4)
j=1
where λ and ej represent the node i’s adjacency matrix’s maximum eigenvalue and eigenvectors of adjacent matrices at. 2.2.4. The modularity There are many different communities in a complex network, which is formed by some countries in the lithium carbonate trade network. The relations between countries in the same community are usually stronger than the relations between countries in different communities. Modularity is an index that evaluates the quality of the partition. The modularity measures the density of links inside communities compared to links between communities. The higher the value of modularity, the better the partition will be. The modularity is defined as Eq. (5) [34]: Q = where m =
1 ∑ 2m 1 2
[Aij −
i,j
∑
i,j
ki kj 2m
] × δ ( Ci , C j )
(5)
Ai,j is the sum of all the weights of the edges in the network. ki =
∑
j
Ai,j is the sum of the weights of
the edges attached to node i. Ci is the community where node i is assigned. δ (Ci , Cj ) is 1 if Ci = Cj and 0 otherwise. 2.2.5. Three types of normalized mutual information Normalized Mutual Information (NMI) is a measure to quantify the statistical information shared between two distributions [31]. It can indicate the similarity of two partitions obtained by the algorithm. The higher the value of the NMI is, the more similar the two partitions are. The NMI between two years is calculated by Eq. (6):
∑k(a) ∑k(b) h=1
NMI(y(a) ,y(b) ) = √ ( (a)
∑k(a)
h=1
(a)
l=1
nh log
nh,l log(
(a ) nh )( n (a )
n×nh,l (a ) (b ) ) nh nl
∑k(b)
l=1
(b)
nl
log
(b) nl ) n(b)
(6)
where y(a) is year a, nh is the number of nodes in cluster h in year a, nh,l denotes the number of nodes both in cluster h in year a and in cluster l in year b. The variable n is the number of nodes in the whole network. In this paper three types of NMI are designed to indicate different features of the communities. If b = a + 1, and cluster h and cluster l are in the same network, the equation calculates the NMI between Year t and Year t + 1 which reflects the stability of the clusters as time goes by. If b = 1, a = t, and cluster h and cluster l are in the same network, the equation calculates the NMI between Year t and Year 1 which indicates to what degree the clusters vary form the first observation year 2000. If b = 1, a = 1, and cluster h and cluster l are in two different networks, the equation calculates the NMI, which reflects the stability between two networks in the same year (see Fig. 1).
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Fig. 2. Ranking of major lithium carbonate trade countries’ degree and weighted degree.
3. Results and analysis This paper establishes 2 complex network models of lithium trade involving more than 200 countries during the 28 years from 1990 to 2017. They analyze the evolution of lithium trade communities. 3.1. World lithium trade network There is a strong heterogeneity between countries and different countries play very different roles in the network [35]. Thus, it is indispensable to analyze each country when studying the whole network. Analyzing the significant nodes in the complex network could help us understand the status of each country in the world lithium trade, and even distinguish the importance of different countries [36,37]. The importance of a country in trade network can be expressed in two aspects, one is the number of trading countries and the volume of trade, it could be expressed in degree and weighted degree; the other is centrality, which can be represented by betweenness centrality and eigenvector centrality. 3.1.1. Degree and weighted degree The importance of trading countries in the network could be analyzed by degree (the quantity of trading countries), weighted in-degree (the volume of import) and weighted out-degree(the volume of export). As it can be seen in Figs. 2 and 3. According to the research, there are three conclusions can be drawn: First, lithium carbonate trading network. In terms of degree, Germany had the most trade countries from 1990 to 2014, but in the next three years, the rank of Germany decreased a little. In addition, China and the United States always had many trade countries. The rank of both Belgium and Netherland were totally increasing in the past years. For weighted-in degree, it is obvious that Japan and the United States are two countries with comparative high rank on the volume of lithium carbonate import. Besides, China and Korea experienced a raising rank while Germany’ rank decreased. As for weighted-out degree, Chile exported most lithium carbonate each year, and its trade volume is always more than half of the total quantity during the whole world’s. Secondly, lithium hydroxide trading network. In terms of degree, China, the United States and the United Kingdom had comparative more trading countries. Belgium experienced an increasing rank while Germany’s rank decreased. For weighted-in degree, the ranks of all the five countries changed greatly, but Japan and Germany were two comparative huge lithium hydroxide importing countries. As for weighted-out degree, the United States is almost always the first lithium hydroxide exporting country. Belgium’s exporting rank increased all in all while the other three countries’ exporting ranks fluctuated. Finally, compare the two kinds of trade networks. The United States, China, Germany and Belgium are four major countries in trading both lithium carbonate and lithium hydroxide commodities. In the aspect of weighted-in degree, the fluctuation of lithium carbonate importing countries’ rank are comparative in order while the rank of lithium hydroxide trading countries varied greatly. As for the weighted-out degree, there are two major exporting countries, Chile for lithium carbonate and the United States for lithium hydroxide. Obviously, Chile occupied a more dominant position in lithium carbonate trade than the United States in lithium hydroxide trade, because Chile’s export volume covered on average 70% of total world’s export volume while the United States’ export volume is far less than that.
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Fig. 3. Ranking of major lithium hydroxide trade countries’ degree and weighted degree.
