The Impact of Countries ’ Roles on the International Photovoltaic Trade Pattern : The Complex Networks Analysis

The expansion of the international PV trade encourages governments to focus on their trade roles in this market, which has increasing impact on their future development of sustainable energy. Thus, an exploration of top traders and their influence on global PV trade pattern is essential as governments seek to develop strategies to improve their global PV market’s discourse power. This study introduces the complex network theory to examine top traders whose default would lead to the collapse of trade pattern and their impactful ways. Moreover, the potential structural reason for top traders’ influence on trade is explored via link prediction. We find that a group of European countries account for 80% of global importation and are the most influential traders and bridges; a group of Asian countries are among the top exporters with half of the global share; and European countries’ high influence is due to their large number of trade partners instead of their trade volume. Above all, a high number of trade partners is more important than trade volume for countries seeking to be top traders. Finally, we discuss these results given the recent promising development of international PV trade.


Introduction
To achieve a global energy-related CO 2 target in 2050 of 50% below current levels and limit global temperature rise by 2050 to 2 ˝C above pre-industrial levels, photovoltaic (PV) energy has a promising future, with faster deployment than anticipated [1].As the essential part of the global economic development of sustainable energy, the international PV trade has engaged hundreds of countries and thousands of trading relations.Thus, the expanding trade pattern encourages countries to seek greater power in the global PV market, which is affected by their trade roles.For example, China, the leading exporter from 2007, has been perceived as an indispensable commodity source, and Germany, the leading importer in most recent years, has always been an important partner for exporters.However, facing a number of economic and non-economic barriers, the fluctuation of global PV trade in the last few years has encouraged governments to reconsider their development strategies, especially their PV trade roles in the international PV market with a lack of proficiency.As a result, exploring the impact of countries' trade roles on the global PV trade pattern is essential for governments to adjust their development strategies.
Previous studies on PV energy have focused on the need to develop and promote its use in individual countries.Yu assessed cycle sustainability and debated whether PV energy is a sustainable option for Australia [2]; Zhao evaluated the external benefit of promoting the use of renewable energy in China [3]; Alboteanu assessed solar irradiation as an important input parameter for Craiova, Romania [4].These studies provide information regarding the development and use of PV energy and clarify the relationship between PV energy deployment and economic or social elements.In recent years, the interactions between economic values and PV energy development have gained the attention of researchers.Carceres studied the installation of PV energy in Santiago from the economic perspective [5], while Yang examined international trade of PV energy to enhance the understanding of the environmental consequences of the Chinese PV industry [6].However, studies on the exporting and importing of PV among countries have not had much attention from researchers, which is an essential part from the economic perspective [7][8][9].In fact, for example, Chinese PV firms have seen obstacles in exporting PV devices in recent years, which has an indirect impact on the country's solar energy development.As a result, it is necessary to study the trade pattern of the global PV trade pattern.In particular, exploring top traders that have the greatest impact on the trade pattern provides a better understanding of the international PV trade, and the analysis on the reasons for their influence is a valuable reference for governments to adjust their strategies.
During the last decade, complex network theory was widely applied to the studies of international trade.Early studies focus on the topological properties of international trade patterns to measure the dynamic evolution [10][11][12][13][14][15][16][17].During the development of network theory and the increase of trade complexity, improved network modeling was adopted to explore the global or local trading feature with the comparison with original network, including the conduction of null models for network models by Fagiolo [18] and Saracco [19], the definition of the notion of extinction analysis by Foti [20], the establishment of residual international trade network by Fagiolo [21], the comparison with international financial network by Schiavo [22], the introduction of energy concept to measure then energy flow by Hao [23], and the improvement network into a weighted multilayer one by Gao [24].Moreover, indirect relations in the competition among countries was analyzed by An [8] and Zhang [25], and the concept of community was studied by Tzekina [26], Barigozzi [27], and Zhong [9] to measure close connections within each group of trade partners.In particular, during the last five years of studies, researchers have provided abundant, meaningful, and interesting debate on the trade pattern, influential traders [7,25,28], and the evolution mechanism [29][30][31][32].For example, Ji has found that geopolitics and diplomatic relations are the two main reasons for the regional oil trade structure [30]; Fagiolo has confirmed the weak trade links among countries by studying the evolution of the world trade web-based on a weighted-network analysis [29]; Guan explored potential crude oil trade links and confirmed that common trade partners is essential for the dynamic evolution [32]; Hoppe confirmed that fluctuations occur mostly between countries with strong dissimilarities of fitness and connectivity [31]; Zhang found that non-OECD countries have become the main driving force for the increase in global competition intensity [25]; Fan engaged in the issue of countries' roles and positions in international trade, and found that the EU, the USA and Japan have highest importance [7]; Ermann introduce the google matrix into the modeling to show the leading role of China and other BRICS countries in world trade [28].However, there are also some questions that need further debate.Firstly, few previous studies have focused on the global PV trade but the modeling of fossil fuel trading or comprehensive commodities.PV trading is an emergent but uncertain and imbalance market with abundant output source, which is the most significant difference with fossil fuel markets.Secondly, there are some conflicts among different research results about countries' roles and status, which confirms that the studies on this should get further development and is still necessary.Last but not least, few studies have combined the research on both trading mechanisms and the countries' trade roles.As a result, our works pay attention to the dynamic evolution of international PV trade pattern with the analysis of countries' trade roles and corresponding explanation from the perspective of structural mechanism, which would be explored based on the complex network theory [33,34] and the link prediction theory respectively [35][36][37][38][39], both of which have confirmed the feasibility of their application on various networks.
In this study, we aim to explore the impact of countries' roles on the international PV trade by answering following four questions.(1) What is the general evolution of the international PV trade?(2) Of the top trading countries, whose exit would result in the collapse of global PV trade?(3) How do top traders have an impact on the international trade pattern?(4) Why are these groups of countries top traders?To answer these questions, we first analyze the evolution of the network structure to determine and understand the changes in the trading environment.Then, to assess the most influential countries, we compare the structure differences between the original network and the default networks of certain continents.Furthermore, our study uses topological indices to evaluate countries' roles from three different perspectives, import volume, export volume, and the core degree in the local trade area.Finally, we study unweighted and weighted PV networks from the link prediction perspective to explore whether high trade volume is primarily responsible for becoming a top trader and to reveal trade promoters in the PV market.This study has extensive applications for studies of various commodities or multi-commodities' international trade, their influential traders, and their pushers.Such research can provide more practical suggestions for governments.
The contribution of our paper is as follows: (1) An analysis of the international PV trade is necessary because of its emerging and disparate fluctuation trade pattern; (2) further verification of countries' PV trade roles is studied from the perspective of import, export, and local importance; (3) the reason for countries' PV trade status is explained according to its structural trading mechanism; (4) a weak tie is further confirmed.
The remainder of this paper is organized as follows.Section 2 introduces the data source, structural indices of the complex network, and the algorithm for the link prediction.Section 3 explores the top traders, their influence, and the reasons for their influence.Section 4 discusses the findings, and Section 5 offers conclusions.

