Time-space evolution of the goods export network of the Belt and Road countries: The view of weighted complex network

Abstract

The weighted complex network is utilized to analyze the evolution of the overall structural features of the goods export network and the role transitions of each country in the network. The research suggests: 1. The network of exports of the Belt and Road countries has transformed from multi-core pattern into one extreme along with multi-core pattern; 2. China, South Korea, Russia, Singapore and Italy are the highest-ranking countries in the network. Among these countries, the influence of China is on the rise, South Korea South Korea’s influence remains basically unchanged., however, Russia, Singapore and Italy are on the decline; 3. The leading edge of Asia-Pacific block in the network has been enhanced year by year. Not only has the trade volume within the block increased to 50% of the whole network, but the trade export to other three blocks has significant increasement. The total volume of trade in European block increased greatly and its block mode has transformed from external to universal. The trade volume of the former Soviet Union block along with the West Asia-Africa block increased significantly as well, but there is still a large gap compared with the European block and Asia-Pacific block.

Keywords

Goods export network the belt and road initiative weighted complex network centrality analysis block mode

1 Introduction

Promoted by differentiated resource endowment and highly complementary industrial structure, the export of goods among the Belt and Road countries grows rapidly. In 2003, the total exports volume 82 sample Belt and Road countries is $750.7 billion US dollars, which rapidly climbs to $3,305.9 US dollars in 2018 with a 2.2 times growth rate compared with that of global exportation volume in the same period. The total trade volume of internal goods export network accounts for 17.6% of global exportation volume in 2018, up from 10.1% in 2003 [2]. The development of exports network of the Belt and Road countries helps undeveloped countries to get rid of the manufacturing-return predicament caused by European and American countries’ “reindustrialization” strategy [3]. Therefore, it is of greatly practical significance to study the time space evolution of goods export network of the Belt and Road countries.With the rise of network analysis methods, scholars have analyzed the topological structure characteristics and evolution laws of trade networks, pointing out that global trade networks have the characteristics of scale-free, heterogeneity, and like a small world [1].

And some scholars find out that a few countries having strong connections in the network are more clustered [4 , 7], thus the network presents a layer structure of “core-semi edge-edge” [6, 8]. Since the launch of the Belt and Road Initiative, many domestic scholars start to utilize network analysis method to study the trade behaviors under the Belt and Road Initiative. Zou and Liu (2016) find out that China is the most important core country in the sub-trade network in the sub-trade network consisting of China and Southeast Asian countries by utilizing cohesive subgroup and core-edge models [9, 11]. Liu, Xu, and Zhang (2019) find out that the trade network of the Belt and Road countries is mainly composed of central and eastern trade blocks along with Asian trade block by using block model. Yang, Du, and Ma (2018) study the topological features and spatial structure of the network and finds out that trade network of the Belt and Road countries has characteristics including small world, scale-free, and “core-edge” and the like [12]. Besides, some scholars also analyze the network structures of high-end manufacturing, steel [10], agricultural products [13], transportation, oil and other subdivided products under the Belt and Road Initiative.

However, most studies are based on undirected topological networks. Topological network is an abstract representing the real network, thus cannot accurately reflect the difference of trading capabilities between countries. Moreover, excessively high threshold setting of topological networks may lead to some small trading countries to be ignored, while excessively low threshold setting fails to distinguish each country’s trading capability [14]. In addition, most studies use the total volume of bilateral trade to measure the trading relationship between two countries, on which the undirected network based cannot show the trade flow relationship between two countries. While merely studying exports, the ability of countries to export commodities, technologies and other heterogeneous resources can be further investigated. Therefore, this paper uses each country’s bilateral exportation data to construct a weighted complex network of goods flows of the Belt and Road countries. Based on the systematic investigation of the overall scale and structure evolution of the network, each country’s centrality status in the network is measured by weighted centrality and PageRank index, and changes of each country’s influence is measured by Hubbell influence index. Finally, the spatial clustering relationships and the correlation relationships among each block can be revealed by utilizing block model. The above studies are helpful to clarify the evolutionary mechanism of the goods export network under the Belt and Road Initiative, identify each country’s role in the network and trade incidence relations among each block, and provide empirical support for the relevant theoretical studies such as division of production network and south-south cooperation to a certain extent.