Fig. 4. The rank (lithium carbonate trading) of betweenness centrality and eigenvector centrality.
Fig. 5. The rank (lithium hydroxide trading) of betweenness centrality and eigenvector centrality.
3.1.2. Centrality of the network In this study, two aspects of network centrality are studied. One is betweenness centrality, a key index of complex network, can reflect the degree of a node’s interference in the network by explaining the number of shortest paths that the node holds, so as to effectively evaluate a country’s importance in the international trade network [38]. Another is eigenvector centrality, which can increase a node’s importance by connecting other important nodes [39] to evaluate its position in international trade. The results from the 2 aspects are comparatively different (Figs. 4 and 5). First, lithium carbonate trading network. The United States is always in a high level of betweenness centrality rank, but not in the rank of eigenvector centrality. It indicates that it is more convenient for a country to trade through the United States, but those countries which trade with the United States are not so important in the trade network. In contrast to the United States, France is only in the top of the eigenvector centrality rank, which suggests that countries trade with France are important in the trade network, but France is not suitable to be a link to other trading countries. Both China
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Fig. 6. The division of lithium hydroxide and lithium carbonate trade communities in 2017.
and Germany appear on the two lists, especially Germany, it is almost at the top of both lists. This shows that China and Germany have a very high priority in the whole trading network under the centrality. Moreover, most of the countries in the 2 lists are European countries, which indicates that the European countries contribute more to build a complete lithium carbonate trade network. Secondly, lithium hydroxide trading network. In the rank of betweenness centrality, the United States is always high while its rank of eigenvector centrality fluctuated obviously. China’s betweenness centrality was not so high until 2005, but its eigenvector centrality cannot appear in the rank. Besides, Germany and the United Kingdom are two vital countries in the network as their high rank in both betweenness centrality and eigenvector centrality. In addition, the same to lithium carbonate trading network, most of the countries in the 2 lists are European countries, which means that the European countries play a very significant role in building a complete lithium hydroxide trade network. Finally, compare the two kinds of trade networks. It is obvious that Germany is the one of the most significant country in lithium trade network as its position in both lithium carbonate trade and lithium hydroxide trade are important. Another clear result is that most of these countries with comparative high centrality of the network are European countries, except China and the United States. It indicates that European is a lithium trade group that can never be overlooked. 3.2. The analysis of trade communities Trade communities formed by some trading countries, it is a subset of network nodes. The connections between the nodes in one subset are dense while the connections between the nodes in different subset are sparse, which means nodes within a community is usually a collection that have some common attributes or similar functions [40]. The different structure of the community means that the network can be divided into several parts [41]. Thus, community analysis is an important part when studying international trade networks, it is helpful to understand the entire network better [38]. 3.2.1. The division of trade communities The modularity of the network can be used to assess the density of connections within the community, high modularity indicates that the differentiation in a network between countries is obvious [42]. In the trade network of lithium carbonate, the modularity fluctuates (Fig. 6). Before 2000, it changes greatly from 0.02 to 0.35, but after 2000, it fluctuated lightly around 0.16. The number of communities changes from 2 to 10 over the years. After 2003, the number of communities fluctuates greatly while it merely changes before 2003. In the trade network of lithium hydroxide (Fig. 7), however, it shows differences compared with that of lithium carbonate. For modularity, it fluctuates greatly before 2002, but after 2002, it shows a constantly increasing trend from 0.12 to 0.57. In addition, the average modularity of lithium hydroxide trade is much bigger than that of lithium carbonate trade. After a further study, it can be concluded that there are only two or four major communities in each year even with a large number of communities. The rest of the communities contain only a few small trading countries. These small trading countries are separated because of their small volume of trade and few neighboring trade countries. This also shows that the international lithium trade is still in the process of fluctuating development.
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Fig. 7. Modularity and quantity of lithium carbonate trade network communities.
Fig. 8. Modularity and quantity of lithium hydroxide trade network communities.
Fig. 9. NMI index of lithium carbonate trade network based on 2000.
3.2.2. The changes of trade communities The changes of the international lithium trade communities can be analyzed by three NMI indices, they are NMI index for lithium carbonate (hydroxide) trade communities based on 2000, NMI index for lithium carbonate (hydroxide) trade communities between next two years and NMI index between lithium carbonate and lithium hydroxide trade communities for the same year. First, it is the NMI index for lithium carbonate and lithium hydroxide trade communities based on 2000 that can reflect the changes of communities. As it is the first year of the 21st century and it is the middle of the period, 2000 is considered as a base year in the analysis. As is shown in Figs. 8 and 9, the highest NMI are about 0.25 in both of the two networks, but the lowest NMI for lithium hydroxide trade network (0.08) is higher than that of lithium carbonate trade network (0.01), lithium carbonate trade NMI fluctuates more violent than lithium hydroxide trade NMI. After 2006, the fluctuation for lithium hydroxide trade reduces. Second, the changes in the division of the communities between next two years can be drawn from Figs. 10 and 11. Generally speaking, compared with the previous year, the division of communities has changed a lot every year in both of the two networks. It is obvious that NMI index for lithium carbonate trade network changes from 0.02 to 0.38 while 0.09 to 0.39 for lithium hydroxide trade network. For lithium carbonate trade network, the NMI declines during fluctuating after 1996/1997. And for lithium hydroxide trade network during fluctuating, the NMI decreases before 2001/2002 and
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Fig. 10. NMI index of lithium hydroxide trade network based on 2000.
