This paper uses complex networks to model trade and investment patterns to explore the correlation between international energy trade and investment.

We define international investment networks as G I n v = V I n v , E I n v , W I n v , where V I n v = v 1 , v 2 , ⋯ , v N are economies involved in international investment and N represents the number of economies. E I n v = e i j | i , j ∈ N , i ≠ j is the collection of edges in the network, representing the investment relationship between economies, and e i j represents the investment from economy i to economy j . W I n v = w i j , where w i j is the number of companies with investment relationships between the two economies. The complex network of international investments is shown in Figure 1. In Figure 1, the dots represent the economies involved in the investment, with larger dots representing more economies making energy investments with that economy. The dot’s color represents the range of the number of investment partners of that economy. The color of the edge is set to pink for better differentiation from the international energy trade network.

We define international trade networks as G T r a = V T r a , E T r a , W T r a , where V T r a = v 1 , v 2 , ⋯ , v N are economies involved in international trade, and N represents the number of economies. E T r a = e i j | i , j ∈ N , i ≠ j is the collection of edges in the network, which represents the trade relationship between economies, and e i j represents the transmission of fossil energy from economy i to economy j . W I n v = w i j , where w i j is the transaction amount of fossil energy between two economies. The complex network of international trade is shown in Figure 2. Figure 2 shows the dots that represent the economies involved in the investment, with larger dots representing more economies making energy investments with that economy. The color of the dot represents the range of the number of investment partners in that economy. The color of the edge is set to green for better differentiation from the international energy trade network.

Complex networks have some fundamental indicators that can measure the network attributes from the global perspective. In this article, two indicators, network distance and network graph density, are selected.

The network distance refers to the maximum value of the shortest distance between any two nodes in the network. If the distance of the network diameter is small, the economies have closer investment or trade relations with each other. It can be defined (Wasserman et al., 1994) as follows: D = max i , j ∈ H L min i , j , (1) where i and j are any two nodes in the complex network H and L min i , j is the shortest distance between nodes i and j .

Network graph density is the ratio of the actual number of connected edges to the number of possible connected edges in a network, which can reflect the closeness of the connection between nodes in the network. It can be defined (Watts and Strogatz, 1998) as follows: G D = 2 m n n − 1 , (2) where n is the total number of nodes and m is the number of edges between nodes.

In this paper, the topological characteristics of trade and investment networks are measured using four centrality indicators, considering the network node level, to characterize the position of each economy in the network and to find those economies that occupy a unique role in both networks. The first indicator is the degree centrality of a node. The degree centrality of a node measures the number of other nodes that are directly connected to it. The higher the degree centrality of a node, the more central the node is in the network and the more power it has. It can be defined (Freeman, 1978) as follows: C D i = ∑ j ≠ i ∈ N δ i j n − 1 , (3) where n is the total number of nodes, δ i j = 1 when there is a directly connected edge between nodes i and j , and 0 otherwise.

The second indicator is the betweenness centrality of a node. The betweenness centrality of a node measures the ratio of the shortest paths through the node to all the shortest paths, indicating the number of shortest paths held by the node. It measures the degree of control a node has over the network’s resources and reflects the importance of an economy as a “bridge” in an investment or trade network (Wasserman et al., 1994). It can be defined as follows: C B i = ∑ s ≠ t ∈ N D s t i D s t , (4) where D s t i is the number of node pairs s and t passing through node i in their shortest path.

The third indicator is the closeness centrality of nodes. The closeness centrality of a node measures the node’s “distance” from all other nodes in the network. It is the ability of a node not to be controlled by other nodes (Freeman, 1978). It can be defined as C C i = n − 1 ∑ j ≠ i ∈ N d i j , (5) where d i j is the distance from node i to node j . In weighted networks, the following definitions are available. d i j = 1 w i k + 1 w k j . (6)

The fourth indicator is the eigenvector centrality of a node. The eigenvector centrality of a node measures the node’s importance in the network, which increases as the node becomes more closely related to other important nodes. It measures a node’s influence across the network (Freeman, 1978; Watts and Strogatz, 1998) and can be defined as C E i = ∑ j ≠ i ∈ N δ i j C D j λ , (7) where C D j is the degree centrality of node j , while λ is the eigenvalue of the adjacency matrix.