Data
The trade data in our paper are obtained from UN Comtrade [40], which is a world authoritative database that includes global export-import trade data for various commodities.The Harmonized System (HS) code of PV is 854140 [41][42][43].From 2000 to 2014, we have retrieved 62,536 records, each of which includes exporter, importer, trading type, and trade value (the unit is dollar).Based on the data of 15 years, we collect 15 data units.

Methodology
To explore the evolution of trade patterns, countries' trading roles, and their impacts on international PV trade, this paper combines the approaches of the complex network and the link prediction.The complex network is used to explore the general trade pattern, and the indices that are based on the statistical characteristics of the complex network are used to measure countries' trade roles.The link prediction is used to study the influence patterns of different countries on trade patterns.

The Construction of Complex Networks
To comprehensively consider the trade flow and trade value among countries, this paper uses countries as nodes, the relation and direction from exporter to importer as edges, and the total trade value of each relation (the unit is the dollar) as the weight of each edge.Thus, we have 15 complex networks.As Figure 1 displays, each node represents a country, the line between each pair of countries proves whether there is PV trade cooperation between these two countries in 2014, the direction of each line is from the export country to the import country, and the thickness of each line shows their trade value in 2014.

Indices Based on Topological Characteristics
Based on the complex network model of international PV trade pattern, structural indicators are always involved in the analysis to measure global or local features from different perspectives.Various indicators are selected by researchers.In this study, we selected three indices based on the topological characteristics of the nodes to measure countries' trade roles, and then selected another five indices based on the topological features of the global network.These indices were used to assess the countries' impact on the trade patterns based on the differences of the pattern structure when we remove specific countries.Simplified definitions and descriptions are as follows.
(1) Weighted in-degree (WID) [44] WID describes the annual import valuation of each country.Thus, WID reflects not only the country's number of import partners but also the value of its imports.Countries with high WID tend to be PV importers.WID is defined as where t and z denote different countries, IN(t) is the set of countries that export PV to t, and w(t,z) represents the total import value from z to t.
(2) Weighted out-degree (WOD) [44] WOD describes the annual export value of each country.Thus, WOD reflects not only the country's number of export partners but also its export value.Countries with high WOD tend to be PV exporters.WOD is defined as where OUT(t) denotes the set of countries that import PV from t and w(z,t) represents the total export value from t to z.