Fig. 11. NMI index of lithium carbonate trade network between next two years.
Fig. 12. NMI index of lithium hydroxide trade network between next two years.
increases after that. Besides, the average NMI for lithium hydroxide trade network (0.24) is higher than that of lithium carbonate trade network (0.18). Finally, the differences between lithium hydroxide and lithium carbonate trade communities are compared as it is shown in Fig. 12. In 1990, the NMI (0.43) is so high while it changes greatly in 1991, the NMI is only (0.004). It can be easily realized that the NMI fluctuates severe before 2000, but after that, the fluctuation of NMI reduces as it changes from 0.012 to 0.13. In short, the divisions of the two trade networks’ communities are comparative different (see Fig. 13). 3.3. The changes of major trade countries in communities In order to study the evolution of trade communities, it is convenient to analyze the evolution of major trade countries in communities. According to the preceding text, the important trade countries are selected and then divided into different communities (Tables 1 and 2). In the two tables, countries with the same color in each column indicate that they belong to the same community in the previous year. In the lithium carbonate trade communities (Table 1), as it reminds before, though there are many communities each year, the major trade countries are divided into about 2 to 4 communities. According to research, the trade network
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Table 1 The division of major countries in lithium carbonate trade communities.
(continued on next page)
can be roughly divided into three major communities: Asia, Europe and the America. Asia, for China, Japan, South Korea and so on; Europe, with the central of Germany, Netherlands, France and so on; America, with the central of the United States, Argentina and so on. The average number of those major trade countries that change their communities compared with the previous year is about 3.6. It is astonished to find that since 1993, Japan and Chile always belong to the same community until 2017. The United States and Argentina are two countries with very intimate trade relationship as they
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Table 1 (continued).
are always in the same community after 1999. Especially after 2004 (except 2009), their community almost consists of only these two major trade countries (additional including China in 2005, 2014 and the United Kingdom in 2004, 2007 and
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Table 2 The division of major countries in lithium hydroxide trade communities.
(continued on next page)
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Table 2 (continued).
Fig. 13. NMI index between lithium hydroxide and lithium carbonate trade network in same year.
2008). Chile, as the largest export country, is always in the community with some Asian countries such as South Korea, China and Japan. China is an interesting country, though it mainly belongs to the Asia Community, it always changes its community from the previous year. But after 2015, China stays stably in the Asia community. In the lithium hydroxide trade communities (Table 2), the major trade countries constitute 2 to 4 communities. According to the study, the average number of those major trade countries that change their communities compared with the previous year is about 2.3. The study shows that the communities’ division of major countries are the same in a 1994, 1995 and 1996. There is a strong connection between Asian countries and American countries, especially Japan and the United States, they are in the same communities for 22 years, including 5 years that their community consists of only these two major trade countries, from 1990 to 2017. After 2000, Belgium and Russian spend 14 years staying together in the same community. In addition, China and Netherlands are together for 16 years. As for two European countries, the United Kingdom and France, they do not appear in same community for 20 years. According to the research, the trade network can be roughly divided into three major communities: Asia–America, Europe based on the United Kingdom and Europe based on France. 4. Conclusions Because of the increasing demand for lithium in the world caused by the boom of electric vehicles, the research on the international trade of lithium has become popular. In this paper, the complex network method is used to model the world lithium trade from 1990 to 2017 in order to analyze the evolution of international lithium trade communities. On the basis of those studies, the following conclusions can be draw. (1) There are many countries involved in the lithium trade, but only a few countries with greater influences. In terms of import and export, China and the United States are two countries that have large volumes of import and export in both
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lithium carbonate and lithium hydroxide. Belgium is a main exporter for both lithium carbonate and lithium hydroxide while Germany and Japan are two major importers. Although Chile’s main lithium product is lithium carbonate only, its large volume of lithium carbonate export makes it the world’s largest exporter of lithium. As for the centrality, most of the major trade countries with high level of centrality are European countries, especially Germany, it is an important country when consider both betweenness centrality and eigenvector centrality in the two lithium products’ trade networks. This may because most of the countries which trade in lithium are European countries and they tend to trade with their geographical neighbors. (2) When compare the communities of the two trade networks, it shows that the similarity of communities’ division between the two networks are always low especially in 1990, 1992 and 1998. But in 1991,1999 and 2001, the similarity of communities’ division between the two networks are comparative high. In addition, the lithium hydroxide trade’s division of communities are more stable than those of lithium carbonate trade. This might because of