Network motifs reflect the local structural characteristics of the network in a modular way. In portraying the functional qualities of the network and identifying the structural evolution in the network, local structural features can play a better role than global structural features by focusing on the statistically significant connections among nodes in the network and the evolution patterns of the connections from the microscopic association patterns of the network (Shen-Orr et al., 2002).

Three-node motifs are the most basic subgraphs in networks. Existing studies show that the motifs of four or more nodes can be formed by the superposition and combination of three-node motifs through different forms (Shen-Orr et al., 2002). Therefore, identifying three-node motifs can satisfy the mining of local features of international investment and trade networks. The main characteristics of the three-node motifs are that the connected edges between nodes are directional and the connected edges do not consider weights. There are 13 possible connecting ways, as shown in Figure 3.

Motif M i is a subgraph with r nodes. If the number of its occurrences in the real network is denoted as R r e a l i , and the total number of occurrences of all subgraphs with r nodes in the real network is denoted as R , then the frequency of the motif is (Wernicke and Rasche, 2006) f x = R r e a l i R . (8)

P-value is the number of subgraph X that appears in a random network more frequently than it appears in the actual network (Bonacich and Lloyd, 2001). Suppose the number of random networks is s , where the frequency of occurrence of subgraph X in t random networks is not less than its frequency of occurrence in the actual network, then the p-value is as follows. p = t s . (9)

The smaller the p-value, the more statistically significant the motifs are in the actual network.

Z-score is also used to measure the statistical significance of network motifs in real networks compared with those in random networks. Z-score can be defined as Z i = R r e a l i − R r a n d i σ r a n d i , (10) where R r e a l i is the number of motif M i in the real network. R r a n d i is the number of motif M i in random networks, R r a n d i is its average, and σ r a n d i is its standard deviation. The greater the value of Z-score, the higher the statistical significance of the motif in the network and the more significant the local structure’s role in the network’s formation and evolution.

If there is a correlation between the international energy investment network and the international energy trade network, it can be reflected through the structure that the country nodes that form the significant motifs in one network have a stronger tendency to connect edges in the other network. This paper uses the conditional probability method to measure this tendency (Gneiting and Katzfuss, 2014). If nodes A and B represent two positions in motif M i (as in Figure 4), three economies in the form of M i are connected in one network, and an edge is generated between two economies in positions A and B in the other network. It can be defined as follows (Schober et al., 2018). P A | I = P A I P I = N M i T r a ∩ N e a b I n v N M i T r a , (11) where P I represents a network in which the three economies A, B, and C are connected in the form of M i , while P A I represents a network in which the three economies A, B, and C are connected in the form of M i , and the economies in the other network at positions A and B are connected edges.

The probability of producing a continuous edge at points B and C is given by P B | I = P B I P I = N M i T r a ∩ N e b c I n v N M i T r a , (12) where P B I represents a network in which the three economies A, B, and C are connected in the form of M i and the economies in the other network at positions B and C are connected edges.

The probability of producing a continuous edge at points B and C is given by P C | I = P C I P I = N M i T r a ∩ N e a c I n v N M i T r a , (13) where P C I represents a network in which the three economies A, B, and C are connected in the form of M i and the economies in the other network at positions A and C are connected edges.