Indices Based on Topological Characteristics
Based on the complex network model of international PV trade pattern, structural indicators are always involved in the analysis to measure global or local features from different perspectives.Various indicators are selected by researchers.In this study, we selected three indices based on the topological characteristics of the nodes to measure countries' trade roles, and then selected another five indices based on the topological features of the global network.These indices were used to assess the countries' impact on the trade patterns based on the differences of the pattern structure when we remove specific countries.Simplified definitions and descriptions are as follows. (1) Weighted in-degree (WID) [44] WID describes the annual import valuation of each country.Thus, WID reflects not only the country's number of import partners but also the value of its imports.Countries with high WID tend to be PV importers.WID is defined as where t and z denote different countries, IN(t) is the set of countries that export PV to t, and w(t,z) represents the total import value from z to t.
(2) Weighted out-degree (WOD) [44] WOD describes the annual export value of each country.Thus, WOD reflects not only the country's number of export partners but also its export value.Countries with high WOD tend to be PV exporters.WOD is defined as where OUT(t) denotes the set of countries that import PV from t and w(z,t) represents the total export value from t to z.
Sustainability 2016, 8, 313 5 of 16 (3) Eigenvector centrality (EC) [45] EC is used to describe the local importance for each country.In particular, countries with high EC are important as they have extensive trade cooperation and also have many trade links with other important countries.EC is defined as where λ is a constant, a_(t,z) = 1 if z is linked to t, and a_(t,z) = 0 otherwise.EC is used to describe the importance of t, which depends not only on the number but also on the importance of t's neighboring trade countries.
(4) Average degree (AD) [44] AD is used to describe the general trading universality.If the network in a certain year has a high AD, then most countries have a high number of trade partners.AD is defined as where N denotes the set of countries in the complex network each year and |N| is the number of these countries.
(5) Average weighted degree (AWD) [44] If the network in a certain year has a high AWD, then most countries tend to have a high trade volume, whether it be in exports or in imports.AWD is defined as Average path length (APL) [46] APL can be used to describe the scale of the trade pattern; thus, this index can reflect the characteristics, excluding that of network diameter, of local relations among certain countries.APL is defined as Network diameter (ND) [46] ND can be used to describe the controllability of the trade pattern.Generally, if the ND is high, the network is difficult to control due to relative low stability.ND is defined as where L_min (t,v) represents the minimum number of paths between t and v.
(8) Average weighted clustering coefficient (AWCC) [47] The weighted clustering coefficient of a country reflects the trade probabilities with its neighboring partners.Furthermore, it reveals whether the country is a core trader in the local area.Thus, the AWCC represents the general clustering abilities of all countries.AWCC is defined as ˆÿ j,l pw pt, jq w pj, lq w pl, tqq Sustainability 2016, 8, 313 6 of 16 where k_t = |IN(t)YOUT(t)|.
In brief, WID, WOD, and EC are used to measure countries' import, export, and local importance, while AD, AWD, APL, ND, and AWCC are selected to estimate the change of global and local feature of the network if any continent's disruption occurs.

Link Prediction Based on Unweighted and Weighted Networks
To further explore why some countries are top traders to promote the evolution of global trade pattern, we introduced the link prediction to measure the structural characteristics for existing trade links.Based on the algorithm steps and common indicators from previous studies [36,37,39,48], we selected unweighted preference attachment (PA) and its weighted one (WPA) as the two structural indicators to describe existing trade links [36,37].It means that we assume that the PV trade cooperation is affected by a countries' number of trade partners.Additionally, we used the ranking score (RankS) to quantify two indicators' description abilities [36,39].The quantitative comparison of these two indicators helps us find out the weak-tie phenomenon [49,50] in the international PV trade pattern.Generally, if the consideration of trading volume cannot describe the distribution of trade links than the one with no consideration, the trade pattern is characterized by weak ties, which suggests that the expansion of trade links is affected by those countries with a relatively high trade volume but not by those countries with the highest trade volume [49,50].
The unified algorithm steps are as follows: (