its less trading countries and lacking absolutely dominant trade countries (such as Chile in lithium carbonate trade). Moreover, the lithium carbonate trade can be roughly divided into three major trading communities: Asia, America and Europe while lithium hydroxide trade can also be approximately divided into three major trading communities: Asia-America, Europe based on the United Kingdom and Europe based on France. But in different years, the three communities will combine in different ways. (3) Some conclusions can be drawn when compare the major countries of both lithium carbonate trade communities and lithium hydroxide trade communities. First of all, there are four more trade countries in lithium carbonate trade communities than in lithium hydroxide trade communities, which may because more trade countries and volumes in lithium carbonate trade. In addition, the number of communities, which consist of major trade countries, are about 2 to 4 in both of the two networks. This could mutual demonstrate the division of the whole network community. Although there are more communities in some years, many of these communities are consist of a few countries, which have limited trade volume. Besides, the volatility of lithium carbonate trade community is stronger than that of lithium hydroxide trade community. The average number of those major trade countries, which change their communities compared with the previous year, is higher in lithium hydroxide trade network than in lithium carbonate trade network. In both of the two networks, Japan is almost always in the same community with countries (Chile and the United States) that have the largest export volume. It is generally acknowledged that Japan is a country with scarce resources, in order to develop their economy, they have to import a large amount all kinds of resources including lithium. Acknowledgments The authors would like to express their gratitude to Mingyue Wang, Tiantian Feng, Xiangyun Gao, they have provided valuable suggestions. Funding This work was supported by the Development Strategy of Important and Mineral Resources in Qinghai Province (China Geological Survey, Grant No. 12120113033031) References [1] P. Zhou, J.R. Tang, T. Zhang, Supply and demand prospect of global lithium resources and some suggestions, Geol. Bull. China 33 (10) (2014) 1532–1538. [2] Daziano, A. Ricardo, Conditional-logit Bayes estimators for consumer valuation of electric vehicle driving range, Resour. Energy Econ. 35 (3) (2013) 429–450. 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Research on the evolution of lithium trade communities based on the complex network ∗
Guang Chen, Rui Kong , Yixin Wang School of Economics and Management, China University of Geosciences, Beijing, 100083, China Key Laboratory of Carrying Capacity Assessment for Resource and Environment, Ministry of Land and Resources, Beijing, 100083, China
article
info
Article history: Received 27 December 2018 Received in revised form 10 July 2019 Available online 11 October 2019 Keywords: Lithium Evolution of communities Complex network
a b s t r a c t In recent years, electric vehicles, a new type of cleaner vehicles, are attracting widespread attention around the world. Therefore, as one of the most important raw materials of lithium battery, which is the main power of electric vehicles, lithium has won considerable concern. Countries engaged in the development of electric vehicles are concerned about steadily importing lithium and resource-rich countries seek to maximize their exporting interests. In this paper, complex network model is introduced to construct the global trade networks for lithium between 1990 and 2017 to analysis the evolution of lithium trade communities. Some conclusions can be drawn from the result, first, the division of communities varies a lot from year to year; second, there are two to four major trading communities in the trade network over the years; besides, the changes of major trade countries in communities are obvious. © 2019 Elsevier B.V. All rights reserved.
1. Introduction Recently, with the prompt development of new energy vehicle, lithium battery, which is the main power of new energy vehicle, has become one of the most rapidly developing areas [1]. The global demand for electric vehicles is increasing [2,3], which means that there is a greater global demand for lithium in the coming decades [4]. The increasing demand will change the price of non-renewable resources [5]. Thus, understanding the international trade pattern of lithium is crucial to the social and economic development of this period [6]. In addition, lithium is a very active metal which mainly exists in the form of compounds, such as lithium carbonate and lithium hydroxide. According to the USGS, almost all of the trade products of lithium resources are lithium carbonate and lithium hydroxide. Especially, the largest lithium consumption in the world is lithium carbonate, and lithium consumption is measured by lithium carbonate equivalent [7]. Therefore, studying the international trade situation of lithium carbonate and lithium hydroxide could help analyze the international trade pattern of lithium minerals. Previous studies on lithium were mostly about the characteristic of lithium battery-related [8], recycling technology [9], etc. Few scholars have studied the material flow of lithium [10,11]and global lithium supply [12]. As for the studies about trade, they are mainly based on traditional international trade theories and models [13–18]. Thus, a systematic model to reflect the global pattern of lithium international trade is needed. Complex Network Method is an effective way to modeling complicated systems, its main idea is to regard the relationship between the various parts of the real system as a complex network and describe the relationship between ∗ Corresponding author at: School of Economics and Management, China University of Geosciences, Beijing, 100083, China. E-mail addresses: [email protected] (G. Chen), [email protected] (R. Kong), [email protected] (Y. Wang). https://doi.org/10.1016/j.physa.2019.123002 0378-4371/© 2019 Elsevier B.V. All rights reserved.