2 The construction and analysis methods of the goods export network under the Belt and Road Initiative

2.1 The construction of the goods export network under the Belt and Road Initiative

Let the Belt and Road countries be marked as nodes, and economic and trade links among each country in the network as edges between each node, then an economic and trade flows system S of the export of goods network of the Belt and Road countries, represented by an ordered quaternion, can be obtained: $S = (N, E, T)$ (1)

In the above formula, N ={ n₁, n₂, ⋯⋯ , n_k } represents node set, and the element n_i represents the Belt and Road countries. E ={ e_ij } represents edge set, and there are two edges between country n_i and n_j in the network, representing export e_ij from n_i to n_j, and reversed export e_ji from n_j to n_i, respectively. T ={ t₁, t₂, ⋯⋯ , t_k } represents trade set, and the elements represent the tangible goods flowing in the network.

2.2 Analysis methods

2.2.1 Network scale analysis

This paper uses node degree, edge weight, node strength to measure each country’s export scope, export scale to a specific country, and total export scale to the other countries in the network: 1. Node degree k_i represents the number of countries who import goods from n_i, then define it as k_i = ∑_j∈Na_ij. If trade value from n_i to n_j is greater than 0, then let a_ij = 1, otherwise, let a_ij = 0; 2. Edge weight w_ij reflects the trade value from n_i to n_j, the greater w_ij is, the closer relation it indicates between n_i and n_j. If w_ij = 0, the trade value from n_i to n_j is 0; 3. Node strength s_i represents the sum of total connected edge weights, then s_i = ∑_j∈Nw_ij.

2.2.2 Analysis of community structure

This paper uses the method of community structure division to identify the internal trade groups (communities) in the goods export network under the Belt and Road Initiative. In complex networks, intricately connected node sets can be regarded as a community, and modularity is an important indicator to measure the advantages and disadvantages of community division. The greater the modularity, the more obvious the differentiation of the network, and the smaller the modularity, the less obvious the differentiation of the network. The division of community includes two processes: First, each country in the network is regarded independent, and it is divided into a community with the countries that can improve the modularity. After that, the community is regarded as a new node to reconstruct the network. This process continues until the modularity of the entire network no longer changes. And the calculation formula of modularity is as follows: $Q = \frac{1}{2 m} \sum_{ij} [A_{ij} - \frac{s_{i} s_{j}}{2 m}] δ (c_{i}, c_{j})$ (2)

In the above formula, A_ij is the sum of total connected edge weights between n_i and n_j, $m = \frac{1}{2} \sum_{ij} A_{ij}$ represents the sum of the weights of all edges, c_i is the community that n_i is divided into. And δ (c_i, c_j) is used to judge whether n_i and n_j are divided into the same community. If so, the return value is 1, otherwise it is 0.

2.2.3 Centrality analysis

This paper uses weighted centrality and PageRank index to measure each country’s centrality status in the network. The weighted centrality Wc_i is based on the network generation principles of connections and flows to measure each country’s centrality status in the network. It comprehensively considers the influence of node degree k_i and strength s_i on each country’s centrality status, and the formula is as follows: ${Wc}_{i} = k_{i}^{λ} \times {(\frac{s_{i}}{k_{i}})}^{(1 - λ)}$ (3)

In the above formula, λ is assignment parameter, referring to the study of Jiao, Wang, and Jin (2016), here it is set as 0.5. The central position of the country in the network measured by PageRank index is feedback based on the principle of network generation, which considers the central transmission problem, that is, cooperation with high-central countries can enhance the central position of the target country in the network. The formula is as follows: ${PR}_{i} = \frac{(1 - σ)}{Q} + σ \sum \frac{{PR}_{j}}{k_{j}}$ (4)

In the above formula, σ is the damping coefficient, referring to the studies of Senanayake, Piraveenan, and Zomaya (2015), it is set as 0.85; Q is the number of countries in the export of goods network, and PR_j is the PageRank index of n_j who has relations with target country.

2.2.4 Influence analysis

The paper chooses Hubbell influence index as a supplement to the centrality analysis, in order to further reveal the degree of mutual influence among countries in the network. The larger the figure is, the greater influence the target country has on other countries. The formula is as follows: $t = {(\frac{1}{α} I - C^{'})}^{- 1} C^{'} u$ (5)

In the above formula, α is damped exponential, it is set as 0.5, and I represents unit matrix, u represents the column vector with the same number of columns as t, and C represents node matrix relation.