The probability that a motif in one network has edges between three identical economies of another can be expressed as P ¯ = P A | I + P B | I + P C | I 3 . (14)

In order to explain these formulas more clearly, we show the example of the significant motifs in the trade network in Figure 4. As shown in Figure 4, the three groups of economies that involve M 7 in the trade network and their location codes are Jordan ( A 1 ), the United States ( B 1 ), and South Africa ( C 1 ); Cyprus ( A 2 ), the United States ( B 2 ), and China ( C 2 ); Israel ( A 3 ), China ( B 3 ), and Britain ( C 3 ). The way these economies are connected in the trade network is shown in Figure 4. In the investment network, an investment relationship is found between Jordan ( A 1 ) and the United States ( B 1 ), and between Cyprus ( A 2 ) and the United States ( B 2 ). Therefore, the probability that the three economies where M 7 is located can have an AB-connected edge is 2/3. There is an investment relationship between Israel ( A 3 ) and Britain ( C 3 ), such that the probability of the AC-connected edge is 1/3. There are investment relations between the United States ( B 1 ) and South Africa ( C 1 ), between the United States ( B 2 ) and China ( C 2 ), and between China ( B 3 ) and Britain ( C 3 ), that is, the probability of the BC-connected edge is 1. We take an average value of 2/3 for the probability of connecting edges among the three economies, that is, the overall properties of the connected edges in the investment network between the different nodes of M 7 in the trade network.

After finding the probabilistic correlation between motifs-to-edges in the investment and trade networks, we further explore the probabilistic correlation between motifs-to-motifs in the two networks, namely, finding the probability that the three countries that constitute the significant motif M i in one network can form the significant motif M r in the other network. It can be defined as follows: P R | I = P R I P I = N M i T r a ∩ N M r I n v N M i T r a , (15) where P I represents a network in which the three economies A, B, and C are connected in the form of M i , while P R I represents a network in which the three economies A, B, and C have a connection pattern of M i , and the three economies at positions A, B, and C in another network have a connection pattern of M r .

The probability that a motif M i in one network generates a significant motif between the same economies in another network can be expressed as P ¯ = P R 1 | I + P R 2 | I + ⋯ + P R z | I z , (16) where z represents the number of connection patterns of significant motifs in another network.

In order to explain these formulas more clearly, the example of the significant motifs in the trade network is shown in Figure 5. As shown in Figure 5, the three groups of economies that involve M 7 in the trade network and their location codes are Jordan ( A 1 ), the United States ( B 1 ), and South Africa ( C 1 ); Cyprus ( A 2 ), the United States ( B 2 ), and China ( C 2 ); Israel ( A 3 ), China ( B 3 ), and Britain ( C 3 ). The way these economies are connected in the trade network is shown in Figure 5. In the investment network, Jordan ( A 1 ), the United States ( B 1 ), and South Africa ( C 1 ) involve M 11 ; Cyprus ( A 2 ), the United States ( B 2 ), and China ( C 2 ) involve M 13 ; and Israel ( A 3 ), China ( B 3 ), and Britain ( C 3 ) involve M 12 , so the conditional probability that the three economies in which M 7 is located can involve M 11 in the investment network is 1/3. The probability of the occurrence of different significant motifs in the investment network is calculated separately, and the analysis reveals the different influences of the connection method of M 7 in the trade network on the formation of motifs in the investment network. After averaging the probabilities of the different significant motifs in the investment network, the analysis reveals the probability of the influence of the connection method of M 7 in the trade network on the formation of significant motifs in the investment network.

In order to quantitatively study the interrelationship between the primary indicators of international energy investment and trade networks, as well as the correlation between the occurrence frequency of significant motifs of investment and trade networks, the Pearson correlation coefficient method is adopted in this paper. Assuming that there are two variables, X and Y, their correlation can be expressed as (Pandia and Bihari, 2015) r = ∑ i X i − X ¯ Y i − Y ¯ ∑ i X i − X ¯ 2 ∑ i Y i − Y ¯ 2 . (17)

In order to further study the correlation between the energy “investment–trade” networks at the economic level, we use four indicators to determine the criticality of the economy. These indicators are degree centrality, intermediate centrality, proximity centrality, and eigenvector centrality. The results are shown in Table 2.

Degree centrality represents the number of economies that have direct investment (trade) dealings with the economy. The larger the value is, the more economies have dealings with the economy. The United States, Britain, France, and the Netherlands all occupy the top 10 positions in the degree centrality of these networks in both 2018 and 2022, indicating that these four countries have a large number of partners in the investment and trade networks and play a relatively important role in investment and trade networks.