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the various parts of the real system in the form of network, so that it could help us better understand the essential characteristics of the real system [19]. Serrano et al. [20] firstly applied the complex network method to the study of international trade network. Complex network theory plays a significant role in the study of world trade networks [21– 23]. Hao et al. [24] studied the distribution of fossil energy international trade network. Chen et al. [25] studied the international trade pattern of liquid natural gas by using complex network, and analyzed the competitiveness of each trading country. Sun et al. [26] studied the stability of the international oil trade network. Tokito et al. [27] took Japan as an example to study the complexity of platinum’s international trade network. Hao et al. [28] analyzed the relationship between importing countries of the iron trade network from the perspective of competition. Community analysis of complex networks can be used to reveal the global pattern of international trade, it has the advantages of discovering clusters and interactive links on multiple nodes [20]. There are only very few scholars have studied the evolution of the community in the trade network. For example, Zhong et al. [29] studied the evolution of communities in international oil trade by complex network models; Dong et al. (2018) analyzed copper international trade network associations based on complex networks and resource dependence; Zhong et al. [30] studied the evolution of the fossil fuel international trade network community. From the existing literatures, it is easy to see that the evolution of communities in the trade network belongs to a relatively new research field. The normalized mutual information (NMI) in the network is used to measure the global pattern of the trading community. NMI indicates the similarity of two results of partitions obtained in the network [31]. In this study, two types of NMI innovatively designed to further quantify the evolution of the global lithium resource trading community. International trade is of vital importance to the global economy, its researches cover a wide range of fields with many perspectives. International trade is a dynamic system of multinational; it is necessary to study not only the trade relations between two or more but also the trade relations between each country from the overall perspective. In this paper, a complex network approach is used to study the international trade communities of lithium resources from 1990 to 2017. This study is divided into 3 parts, international trade networks, the analysis of trade communities and the changes of major trade countries in communities. Through the analysis of the above contents, this study finds the process of trade communities’ evolution. Besides, by analyzing many trade countries in the communities, it helps those countries who engaged in the development of electric vehicles realize more about how to import lithium steadily with their partner countries in the community, and helps some resource-rich countries seek to maximize their exporting interests. 2. Data and methodology 2.1. Data The data of international trade of lithium carbonate (the HS code is 2836910000) and lithium hydroxide (the HS code is 2825201000) are from the website of UN Comtrade, which contains all export and import flows more than 200 countries or regions in the world. The annual trade data of all the available countries from 1990 to 2017 are included in this study. It defined each country or region as a node, trade relations between countries as an edge and trade volume was used to define the weight of edges. 2.2. Methodology 2.2.1. Construction of the trade network In this study, the international trade network can be abstracted as a connected network (i, j) by node i and node j (i and j represent different countries or regions). If country i imports from country j, the direction of the edge is from j to i. Conversely, if country i exports to country j, the direction of the edge is from i to j. If country j import from country i in year t, then aij (t) = 1, otherwise aij (t) = 0. Besides, the trade volume was considered as the weight of the edge, and ωij (t) was used to define the weight of country j import from country i in year t. 2.2.2. The betweenness centrality Betweenness centrality is used to analyze which countries are intermediaries in the lithium carbonate network. We assume that there are n shortcuts between node j and node k. A node i’s betweenness centrality relative to node j and node k refers to the ability of this node in the shortcut between these two nodes. The betweenness centrality measures the intermediary of a country in the network, and it is calculated by Eq. (1) [32]: CRBi = CABi =
2CABi
(1)
CPax n n ∑ ∑ j
bjk(i), j ̸ = k ̸ = i, j < k, bjk(i) =
k
CPax = (n2 − 3Q + 2)/2
gjk(i) gjk
(2) (3)
where gjk denotes the number of shortcuts between node j and node k, and gjk(i) represents the number of shortcuts node i had in the two nodes.
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Fig. 1. Three types of NMI.
2.2.3. The eigenvector centrality Eigenvector centrality comes from calculating the normalized eigenvectors corresponding to the maximum eigenvalues of adjacent matrices. In many cases, the importance of nodes in the network is increased by connecting with other vital nodes, it is calculated by Eq. (4) [33]: Ei = λ−1
N ∑
Aij ej
(4)
j=1
where λ and ej represent the node i’s adjacency matrix’s maximum eigenvalue and eigenvectors of adjacent matrices at. 2.2.4. The modularity There are many different communities in a complex network, which is formed by some countries in the lithium carbonate trade network. The relations between countries in the same community are usually stronger than the relations between countries in different communities. Modularity is an index that evaluates the quality of the partition. The modularity measures the density of links inside communities compared to links between communities. The higher the value of modularity, the better the partition will be. The modularity is defined as Eq. (5) [34]: Q = where m =
1 ∑ 2m 1 2
[Aij −
i,j
∑
i,j
ki kj 2m
] × δ ( Ci , C j )
(5)
Ai,j is the sum of all the weights of the edges in the network. ki =
∑
j
Ai,j is the sum of the weights of
the edges attached to node i. Ci is the community where node i is assigned. δ (Ci , Cj ) is 1 if Ci = Cj and 0 otherwise. 2.2.5. Three types of normalized mutual information Normalized Mutual Information (NMI) is a measure to quantify the statistical information shared between two distributions [31]. It can indicate the similarity of two partitions obtained by the algorithm. The higher the value of the NMI is, the more similar the two partitions are. The NMI between two years is calculated by Eq. (6):
∑k(a) ∑k(b) h=1
NMI(y(a) ,y(b) ) = √ ( (a)
∑k(a)
h=1
(a)
l=1
nh log
nh,l log(
(a ) nh )( n (a )
n×nh,l (a ) (b ) ) nh nl
∑k(b)
l=1
(b)
nl
log
(b) nl ) n(b)
(6)
where y(a) is year a, nh is the number of nodes in cluster h in year a, nh,l denotes the number of nodes both in cluster h in year a and in cluster l in year b. The variable n is the number of nodes in the whole network. In this paper three types of NMI are designed to indicate different features of the communities. If b = a + 1, and cluster h and cluster l are in the same network, the equation calculates the NMI between Year t and Year t + 1 which reflects the stability of the clusters as time goes by. If b = 1, a = t, and cluster h and cluster l are in the same network, the equation calculates the NMI between Year t and Year 1 which indicates to what degree the clusters vary form the first observation year 2000. If b = 1, a = 1, and cluster h and cluster l are in two different networks, the equation calculates the NMI, which reflects the stability between two networks in the same year (see Fig. 1).