2.2.5 Block model

The block model is mainly based on the principle of “structural equivalence”, clustering nodes in the network into different blocks and analyzing the relationship between them. This paper uses the block model to reveal the spatial clustering relation of each country and the correlation relation between blocks in the goods export network under the Belt and Road Initiative. According to the difference of internal block and external trade’s correlation relations, the blocks are divided into four categories: the first is external block, which has less or none internal relations, but more external trade relations; second, internal block, which has more internal trade, but less or none external relations; third is balanced block, which has both more internal and external relations; the fourth is isolated block, with little or no internal or external relations.

3 The whole scale and structure evolution of exports network under the Belt and Road Initiative

With continuous expansion of the scale of the economic and trade cooperation of the Belt and Road Initiative, the characteristics of spatial unbalanced development in the goods export network becomes more and more obvious, and the network presents a “core-edge” layer structure (see Fig. 1).

Fig. 1

The evolution of export of goods network under the Belt and Road Initiative.

(In the same year, the larger the legend of the node, the darker the color of the legend, indicating the larger the export volume of the country. The thicker the line between the nodes, the greater the export volume between the two countries. However, the node legend size, color depth and line thickness in different years are not equal to the proportion of actual export volume.)

In 2003, a network structure was established with China, Italy, South Korea, Singapore and Russia as core, and Malaysia, Austria, Thailand and Indonesia as second-tier core in the exports network under the Belt and Road Initiative. In the network, 682 relations with an export value of more than US $100 million have been established, of which China and Italy have established relationships with an export value of more than US $100 million with more than half of the sample countries. The calculated modularity value is 0.369, showing that the community in goods export network under the Belt and Road Initiative is obviously divided. As research shows: the goods export network under the Belt and Road Initiative has primary formed intra-European and CIS trade network with Italy, Russia and other countries as the main body, the Asia-Pacific intra-trade network with China, South Korea, Singapore, Malaysia, Thailand and Indonesia as the main body, as well as the West Asia and Africa intra-trade networks and the Central and South America intra-trade networks whose trade volume are relatively small. China, Italy, South Korea, Singapore and Russia are not only the hubs of the sub-level trade network, but also the hubs of goods exports under the Belt and Road Initiative. China, Italy, South Korea, Singapore and Russia, the trade values (node strength) these five countries export to other countries in the network are 98.237, 78.714, 74.665, 74.160 and 71.220 billion US dollars respectively, and they contribute the greatest weight in the network (see Table 1 for more detailed information).

Table 1

The top 15 Edge Weights of goods exports network under the Belt and Road Initiative from 2003 to 2018

Rank	2003		2008		2013		2018
	Path	Edge Weights	Path	Edge Weights	Path	Edge Weights	Path	Edge Weights
1	KOR⟶CHN	351.10	KOR⟶CHN	913.89	KOR⟶CHN	1458.69	KOR⟶CHN	1621.25
2	SGP⟶MYS	227.80	CHN⟶KOR	739.32	CHN⟶KOR	911.65	CHN⟶KOR	1090.29
3	CHN⟶KOR	200.95	RUS⟶ITA	419.56	SGP⟶MYS	518.94	CHN⟶VNM	840.16
4	MYS⟶SGP	165.23	SGP⟶MYS	411.45	CHN⟶RUS	495.91	RUS⟶CHN	560.20
5	SGP⟶IDN	157.81	SGP⟶IDN	367.70	SGP⟶CHN	492.62	SGP⟶CHN	503.96
6	SGP⟶CHN	101.28	CHN⟶RUS	330.76	CHN⟶VNM	485.86	CHN⟶SGP	498.18
7	CHN⟶SGP	88.64	CHN⟶SGP	323.06	CHN⟶MYS	459.31	KOR⟶VNM	486.22
8	RUS⟶ITA	85.15	SGP⟶CHN	310.85	CHN⟶SGP	458.32	CHN⟶RUS	480.05
9	RUS⟶CHN	82.58	MYS⟶SGP	290.64	SGP⟶IDN	436.34	CHN⟶MYS	458.48
10	AUT⟶ITA	80.11	RUS⟶TUR	276.63	CHN⟶IDN	369.30	SGP⟶MYS	448.91
11	RUS⟶BLR	76.02	CHN⟶ITA	266.29	RUS⟶CHN	356.25	CHN⟶IDN	432.46
12	RUS⟶UKR	75.98	RUS⟶BLR	236.97	CHN⟶ARE	334.11	CHN⟶THA	429.74
13	ITA⟶AUT	69.68	CHN⟶ARE	236.44	CHN⟶THA	327.18	VNM⟶CHN	413.66
14	MYS⟶CHN	68.10	RUS⟶UKR	235.68	MYS⟶SGP	317.79	CHN⟶PHL	351.11
15	CHN⟶ITA	66.52	CHN⟶MYS	214.55	MYS⟶CHN	307.75	MYS⟶SGP	344.71