1) Define indicators based on local characteristics for countries
In our study, we adopted preference attachment (PA) as the indicator, which is defined as Equation (9).At the same time, their corresponding indicators based on weighted networks is weighted preference attachment (WPA), which is defined as Equation (10).
" max ´SWID ptq , S WOD ptq ¯ˆmax ´SWID pvq , S WOD pvq ¯(10) Γ ptq " IN ptq Y OUT ptq is the amount of direct trade partners.As a result, PA and WPA reflect the importance of each country in the perspective of their trading universality. (2) Get 10% test links from existing trade links This step aims to explore the structural characteristics compared with unknown trade links.The rest of existing trade links was used to be the database for the calculation of indicators.If most test links have a higher value of an indicator than unknown ones, this confirms that this indicator describes a common characteristic for test links.This means that trade links are constructed based on this characteristic, which reflects corresponding realistic affects. (3) Calculate the score of each indicator for them and unknown trade links In order to examine the precision of indicators to describe trade link distribution, this step aims to apply the indicator on a small part of existing trade links in comparison with non-existing trade links.Generally, the higher the indicator value is, the more possibility the trade link has to be constructed.(4) Quantify the distribution of test trade links respectively To make the comparison of indicators convenient and equal, we needed to quantify the distribution of test trade links for the evaluation results of each indicator.Firstly, we ranked test and unknown trade links from the maximum to the minimum based on their indicator's value, respectively.Then, we used a test index to measure the distribution of test links.We selected Ranking Score (RankS) as the test index and it is defined as: RankS " 1 ˇˇE P ˇˇÿ iPE P r i ˇˇU ´ET ˇˇ (11) where r_i is the rank of the test link i, E P is the set of test links, E T is the set of rest existing trade links, and U is the set of all existing trade links and unknown trade links.RankS is used to measure the average rank of test trade links.As a result, the lower the value of RankS is, the better the indicator describes. (5) Compare the quantification results of different indicators Based on the same test data, in each year, link prediction provides a unified platform to compare different indicators.The indicator with lower RankS is more close to the linking mechanism of international PV trade networks.

The Evolution of Trade Patterns
To explore the dynamic evolution of international PV trade pattern, we measured the trade scale from the fluctuation of both countries and trade relations.For each year from 2001 to 2014, we counted the fluctuations in the number of nodes and edges and compared them to the previous year's data (Figure 2).The evolution of the ratios between edges and nodes is also presented in Figure 2. the average rank of test trade links.As a result, the lower the value of RankS is, the better the indicator describes. (

5) Compare the quantification results of different indicators
Based on the same test data, in each year, link prediction provides a unified platform to compare different indicators.The indicator with lower RankS is more close to the linking mechanism of international PV trade networks.

The Evolution of Trade Patterns
To explore the dynamic evolution of international PV trade pattern, we measured the trade scale from the fluctuation of both countries and trade relations.For each year from 2001 to 2014, we counted the fluctuations in the number of nodes and edges and compared them to the previous year's data (Figure 2).The evolution of the ratios between edges and nodes is also presented in Figure 2.  In the first stage, fluctuations occurred mainly in North America partly because the United States began to decrease their import and export volume.In 2013, European countries led the fluctuation in trade links; however, in the following year, China and other Asian countries lost a large number of trade partners.The reason for this is the PV trade has conflicted between European Union (EU) countries and China in recent years.Furthermore, the anti-dumping duties imposed by the EU created obstacles for China's PV enterprises, resulting in lower export volume than in previous years.
The general evolution of the international PV trade pattern continues to expand other than when it faces certain crises.According to this pattern, countries would have their own roles and positions, which would fluctuate over time.