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Fig. 2. Ranking of major lithium carbonate trade countries’ degree and weighted degree.
3. Results and analysis This paper establishes 2 complex network models of lithium trade involving more than 200 countries during the 28 years from 1990 to 2017. They analyze the evolution of lithium trade communities. 3.1. World lithium trade network There is a strong heterogeneity between countries and different countries play very different roles in the network [35]. Thus, it is indispensable to analyze each country when studying the whole network. Analyzing the significant nodes in the complex network could help us understand the status of each country in the world lithium trade, and even distinguish the importance of different countries [36,37]. The importance of a country in trade network can be expressed in two aspects, one is the number of trading countries and the volume of trade, it could be expressed in degree and weighted degree; the other is centrality, which can be represented by betweenness centrality and eigenvector centrality. 3.1.1. Degree and weighted degree The importance of trading countries in the network could be analyzed by degree (the quantity of trading countries), weighted in-degree (the volume of import) and weighted out-degree(the volume of export). As it can be seen in Figs. 2 and 3. According to the research, there are three conclusions can be drawn: First, lithium carbonate trading network. In terms of degree, Germany had the most trade countries from 1990 to 2014, but in the next three years, the rank of Germany decreased a little. In addition, China and the United States always had many trade countries. The rank of both Belgium and Netherland were totally increasing in the past years. For weighted-in degree, it is obvious that Japan and the United States are two countries with comparative high rank on the volume of lithium carbonate import. Besides, China and Korea experienced a raising rank while Germany’ rank decreased. As for weighted-out degree, Chile exported most lithium carbonate each year, and its trade volume is always more than half of the total quantity during the whole world’s. Secondly, lithium hydroxide trading network. In terms of degree, China, the United States and the United Kingdom had comparative more trading countries. Belgium experienced an increasing rank while Germany’s rank decreased. For weighted-in degree, the ranks of all the five countries changed greatly, but Japan and Germany were two comparative huge lithium hydroxide importing countries. As for weighted-out degree, the United States is almost always the first lithium hydroxide exporting country. Belgium’s exporting rank increased all in all while the other three countries’ exporting ranks fluctuated. Finally, compare the two kinds of trade networks. The United States, China, Germany and Belgium are four major countries in trading both lithium carbonate and lithium hydroxide commodities. In the aspect of weighted-in degree, the fluctuation of lithium carbonate importing countries’ rank are comparative in order while the rank of lithium hydroxide trading countries varied greatly. As for the weighted-out degree, there are two major exporting countries, Chile for lithium carbonate and the United States for lithium hydroxide. Obviously, Chile occupied a more dominant position in lithium carbonate trade than the United States in lithium hydroxide trade, because Chile’s export volume covered on average 70% of total world’s export volume while the United States’ export volume is far less than that.
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Fig. 3. Ranking of major lithium hydroxide trade countries’ degree and weighted degree.
Fig. 4. The rank (lithium carbonate trading) of betweenness centrality and eigenvector centrality.
Fig. 5. The rank (lithium hydroxide trading) of betweenness centrality and eigenvector centrality.
3.1.2. Centrality of the network In this study, two aspects of network centrality are studied. One is betweenness centrality, a key index of complex network, can reflect the degree of a node’s interference in the network by explaining the number of shortest paths that the node holds, so as to effectively evaluate a country’s importance in the international trade network [38]. Another is eigenvector centrality, which can increase a node’s importance by connecting other important nodes [39] to evaluate its position in international trade. The results from the 2 aspects are comparatively different (Figs. 4 and 5). First, lithium carbonate trading network. The United States is always in a high level of betweenness centrality rank, but not in the rank of eigenvector centrality. It indicates that it is more convenient for a country to trade through the United States, but those countries which trade with the United States are not so important in the trade network. In contrast to the United States, France is only in the top of the eigenvector centrality rank, which suggests that countries trade with France are important in the trade network, but France is not suitable to be a link to other trading countries. Both China
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Fig. 6. The division of lithium hydroxide and lithium carbonate trade communities in 2017.