In 2008, the scale of the exports network under the Belt and Road Initiative significantly expanded. The relations with export value greater than $100 million US dollars were 1144, and the total export value within the network increased to $2323.794 billion US dollars as well. The increase of node degree and node strength are far much greater than the other countries, with a more obvious centrality status, while Russia, South Korea, Italy and Singapore have become the core of the second echelon. Judging from the evolution of the community structure of the goods export network under the Belt and Road Initiative, the value of modularity has risen to 0.370, indicating that the community differentiation is more obvious. Research shows that the network has further evolved into three internal trade networks of Europe and CIS, Asia Pacific and Africa, among which the internal trade of Europe and CIS network and Asia-Pacific network are the most prominent. The former’s internal trade volume accounted for 37.92% of the total intra-regional trade under the Belt and Road Initiative from 36.80% in 2003, while the latter’s proportion increased to 40.78% from 37.36% in 2003. In addition to the significant increase in intra-network trade in subnetworks, the proportion of trade between European and CIS networks and Asia-Pacific networks has also increased. At that time, the bilateral exports of South Korea and China, Russia’s exports to Italy and Singapore’s exports to Malaysia and Indonesia constituted the greatest weighted advantages (see Table 1 for more detailed information).

Due to the international financial crisis, in 2013 the increasing speed of the scale of goods export network under the Belt and Road Initiative declined significantly. The number of relations with export value greater than $100 million US dollars increased slightly to 1,300, and the total export value increased to $3019.268 billion US dollars. Among the core countries, China, South Korea and Singapore bucked the trend and further strengthened their centrality status with a relatively high node strength. However, the centrality status of Russia and Italy declined slightly due to the decrease of trade value. Judging from the evolution of the community structure of the goods export network under the Belt and Road Initiative, the value of modularity has dropped to 0.334, indicating that the degree of community differentiation of the network has decreased, but the value of modularity is still relatively high, indicating that the community differentiation of the network is still obvious. Research shows that the network can be divided into three intra-trade networks: Europe and CIS, Asia Pacific, and Africa. At this stage, the proportion of intra-trade of Europe and CIS dropped sharply to 28.66%, while the proportion of intra-trade in Asia-Pacific increased to 48.66%, and the proportion of trade between Europe and CIS networks and Asia-Pacific networks changed little. The results of this change were also vividly reflected in the edge weight ranking in the network: among the top ten weighted edges, except for the edge of China and Russia, the rest are all the edges of the Asia-Pacific countries (see Table 1 for more detailed information).

In 2018, affected by the global economic downturn and anti-globalization, the scale growth rate of export of goods network under the Belt and Road Initiative continued to slow down. The number of bilateral relations with trade volume exceeding 100 million US dollars has gradually increased to 1,366, and the total export volume has increased to 3305.936 billion US dollars. Among the core countries, China went up against the trend and its node strength rose to 805.983 billion US dollars. In terms of node strength, South Korea and Russia are far below China and are in the second tier of core countries, while Singapore and Italy fell into third-tier. The top ten weighted edges were mainly the edges between the Asia-Pacific countries, of which, China accounts for half. By far, the pattern of the network has evolved from multi-core in 2003 to one extreme (China) and multi-core (South Korea, Singapore, Russia and Italy) in 2018. In this stage, the value of modularity continues to drop to 0.316, indicating that the degree of differentiation of communities in the goods export network under the Belt and Road Initiative is further decreased, but the value of modularity is still relatively high, indicating that the differentiation of network associations is still obvious. Research shows that the network is still dominated by Europe and CIS and Asia-Pacific. The proportion of intra-European and CIS trade has further dropped to 26.59%, while the proportion of intra-Asia-Pacific network trade has risen to 51.05%. The top 15 sides are mainly the links in the Asia-Pacific intra-trade network, of which China issued 8 sides, compared with 3 sides in 2013 (see Table 1 for more detailed information).