Countries' Influence on Trade Patterns
Under the fluctuant evolution period, we tried to explore countries' influence on the trade pattern.This helped us learn which groups of countries have most importance on both local and global trade pattern.We sought to identify which countries exert a significant impact on the structure of the whole trade pattern in 2014.This means that the absence of an influential country would cause changes in the network, such as fluctuating values of indices.Therefore, we eliminated the group of countries that belong to the same continent and that are among the top 10 rated importers or exporters and among the 10 countries with the highest EC in 2014.We then compared five indicators of the original network with networks without specific continent countries.These five indicators, AD, AWD, ND, AWCC, and APL, were used to comprehensively measure the differences between local and global perspectives.
Table 1 indicates that the network without any major European countries exhibits the most apparent changes.Accordingly, the absence of these countries results in much lower AD, AWD, and AWCC, but higher APL and ND.This is especially true for the ND index, as European countries are the only ones that destroy the original structure, which indicates that, because of their strong connective force, their default or absence will disrupt the network, leading to the uncontrollability of the trade patterns.It also demonstrates that the entire trade pattern is composed of many groups of countries that have almost no links among them and that the relations among different groups of countries often serve as indirect links through other countries.Similar to ND, the increase in APL and the decrease in AWCC suggest that European countries are important in bridging the trade links among different groups of countries and in compacting the trade pattern.Moreover, the decrease in AD and AWD proves that European countries not only have a high number of trade partners, but they also have a high trade volume.Similar to European countries, countries from North America are also core traders, though they have much less influence on the trade pattern.Other bridging traders include countries from South America.The default or absence of these countries leads to an increase in AWD, but a decrease in APL, which means that they have many cooperating partners and that their target is to transfer PV without engaging in a high degree of importing or exporting.This explains why their corresponding default network has low AWCC.However, only the absence of Asian countries causes an increase in AWCC, suggesting that there is a relatively low number of relations among Asian countries' trade partners [51].That is, these countries tend to export PV energy to other countries, but their partners do not engage in further cooperation with each other.
It is concluded that the default of countries from these five continents will exert a different collapsing force on the international PV trade pattern where European countries are the most influential ones, followed by countries from North America and Australia.On the other hand, Asian countries always have more unidirectional trade cooperation, while South America countries tend to serve as bridging countries.

The Evolution of Countries' Roles
It is acknowledged that the group of European countries is the most influential group and that their absence would cause the collapse of the global PV trade pattern.Thus, it is important to understand how countries impact the trade patterns.As the trade role of each country differs, their influence on the evolution of international PV trade also differs.Similarly and simultaneously, the fluctuations in the trade pattern encourage countries to change their trading roles.Thus, by examining countries' trade roles from a global and local perspective, governments will be better prepared to adjust their PV trade strategies.We adopt WID, WOD, and EC as the indices that describe countries' roles from three perspectives.WID is used to describe importers, WOD describes exporters, and EC is used to identify those countries that are core traders and thus important hubs.We select the leading 10 countries for each index and analyze the most powerful importers (Figure 3), exporters (Figure 4), and core traders (Figure 5).To avoid trivial analysis of our results, we divide the countries by continent.Yellow represents countries from North America; green represents countries from Europe; blue represents countries from Asia; orange represents countries from South America; purple represents countries from Africa; and grey represents countries from Australia.The numbers in the figures are the country's rank in the corresponding year.
From the evolution of the 10 leading importers, we find that (1) the continent with the most number of importers has changed from Asia to Europe; (2) the country with the largest number of imports has changed from the United States and Mexico to Germany; (3) North America has gradually recovered its import status in recent years; (4) countries from Africa and Australia have evolved as a team of importers in recent years; and (5) Japan has recovered its near-top importation in the last three years.Figure 6 indicates that, in 2000, countries from Asia accounted for 31.89% of the global imports, which was only slightly more than North America's 24.81% and Europe's 14.71%.Especially, the United States and Germany accounted for 21.63% and 10.68%, respectively, of the global imports.However, in 2007, Europe accounted for 83% of the global PV imports, which is far greater than any other continent, and this trend continues until 2014 when Europe accounted for 56.62% of the total imports.In other words, it is evident that European countries have become major importers of global PV trade.
The evolution of the 10 leading exporters reveals that (1) an increasing number of European countries have become important PV exporters; (2) Asian countries are the main exporters, but they have gradually been reduced to include China, Malaysia, Philippines, and Rep. of Korea; (3) since 2007, Japan and United States have decreased their exports, and China has replaced them; and (4) Germany is both a leading importer and exporter in Europe.Figure 6 also reveals detailed information regarding countries' export behaviors.From 2000 to 2014, Asian countries have accounted for half of the global exports; European countries gradually reduced this difference in 2007, but then increased the gap in 2014.At the same time, the total export amount of North America was decreasing from 16.74% to 3.21%, which is mainly affected by the USA's apparent PV export drop, while the results show that Asian countries, especially China, Malaysia, Philippines, and the Rep. of Korea, are the main exporters.Countries from Europe, especially Germany and the Netherlands, are also important sources of global exports.These three perspectives allow us to assess the roles that various countries play in influencing the international trade pattern.European countries are both major exporters and importers; as such, they are important core traders that bridge cooperation among countries.Asian countries, especially since 2007, export significantly more than they import.While North American countries have decreased their exports, they have exhibited growth in imports in recent years.Moreover, Australia, Africa, and South America have shown growth and involvement in recent years with respect to the trade pattern and have thus increased their position in the trade market.Because the roles of these traders differ, their influence on the evolution of the trade pattern also differs.