and Germany appear on the two lists, especially Germany, it is almost at the top of both lists. This shows that China and Germany have a very high priority in the whole trading network under the centrality. Moreover, most of the countries in the 2 lists are European countries, which indicates that the European countries contribute more to build a complete lithium carbonate trade network. Secondly, lithium hydroxide trading network. In the rank of betweenness centrality, the United States is always high while its rank of eigenvector centrality fluctuated obviously. China’s betweenness centrality was not so high until 2005, but its eigenvector centrality cannot appear in the rank. Besides, Germany and the United Kingdom are two vital countries in the network as their high rank in both betweenness centrality and eigenvector centrality. In addition, the same to lithium carbonate trading network, most of the countries in the 2 lists are European countries, which means that the European countries play a very significant role in building a complete lithium hydroxide trade network. Finally, compare the two kinds of trade networks. It is obvious that Germany is the one of the most significant country in lithium trade network as its position in both lithium carbonate trade and lithium hydroxide trade are important. Another clear result is that most of these countries with comparative high centrality of the network are European countries, except China and the United States. It indicates that European is a lithium trade group that can never be overlooked. 3.2. The analysis of trade communities Trade communities formed by some trading countries, it is a subset of network nodes. The connections between the nodes in one subset are dense while the connections between the nodes in different subset are sparse, which means nodes within a community is usually a collection that have some common attributes or similar functions [40]. The different structure of the community means that the network can be divided into several parts [41]. Thus, community analysis is an important part when studying international trade networks, it is helpful to understand the entire network better [38]. 3.2.1. The division of trade communities The modularity of the network can be used to assess the density of connections within the community, high modularity indicates that the differentiation in a network between countries is obvious [42]. In the trade network of lithium carbonate, the modularity fluctuates (Fig. 6). Before 2000, it changes greatly from 0.02 to 0.35, but after 2000, it fluctuated lightly around 0.16. The number of communities changes from 2 to 10 over the years. After 2003, the number of communities fluctuates greatly while it merely changes before 2003. In the trade network of lithium hydroxide (Fig. 7), however, it shows differences compared with that of lithium carbonate. For modularity, it fluctuates greatly before 2002, but after 2002, it shows a constantly increasing trend from 0.12 to 0.57. In addition, the average modularity of lithium hydroxide trade is much bigger than that of lithium carbonate trade. After a further study, it can be concluded that there are only two or four major communities in each year even with a large number of communities. The rest of the communities contain only a few small trading countries. These small trading countries are separated because of their small volume of trade and few neighboring trade countries. This also shows that the international lithium trade is still in the process of fluctuating development.
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Fig. 7. Modularity and quantity of lithium carbonate trade network communities.
Fig. 8. Modularity and quantity of lithium hydroxide trade network communities.
Fig. 9. NMI index of lithium carbonate trade network based on 2000.
3.2.2. The changes of trade communities The changes of the international lithium trade communities can be analyzed by three NMI indices, they are NMI index for lithium carbonate (hydroxide) trade communities based on 2000, NMI index for lithium carbonate (hydroxide) trade communities between next two years and NMI index between lithium carbonate and lithium hydroxide trade communities for the same year. First, it is the NMI index for lithium carbonate and lithium hydroxide trade communities based on 2000 that can reflect the changes of communities. As it is the first year of the 21st century and it is the middle of the period, 2000 is considered as a base year in the analysis. As is shown in Figs. 8 and 9, the highest NMI are about 0.25 in both of the two networks, but the lowest NMI for lithium hydroxide trade network (0.08) is higher than that of lithium carbonate trade network (0.01), lithium carbonate trade NMI fluctuates more violent than lithium hydroxide trade NMI. After 2006, the fluctuation for lithium hydroxide trade reduces. Second, the changes in the division of the communities between next two years can be drawn from Figs. 10 and 11. Generally speaking, compared with the previous year, the division of communities has changed a lot every year in both of the two networks. It is obvious that NMI index for lithium carbonate trade network changes from 0.02 to 0.38 while 0.09 to 0.39 for lithium hydroxide trade network. For lithium carbonate trade network, the NMI declines during fluctuating after 1996/1997. And for lithium hydroxide trade network during fluctuating, the NMI decreases before 2001/2002 and
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Fig. 10. NMI index of lithium hydroxide trade network based on 2000.
Fig. 11. NMI index of lithium carbonate trade network between next two years.
Fig. 12. NMI index of lithium hydroxide trade network between next two years.
increases after that. Besides, the average NMI for lithium hydroxide trade network (0.24) is higher than that of lithium carbonate trade network (0.18). Finally, the differences between lithium hydroxide and lithium carbonate trade communities are compared as it is shown in Fig. 12. In 1990, the NMI (0.43) is so high while it changes greatly in 1991, the NMI is only (0.004). It can be easily realized that the NMI fluctuates severe before 2000, but after that, the fluctuation of NMI reduces as it changes from 0.012 to 0.13. In short, the divisions of the two trade networks’ communities are comparative different (see Fig. 13). 3.3. The changes of major trade countries in communities In order to study the evolution of trade communities, it is convenient to analyze the evolution of major trade countries in communities. According to the preceding text, the important trade countries are selected and then divided into different communities (Tables 1 and 2). In the two tables, countries with the same color in each column indicate that they belong to the same community in the previous year. In the lithium carbonate trade communities (Table 1), as it reminds before, though there are many communities each year, the major trade countries are divided into about 2 to 4 communities. According to research, the trade network
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Table 1 The division of major countries in lithium carbonate trade communities.