4 The changes of each country’s centrality status and influence

4.1 Centrality analysis

Table 2 shows the top ten countries based on centrality analysis, the higher the ranking, the higher the country’s position in the network. According to weighted centrality, China, South Korea, Russia, New Zealand and Italy consistently have been ranked high from 2003 to 2018. Because of its advantages of geographical location, human resources and opening policy, Vietnam’s trade scale has increased rapidly and its centrality position in the network has enhanced to top ten in 2018. The PageRank index ranking is similar with weighted centrality ranking. The PageRank index ranking of Italy, the United Arab Emirates and other countries is higher than their weighted centrality ranking, which indicates that their partner countries have a higher centrality position in the network. In the four annual surveys, China, South Korea, Russia, New Zealand and Italy all ranked in the top five in terms of weighted centrality and PageRank index, indicating that these five countries have the most directly available trading countries on the one hand. The significant centrality advantage of the five countries make them easier to bring radiate influence on the rest countries in the network. The five countries can transfer their momentum of industrial development to other countries, thus playing a role of “engine”. On the other hand, the partner countries of these five countries are also relatively high ranked countries in weighted centrality, therefore, the five countries own absolute advantages of controlling information and resources in the network, thus becoming more powerful appeal so as to maintain a better collaborative network competition pattern, perfect the organizational governance under the Belt and Road Initiative, and play its “bridge” role to the maximum.

Table 2
The top 10 countries in the centrality analysis of goods export network under the Belt and Road initiative

Rank Weighted centrality PageRank

2003 2008 2013 2018 2003 2008 2013 2018

1 CHN CHN CHN CHN CHN CHN CHN CHN

(31.343) (65.155) (81.544) (89.777) (0.097) (0.105) (0.136) (0.153)

2 ITA RUS KOR KOR ITA RUS KOR KOR

(28.056) (50.212) (54.796) (56.931) (0.083) (0.08) (0.071) (0.072)

3 KOR KOR RUS RUS SGP ITA RUS RUS

(27.325) (45.435) (48.881) (50.109) (0.071) (0.07) (0.069) (0.064)

4 SGP ITA SGP SGP RUS KOR SGP ITA

(27.232) (41.712) (47.273) (45.218) (0.068) (0.064) (0.055) (0.051)

5 RUS SGP ITA ITA KOR SGP ITA SGP

(26.687) (41.355) (40.684) (41.145) (0.067) (0.059) (0.054) (0.049)

6 MYS MYS MYS MYS MYS MYS MYS MYS

(20.530) (30.804) (34.713) (36.218) (0.046) (0.037) (0.036) (0.033)

7 AUT THA THA THA IDN ARE ARE ARE

(17.249) (27.801) (32.928) (34.447) (0.032) (0.032) (0.035) (0.03)

8 THA POL IDN VNM THA THA IDN THA

(16.974) (26.212) (30.196) (33.014) (0.031) (0.03) (0.03) (0.03)

9 IDN AUT POL IDN ARE POL THA POL

(15.349) (26.0174) (28.23) (30.806) (0.026) (0.028) (0.03) (0.029)

10 CZE IDN CZE POL AUT IDN POL VNM

(13.016) (24.51) (25.466) (30.7) (0.025) (0.028) (0.026) (0.029)

Rank	Weighted centrality	PageRank
1	CHN	CHN	CHN	CHN	CHN	CHN	CHN	CHN
	(31.343)	(65.155)	(81.544)	(89.777)	(0.097)	(0.105)	(0.136)	(0.153)
2	ITA	RUS	KOR	KOR	ITA	RUS	KOR	KOR
	(28.056)	(50.212)	(54.796)	(56.931)	(0.083)	(0.08)	(0.071)	(0.072)
3	KOR	KOR	RUS	RUS	SGP	ITA	RUS	RUS
	(27.325)	(45.435)	(48.881)	(50.109)	(0.071)	(0.07)	(0.069)	(0.064)
4	SGP	ITA	SGP	SGP	RUS	KOR	SGP	ITA
	(27.232)	(41.712)	(47.273)	(45.218)	(0.068)	(0.064)	(0.055)	(0.051)
5	RUS	SGP	ITA	ITA	KOR	SGP	ITA	SGP
	(26.687)	(41.355)	(40.684)	(41.145)	(0.067)	(0.059)	(0.054)	(0.049)
6	MYS	MYS	MYS	MYS	MYS	MYS	MYS	MYS
	(20.530)	(30.804)	(34.713)	(36.218)	(0.046)	(0.037)	(0.036)	(0.033)
7	AUT	THA	THA	THA	IDN	ARE	ARE	ARE
	(17.249)	(27.801)	(32.928)	(34.447)	(0.032)	(0.032)	(0.035)	(0.03)
8	THA	POL	IDN	VNM	THA	THA	IDN	THA
	(16.974)	(26.212)	(30.196)	(33.014)	(0.031)	(0.03)	(0.03)	(0.03)
9	IDN	AUT	POL	IDN	ARE	POL	THA	POL
	(15.349)	(26.0174)	(28.23)	(30.806)	(0.026)	(0.028)	(0.03)	(0.029)
10	CZE	IDN	CZE	POL	AUT	IDN	POL	VNM
	(13.016)	(24.51)	(25.466)	(30.7)	(0.025)	(0.028)	(0.026)	(0.029)