Structural Characteristics of Global PV Trade Links
To understand why European countries have such a major influence on the international PV trade pattern and why the European countries are the major trade pushers, this section explores the linking mechanism to explain these trade issues.
Figure 7 provides the RankS values of PA and WPA from 2000 to 2014.The comparison with previous studies confirms that the RankS values in our research are relative low, which entails a high precision of describing the real trade links.As a result, PA and WPA have the ability to describe the distribution of real trade links.However, it is apparent that, no matter which year is examined, the RankS of PA is lower than that of WPA, which confirms that the global PV trade pattern exhibits weak ties.This classic theory states that countries expand their trade cooperation through countries that exhibit a medium-level trading volume rather than through countries that are characterized by one of the highest volume of trading.Accordingly, this explains why the pushers or promoters of international PV trade are the European countries rather than the Asian countries.Specifically, from our statistical results, in 2014, 75% of 20 countries that have the highest number of trade partners are from Europe.For example, Germany had $387 million worth of PV trading volume, which is similar to China's trading volume ($384 million).However, there are 272 Interestingly, the results from the perspective of a countries' importance indicate that (1) North America and Europe are the two most important continents from 2000 to 2014; (2) the leading core trader in North America is the United States before 2007 and Mexico after 2007; (3) there is a wide range of European countries that promote the strong influence of the EU; (4) Brazil represents South America as the critical trader with both low import and export volumes; and (5) China is the only Asian country that appears to be significant in the trade market in the past five years.To our surprise, Asian countries do not have a substantial influence on global trading cooperation.Unlike the trade of traditional energy and resources, such as crude oil, natural gas, and coal, the trade of PV energy reveals that exporters are more dependent on importers and that the opposite does not hold.Accordingly, major importing and exporting countries from Europe and North America are the core international PV traders.These three perspectives allow us to assess the roles that various countries play in influencing the international trade pattern.European countries are both major exporters and importers; as such, they are important core traders that bridge cooperation among countries.Asian countries, especially since 2007, export significantly more than they import.While North American countries have decreased their exports, they have exhibited growth in imports in recent years.Moreover, Australia, Africa, and South America have shown growth and involvement in recent years with respect to the trade pattern and have thus increased their position in the trade market.Because the roles of these traders differ, their influence on the evolution of the trade pattern also differs.

Structural Characteristics of Global PV Trade Links
To understand why European countries have such a major influence on the international PV trade pattern and why the European countries are the major trade pushers, this section explores the linking mechanism to explain these trade issues.
Figure 7 provides the RankS values of PA and WPA from 2000 to 2014.The comparison with previous studies confirms that the RankS values in our research are relative low, which entails a high precision of describing the real trade links.As a result, PA and WPA have the ability to describe the distribution of real trade links.However, it is apparent that, no matter which year is examined, the RankS of PA is lower than that of WPA, which confirms that the global PV trade pattern exhibits weak ties.This classic theory states that countries expand their trade cooperation through countries that exhibit a medium-level trading volume rather than through countries that are characterized by one of the highest volume of trading.Accordingly, this explains why the pushers or promoters of international PV trade are the European countries rather than the Asian countries.
examined, the RankS of PA is lower than that of WPA, which confirms that the global PV trade pattern exhibits weak ties.This classic theory states that countries expand their trade cooperation through countries that exhibit a medium-level trading volume rather than through countries that are characterized by one of the highest volume of trading.Accordingly, this explains why the pushers or promoters of international PV trade are the European countries rather than the Asian countries.Specifically, from our statistical results, in 2014, 75% of 20 countries that have the highest number of trade partners are from Europe.For example, Germany had $387 million worth of PV trading volume, which is similar to China's trading volume ($384 million).However, there are 272 Specifically, from our statistical results, in 2014, 75% of 20 countries that have the highest number of trade partners are from Europe.For example, Germany had $387 million worth of PV trading volume, which is similar to China's trading volume ($384 million).However, there are 272 trade partners for Germany, which is twice the amount of China's (123).Moreover, some European countries with low trade volume also have a high number of trade partners.For example, Sweden only has $6.44 million worth of trading volume, but its number of trade cooperation is 163, which is even higher than China's.It can be seen that this is a general phenomenon for most European countries that have high trading universality.Apart from countries from Europe, Mexico, Australia, Brazil, China, and the USA are another five countries among top 20 countries with the highest number of trade partners.In addition, the trading universality of Brazil with its low trade volume enables its status in local trading area.As a result, our results confirm that, for the international PV trade, being the local core trader is influenced by countries' extensive trading cooperation.
Based on the link prediction from unweighted and weighted indicators, we understand why the European countries serve as bridges and why they have a greater impact on the structure of the trade pattern.Their medium volume combined with their high universality leads the European countries to act as the drivers behind the evolution of international PV trade.