(continued on next page)
can be roughly divided into three major communities: Asia, Europe and the America. Asia, for China, Japan, South Korea and so on; Europe, with the central of Germany, Netherlands, France and so on; America, with the central of the United States, Argentina and so on. The average number of those major trade countries that change their communities compared with the previous year is about 3.6. It is astonished to find that since 1993, Japan and Chile always belong to the same community until 2017. The United States and Argentina are two countries with very intimate trade relationship as they
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Table 1 (continued).
are always in the same community after 1999. Especially after 2004 (except 2009), their community almost consists of only these two major trade countries (additional including China in 2005, 2014 and the United Kingdom in 2004, 2007 and
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Table 2 The division of major countries in lithium hydroxide trade communities.
(continued on next page)
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Table 2 (continued).
Fig. 13. NMI index between lithium hydroxide and lithium carbonate trade network in same year.
2008). Chile, as the largest export country, is always in the community with some Asian countries such as South Korea, China and Japan. China is an interesting country, though it mainly belongs to the Asia Community, it always changes its community from the previous year. But after 2015, China stays stably in the Asia community. In the lithium hydroxide trade communities (Table 2), the major trade countries constitute 2 to 4 communities. According to the study, the average number of those major trade countries that change their communities compared with the previous year is about 2.3. The study shows that the communities’ division of major countries are the same in a 1994, 1995 and 1996. There is a strong connection between Asian countries and American countries, especially Japan and the United States, they are in the same communities for 22 years, including 5 years that their community consists of only these two major trade countries, from 1990 to 2017. After 2000, Belgium and Russian spend 14 years staying together in the same community. In addition, China and Netherlands are together for 16 years. As for two European countries, the United Kingdom and France, they do not appear in same community for 20 years. According to the research, the trade network can be roughly divided into three major communities: Asia–America, Europe based on the United Kingdom and Europe based on France. 4. Conclusions Because of the increasing demand for lithium in the world caused by the boom of electric vehicles, the research on the international trade of lithium has become popular. In this paper, the complex network method is used to model the world lithium trade from 1990 to 2017 in order to analyze the evolution of international lithium trade communities. On the basis of those studies, the following conclusions can be draw. (1) There are many countries involved in the lithium trade, but only a few countries with greater influences. In terms of import and export, China and the United States are two countries that have large volumes of import and export in both
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lithium carbonate and lithium hydroxide. Belgium is a main exporter for both lithium carbonate and lithium hydroxide while Germany and Japan are two major importers. Although Chile’s main lithium product is lithium carbonate only, its large volume of lithium carbonate export makes it the world’s largest exporter of lithium. As for the centrality, most of the major trade countries with high level of centrality are European countries, especially Germany, it is an important country when consider both betweenness centrality and eigenvector centrality in the two lithium products’ trade networks. This may because most of the countries which trade in lithium are European countries and they tend to trade with their geographical neighbors. (2) When compare the communities of the two trade networks, it shows that the similarity of communities’ division between the two networks are always low especially in 1990, 1992 and 1998. But in 1991,1999 and 2001, the similarity of communities’ division between the two networks are comparative high. In addition, the lithium hydroxide trade’s division of communities are more stable than those of lithium carbonate trade. This might because of its less trading countries and lacking absolutely dominant trade countries (such as Chile in lithium carbonate trade). Moreover, the lithium carbonate trade can be roughly divided into three major trading communities: Asia, America and Europe while lithium hydroxide trade can also be approximately divided into three major trading communities: Asia-America, Europe based on the United Kingdom and Europe based on France. But in different years, the three communities will combine in different ways. (3) Some conclusions can be drawn when compare the major countries of both lithium carbonate trade communities and lithium hydroxide trade communities. First of all, there are four more trade countries in lithium carbonate trade communities than in lithium hydroxide trade communities, which may because more trade countries and volumes in lithium carbonate trade. In addition, the number of communities, which consist of major trade countries, are about 2 to 4 in both of the two networks. This could mutual demonstrate the division of the whole network community. Although there are more communities in some years, many of these communities are consist of a few countries, which have limited trade volume. Besides, the volatility of lithium carbonate trade community is stronger than that of lithium hydroxide trade community. The average number of those major trade countries, which change their communities compared with the previous year, is higher in lithium hydroxide trade network than in lithium carbonate trade network. In both of the two networks, Japan is almost always in the same community with countries (Chile and the United States) that have the largest export volume. It is generally acknowledged that Japan is a country with scarce resources, in order to develop their economy, they have to import a large amount all kinds of resources including lithium. Acknowledgments The authors would like to express their gratitude to Mingyue Wang, Tiantian Feng, Xiangyun Gao, they have provided valuable suggestions. Funding This work was supported by the Development Strategy of Important and Mineral Resources in Qinghai Province (China Geological Survey, Grant No. 12120113033031) References [1] P. Zhou, J.R. Tang, T. Zhang, Supply and demand prospect of global lithium resources and some suggestions, Geol. Bull. China 33 (10) (2014) 1532–1538. [2] Daziano, A. Ricardo, Conditional-logit Bayes estimators for consumer valuation of electric vehicle driving range, Resour. Energy Econ. 35 (3) (2013) 429–450. 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