4.2 Influence analysis

According to the changes of Hubbell influence, China’s influence is on the rise, and South Korea’s influence remains constant, while Russia, Singapore and Italy are on the decline (see Table 3 for more detailed information). What is noticeable is that Vietnam has done a great job in the network. Within 15 years, Vietnam’s influence ranking rocketed from 27th to 8th, becoming one of the most influential countries.

Table 3
The top 10 countries in the Hubbell influence index of goods export network under the Belt and Road Initiative

RankYear 1 2 3 4 5 6 7 8 9 10

2003 CHN ITA KOR SGP RUS MYS AUT THA IDN CZE

(1.067) (1.053) (1.052) (1.051) (1.048) (1.029) (1.02) (1.02) (1.016) (1.011)

2008 CHN RUS KOR ITA SGP MYS THA AUT POL CZE

(1.093) (1.055) (1.047) (1.038) (1.038) (1.021) (1.017) (1.015) (1.015) (1.013)

2013 CHN KOR RUS SGP ITA MYS THA IDN POL CZE

(1.112) (1.053) (1.041) (1.038) (1.028) (1.021) (1.019) (1.016) (1.013) (1.011)

2018 CHN KOR RUS SGP ITA MYS THA VNM IDN POL

(1.124) (1.052) (1.039) (1.032) (1.026) (1.021) (1.019) (1.018) (1.015) (1.014)

RankYear	1	2	3	4	5	6	7	8	9	10
2003	CHN	ITA	KOR	SGP	RUS	MYS	AUT	THA	IDN	CZE
	(1.067)	(1.053)	(1.052)	(1.051)	(1.048)	(1.029)	(1.02)	(1.02)	(1.016)	(1.011)
2008	CHN	RUS	KOR	ITA	SGP	MYS	THA	AUT	POL	CZE
	(1.093)	(1.055)	(1.047)	(1.038)	(1.038)	(1.021)	(1.017)	(1.015)	(1.015)	(1.013)
2013	CHN	KOR	RUS	SGP	ITA	MYS	THA	IDN	POL	CZE
	(1.112)	(1.053)	(1.041)	(1.038)	(1.028)	(1.021)	(1.019)	(1.016)	(1.013)	(1.011)
2018	CHN	KOR	RUS	SGP	ITA	MYS	THA	VNM	IDN	POL
	(1.124)	(1.052)	(1.039)	(1.032)	(1.026)	(1.021)	(1.019)	(1.018)	(1.015)	(1.014)

After a further analysis of the effects that the five most influential countries make on the other countries, it is found that: China, South Korea and Singapore, have the greatest impact on Southeast Asian countries, Russia has the greatest impact on China, South Korea and European countries, and Italy has the greatest impact on China and European countries (see Table 4). From the perspective of evolution, China’s impact on Vietnam, South Korea, Indonesia, Thailand and other countries has increased most significantly; South Korea’s impact on Vietnam, China and Poland has increased greatly, while its impact on Malaysia, Singapore, Thailand, Greece, Italy and the United Arab Emirates has declined. Russia’s influence on China, South Korea, Vietnam, Egypt and Malaysia has risen greatly, its influence on Estonia, Hungary and Romania and other eight countries has decreased. Singapore’s influence on Cambodia and China have increased significantly, while that in the Philippines, South Korea, Thailand, Indonesia, and Malaysia has declined; Italy’s influence in the network is declining, particularly on Greece, Austria, Romania, Russia, Turkey and other 21 countries.