Discussion
Based on the analysis of international PV trade between 2000 and 2014, we explored countries' trade roles and their impact on the global PV trade pattern.First, we studied the general evolution of countries with respect to their trade relations by analyzing changes of the trade pattern scale.Then, we identified top traders that have most influence on trade pattern by studying the impact of their collapse when they default.Furthermore, the roles the countries play in the trade market were explored by considering their importation, exportation, and their local trading status.Finally, we explain the reason that European countries with medium trade volume are the most influential ones from the perspective of structural linking characteristics.Based on our results, we offer the following discussions and conclusions. (1) Expanding global PV trade pattern and significant changes of countries' trade roles The increasing number of countries and trade links indicates that the international PV trade pattern has expanded and become increasingly more complex, while also suffering shocks in 2007, 2013, and 2014.
Under this trade pattern, the trade roles of countries, which are their way of impacting global trade, are always evolving.European countries are the main importers, with approximately 83% of the world imports in 2007 and 56.62% in 2014.Moreover, they are also important exporters, with approximately 30% of the world export market in recent years.However, the major exporters are Asian countries, with nearly half of the global export market, while their share of the import market has been decreasing since 2007.On the other hand, North American countries have reduced their levels of both importing and exporting since approximately 2007, while Mexico has increased its role in the export market in the last five years.In addition, countries from the continents of Africa, South America, and Australia are also part of the trade pattern, which leads to increased trade competition.
No matter for importers or exporters, 2007 is the year that most countries' PV trade roles begin to change significantly.For this phenomenon, the financial crisis in this period is probably the best explanation, which involves a high number of countries like the USA, Japan, and European countries.For the USA and Japan, they cannot invest a similar amount of fund on sustainable energy development under the financial pressure.However, for European countries, their high attention on the solar energy development encourages the maintenance of PV importation to fulfill their PV deployment targets.At the same time, a relatively low impact from global financial crisis and the low labor costs helped Asian countries acquire the opportunity to develop their PV production, which leads to the recovery of the exportation gap between European countries and Asian countries.
The interactions between the trade roles of the countries and the global trade pattern are worth considering, as the solar energy development strategies impact the countries' choice of trade roles, and a corresponding change would cause a fluctuation in the global trade pattern.At the same time, changes of the trade pattern pushes countries to adjust their solar energy development strategies.As a result, the trade pattern is likely to evolve with changing various trade links and the fluctuant number of participating countries. (2) European countries' top impact on the international PV trade pattern Because of their trading universality and the weak-tie characteristics of the global trade pattern, European countries are the most influential traders; as such, they are aggressively promoting the expansion of trade relations.
Our results indicate that during the evolution of the international PV trade pattern, the production capacity could not equal the level of international influence on trade patterns.In other words, high-volume export countries do not always have status and power in the PV energy market.Although countries from Asia are among the high-volume export countries, it is the European countries that have the greatest influence on and control of the international PV trade.This may explain why China decreased its exports from 1.73 billion dollars in 2012 to 0.38 billion dollars in 2014.European countries hold greater power, and this power helps them to promote their anti-dumping taxes, which are huge obstacles for China's PV energy enterprises.
Results also show that global PV trade tends to be a buyer's market, which means that the EU has more control on the global trading pattern.On the one hand, there is oversupply in this market, which leads to the imbalance of supply and demand.On the other hand, the EU's development policies of renewable energy encourage it to be the main import trader and to compose main demand market [41].Unlike the fossil fuel energy market, the low supply risk stops the PV market from having a fixed export source.This is because the fluctuation of PV price can easily promote demand sides to select other import sources.As a result, the EU get higher discourse power than Asian countries, and the competition among exporters is higher than that among importers [7,42].
(3) Suggestions for trade strategies From our results, we extract three suggestions for the policy design.Firstly, as the expanding of global PV trade pattern, the subsidy stimulation is still necessary for promoting more companies involved in the international PV development.Secondly, countries should realize their status of different trade roles, which would be good for their policy adjustment.Last but not least, while it is acknowledged that the European countries are the most influential in international PV trade, Asian countries have a far greater trade volume.Based on the results herein, we proffer the bold suggestion that countries should focus on enhancing their number of trade cooperation rather than on merely increasing their volume of exportation, as the country with expanded trade relations will become the core trader in the local trading area and serve as the essential bridge for the entire trade pattern.As a result, policies should not only focus on the subsidies for electricity generating or the production capacity, but also for the cooperation with countries that were not common before.In this way, governments will increase their influence and their position in dialogues, both of which are significant for future development.
Due to the limits of the data, future studies will analyze the international trade of more renewable energy-related commodities.Additionally, economic factors, policies, and other elements will be analyzed with respect to international trade and renewable energy related commodities.