Table 4

Countries in the network most affected by China, South Korea, Russia, Singapore and Italy

Rank	CHN		KOR		RUS		SGP		ITA
	2003	2018	2003	2018	2003	2018	2003	2018	2003	2018
1	KOR	KOR	CHN	CHN	CHN	CHN	MYS	CHN	AUT	CHN
	(0.013)	(0.017)	(0.023)	(0.025)	(0.006)	(0.009)	(0.015)	(0.008)	(0.005)	(0.002)
2	SGP	VNM	SGP	VNM	ITA	KOR	IDN	MYS	GRC	POL
	(0.006)	(0.013)	(0.003)	(0.008)	(0.006)	(0.003)	(0.011)	(0.007)	(0.004)	(0.002)
3	ITA	SGP	MYS	SGP	UKR	ITA	CHN	IDN	TUR	TUR
	(0.005)	(0.008)	(0.003)	(0.002)	(0.005)	(0.003)	(0.007)	(0.005)	(0.004)	(0.002)
4	MYS	IDN	ITA	IDN	BLR	POL	KOR	KOR	CHN	AUT
	(0.004)	(0.007)	(0.002)	(0.002)	(0.005)	(0.003)	(0.004)	(0.003)	(0.003)	(0.002)
5	RUS	MYS	ARE	MYS	TUR	TUR	THA	VNM	RUS	KOR
	(0.004)	(0.007)	(0.002)	(0.002)	(0.003)	(0.003)	(0.004)	(0.002)	(0.003)	(0.001)

5 Block model analysis on the goods export network under the Belt and Road Initiative

The results of block model show that the network was divided into four blocks in 2003 : 1. The European block mainly consisting of 23 European countries such as Austria and Czech; 2. The former Soviet Union block consisting of 15 countries such as Russia and Ukraine; 3. The West-Asian and African countries consisting of 22 countries such as South Africa and the United Arab Emirates; 4. The Asia-Pacific block mainly consisting of 22 Asia-Pacific countries such as China, South Korea and Chile. The European block and the former Soviet Union block’s internal trade value is far smaller than external trade value, thus considered as isolated block; The exports of Asia-Pacific mainly focus on the internal block, thus seen as internal block (see Table 5).

Table 5
Four blocks of goods export network under the Belt and Road Initiative in 2003

Block The trade matrix (billion US dollars) The density matrix

The European block The former Soviet Union block The West-Asian and African block The Asia-Pacific block The European block The former Soviet Union block The West-Asian and African block The Asia-Pacific block

The European block 627.19 587.76 67.96 91.80 1.24 1.70 0.13 0.18

The former Soviet 852.15 747.95 91.11 288.78 2.47 3.56 0.28 0.88

Union block

The West-Asian and 38.67 33.66 152.86 92.78 0.08 0.10 0.33 0.19

African block

The Asia-Pacific block 283.59 291.63 327.93 2 931.37 0.56 0.88 0.68 6.35

Block	The trade matrix (billion US dollars)	The density matrix
The European block	627.19	587.76	67.96	91.80	1.24	1.70	0.13	0.18
The former Soviet	852.15	747.95	91.11	288.78	2.47	3.56	0.28	0.88
Union block
The West-Asian and	38.67	33.66	152.86	92.78	0.08	0.10	0.33	0.19
African block
The Asia-Pacific block	283.59	291.63	327.93	2 931.37	0.56	0.88	0.68	6.35

In 2018, the composition, relations and types of the four blocks have some changes. To be specific, eight countries have left the European block, and new joint countries are Italy, Slovakia and Cyprus joined; Six countries have left the former Soviet Union block, with Turkey and Malta as new entrants; Seven countries left the West-Asian and African block, then Egypt, Lebanon and other ten countries joined; Four countries in the Asia-Pacific block left, with nine new entrants such as Russia and South Africa. The trade matrix and density matrix in Table 6 show that both internal and external relations of the four blocks have become much closer. Among them, the types of the former Soviet Union block, West-Asian, African block and Asia-Pacific black remain unchanged, while the difference between the huge improvement on internal trade relations and external relations of the European block is not significant, thus its block type converted from external type to balanced type.

Table 6

Four blocks of goods export network under the Belt and Road Initiative in 2018

Block	The trade matrix (billion US dollars)				The density matrix
	The European block	The former Soviet Union block	The West-Asian and African block	The Asia-Pacific block	The European block	The former Soviet Union block	The West-Asian and African block	The Asia-Pacific block
The European block	4 338.99	716.36	390.95	1 084.76	14.18	3.62	0.78	2.41
The former Soviet Union block	763.40	391.33	209.83	612.45	3.86	3.56	0.68	2.23
The West-Asian and African block	150.06	131.87	1076.70	650.59	0.30	0.43	1.42	0.93
The Asia-Pacific block	2 370.20	1 528.87	2 207.58	16 435.42	5.27	5.56	3.15	27.39

In this paper, the values of the density matrix which are greater than the overall network density in the same year are assigned to 1, otherwise 0, and the correlation diagram of each block is drawn (see Fig. 2). It can be seen that the Asia-Pacific block is the hub of the entire network. In 2003, the internal trade relations of the Asia-Pacific block accounted for 39.05% of the total volume of internal trade relations in the network, which further increased to 49.71% in 2018. The Asia-Pacific Group has not only established close internal trade relations, but also has strong export capacity. In 2003, imports from the Asia-Pacific Group, the former Soviet Union Group, the West Asia Group and the African Group in the European Group accounted for 15.74%, 17.56% and 51.25% of the total imports respectively. This proportion increased to 31.09%, 55.23% and 56.82% respectively in 2018, indicating that the Asia-Pacific block has a leading advantage of importing in the network, which can boost the commodity flow throughout the entire network. The European block is the second-tier core block after the Asia-Pacific block in the network. However, the exports of the European block are mainly concentrated among the countries within the block, and the exports to the former Soviet Union block and the West Asia-Asia-Africa block are relatively small. The scale of trade between the former Soviet Union and the West Asia-Asia-Africa block has increased significantly. The West Asia-Asia-Africa block not only has significant internal trade relations, but also has close trade relations with the Asia-Pacific block. However, there is still a huge gap between these two blocks and the European block and the Asia-Pacific block.

Fig. 2

The incidence relation of the four blocks of export of goods network on the Belt and Road.

(The circular arrow in Fig. 2 indicates that the export relation density among countries within the block is greater than the overall network density, that is, the export relation within the block is significant. The straight arrow indicates that the relation density of blocks’ exports to other blocks is greater than the overall density of the network, that is, the relation between blocks’ exports to other blocks is significant.)

6 Conclusions and implications

Based on the above studies, we find that: 1. There is a “core-edge” layer structure in the export of goods network of the Belt and Road. Further, among the core countries, the centrality position of China, South Korea, Singapore has been significantly enhanced, while the centrality position of Russia and Italy has been slightly declined, thus the pattern of the network transformed from multi-core to one extreme and multi-core; 2. The weighted centrality and PageRank index of China, South Korea, Russia, Singapore and Italy always rank the top five, which indicates that these five countries are in the absolute center of controlling position in the network, and playing the roles of “engine” and “bridge”; 3. China, South Korea, Russia, Singapore and Italy are the countries having the most influential power. From the perspective of evolution, the influence of China is on the rise, and that of South Korea remains constant, while that of Russia, Singapore and Italy are on the decline; 4. The leading edge of Asia-Pacific block in the network has been increasing over the years. Not only has the internal trade volume increased to the half of the total trade volume of the entire network, but also its trade export to other three blocks have been significantly increased. The total trade value within the European block have been increased greatly, and its block type has transformed from external type to balanced type. The trade scale of the former Soviet Union block and West-Asian and African blocks have been improved significantly, but still a gap compared with the European block and the Asia-Pacific block.

The above conclusions have the following implications: First, strengthen China’s trade relations with the core countries in the network and other second-tier core countries. We should attach importance to cooperation with countries with high central status and great influence, and use the relationship between core countries and peripheral countries to enhance China’s control in the entire network. Second, promote the integration between the European production network and the exports network under the Belt and Road Initiative. European countries and the Belt and Road Initiative countries have complementary factors, endowment structure and differentiated industrial structures. Through bilateral or multilateral agreements and other methods to make European countries blend into the exports network under the Belt and Road Initiative, which is not only helpful for less developed countries to absorb technology spillover from European countries, but also expand external markets for countries in the network, thus reducing the damage to the domestic economy caused by the continuous economic downturn. And the third is to taking advantage of China’s central superiority in the network, actively construct the value circulation of the exports network under the Belt and Road Initiative. China uses its functions of “engine” and “bridge” in the network to help backward countries improve their technological level and promote their status of international division of labor, so that they can reap more benefits of division of labor in the value division of export network.

Footnotes

Acknowledgments

This work was financially supported by National Social Science Foundation of China (No. 17BJL005), Social Science Foundation of Shaanxi (No.2017D024), the project “Innovation capability support plan of Shaanxi” (No. 2019KRM086), and the Special scientific research project from department of education of Shaanxi (No. 19JK0608).

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