Conclusions
In this study, we aim at exploring countries' roles on the international PV trade.Based on complex network theory and link prediction theory, we have acquired analysis results on global and local structural characteristics of the international PV trade pattern.Results help to resolve the following issues: (1) the general evolution trend of the global PV trade pattern; (2) countries' impact on the trade pattern; (3) three impacting way for top countries; and (4) the reason for countries' influence on the global PV trade pattern.Results confirm that international PV trade is a buyer's market, which is different from other traditional energy markets.Moreover, the weak-tie feature of PV trade pattern demonstrates that the international influence is more important for countries' discourse power in the PV market than their production capacity.In particular, European countries are the most influential traders for both local and global trading relations with a high amount of import.Main exports are from Asian countries, but an increasing number of European countries is also joining the PV export market.North American countries have been decreasing their influence levels of both importing and exporting since approximately 2007, while Mexico has increased its role in the export market in the last five years.Our results would be helpful for governments to make a selection between production capacity and cooperation universality, which is an essential issue for countries' sustainable development strategies.
Further studies should aim to analyze countries' PV trading roles with combination of improved indicators from various perspectives, which would provide more precise suggestion for governments.

Figure 1 .
Figure 1.Complex network of the international PV trade, 2014.Data source is from UN Comtrade [40].

Figure 1 .
Figure 1.Complex network of the international PV trade, 2014.Data source is from UN Comtrade [40].

Figure 2 .
Figure 2. Number of nodes and edges compared to previous year, 2001 to 2014.

Figure 2 .
Figure 2. Number of nodes and edges compared to previous year, 2001 to 2014.

Figure 3 .
Figure 3. Top 10 highest volume import countries, 2000 to 2014.Top1 country has most import volume and so on; yellows are North America; blues are Asia; greens are Europe; grays are Australia; purples are Africa).

Figure 4 .
Figure 4. Top 10 highest volume export countries, 2000 to 2014.Top1 country has most export volume and so on; yellows are North America; blues are Asia; greens are Europe; grays are Australia).

Figure 5 .
Figure 5. Top 10 countries with the highest EC values, 2000 to 2014.Top1 country has highest EC value and so on; yellows are North America; blues are Asia; greens are Europe; grays are Australia; purples are Africa; oranges are South America).

Figure 3 . 16 Figure 3 .
Figure 3. Top 10 highest volume import countries, 2000 to 2014.Top1 country has most import volume and so on; yellows are North America; blues are Asia; greens are Europe; grays are Australia; purples are Africa).

Figure 4 .
Figure 4. Top 10 highest volume export countries, 2000 to 2014.Top1 country has most export volume and so on; yellows are North America; blues are Asia; greens are Europe; grays are Australia).

Figure 5 .
Figure 5. Top 10 countries with the highest EC values, 2000 to 2014.Top1 country has highest EC value and so on; yellows are North America; blues are Asia; greens are Europe; grays are Australia; purples are Africa; oranges are South America).

Figure 4 . 16 Figure 3 .
Figure 4. Top 10 highest volume export countries, 2000 to 2014.Top1 country has most export volume and so on; yellows are North America; blues are Asia; greens are Europe; grays are Australia).

Figure 4 .
Figure 4. Top 10 highest volume export countries, 2000 to 2014.Top1 country has most export volume and so on; yellows are North America; blues are Asia; greens are Europe; grays are Australia).

Figure 5 .
Figure 5. Top 10 countries with the highest EC values, 2000 to 2014.Top1 country has highest EC value and so on; yellows are North America; blues are Asia; greens are Europe; grays are Australia; purples are Africa; oranges are South America).

Figure 5 .
Figure 5. Top 10 countries with the highest EC values, 2000 to 2014.Top1 country has highest EC value and so on; yellows are North America; blues are Asia; greens are Europe; grays are Australia; purples are Africa; oranges are South America).

Table 1 .
Networks without specific continent countries and their corresponding indices, 2014.