Betweenness centrality represents the shortest investment (trade) transaction routes of an economy control. In 2018, the United States, Britain, and the Netherlands all occupied the top 10 positions in the betweenness centrality of the two networks, indicating that these three countries are located on the shortest path between a large number of other economies and have a relatively high degree of control over fossil energy investment and trade resources. They are essential media for other countries’ transactions, crucial investment and trade hubs, and energy commodity transfer stations. Furthermore, in 2022, in addition to the United States, Britain, and the Netherlands, France occupied the top 10 position regarding intermediary centrality.

Closeness centrality represents the “distance” of investment (trade) transactions between the economy and other economies. Five countries—the United States, Britain, France, the Netherlands, and Germany—occupy the top 10 positions in both networks in terms of closeness centrality, indicating that these five countries are less dependent on other countries for investment transactions and trade imports and exports, and have a higher ability to trade without the influence and control of other countries.

Eigenvector centrality represents the influence of the economy on the investment (trade) transactions of other essential economies in the network. In 2018, the United States, Britain, and India occupied the top 10 positions in both networks regarding eigenvector centrality, indicating that these three countries have more investment (trade) dealers and the countries they deal with are also influential countries in the network. Moreover, in 2022, in addition to the United States, Britain, and India, France occupied the top 10 position for eigenvector centrality.

It is easy to see that France is becoming increasingly important in the international energy “investment–trade” networks, comparing the key economic indicators for 2022 with 2018, mainly regarding the shortest transaction path and the closeness of investment (trade) transactions with other essential economies.

By comparing the top 10 countries in the critical indicators of the investment network with their rankings in the trade network, we observed that Bermuda, the Cayman Islands, and the Virgin Islands all ranked high in the four centrality indicators in the investment network in 2018 and 2022, indicating that they occupied a more important position in the investment network, with a large number of countries in which they invest and a high position in the investment network. However, in the trade network, the centrality indicator is only at a low-to-medium level. This condition confirms the attractiveness of the investment policies of Bermuda, the Cayman Islands, and the Virgin Islands as the world’s top three offshore financial centers. It also indicates that they do not have the stockpile and geographical advantages in terms of fossil energy trade transactions.

By comparing the top 10 countries in the critical indicators of the trade network with their rankings in the investment network, we observed that three countries—Korea, Germany, and the United Arab Emirates—all ranked highly in the centrality indicators in 2018. It indicates that these three countries are essential intermediaries in the trade network. However, in the investment network, the indicator of eigenvector centrality ranks only in the medium-to-low range. This condition suggests that Korea, Germany, and the United Arab Emirates are transit countries in a pivotal position for international fossil energy trade. However, the countries where they conduct investment transactions are not very important in international investment transactions. In 2022, Belgium and Italy are countries that were at the top of the trade network centrality index, but at the bottom of the investment network centrality index.

Correlation tests based on network indicators at the individual level of economies are conducted for economies co-owned in the international energy “investment–trade” networks. The network indexes use degree centrality, betweenness centrality, closeness centrality, and eigenvector centrality of nodes using the Pearson correlation test. In 2018, the number of shared economies was 117, while in 2022, the number of shared economies was 95.

The results are presented in Figure 6. The analysis of the results shows that in the international energy sector investment and trade network in 2018, 87% of the economies have positive correlations between critical indicators, with 65% having strong correlations. In 2022, positive correlations among critical indicators are found in 84% of economies, with strong correlations found in 66%. These data suggest two things: first, the economies occupying an important position in the investment network have a high probability of occupying a vital position in the trade network. It is a similar situation in the trade networks. Second, by comparing the data for 2018 and 2022, it is clear that the share of economies with positive correlations between critical indicators decreases. However, the share of economies with strong correlations increases. This indicates that after the epidemic and the Russo-Ukrainian War, energy investment and energy trade economies have become less consistent in their market positions in energy investment transactions and energy trade trading activities. However, the degree of consistency has increased for economies with consistent market positions.

The high positive correlation between the critical indicators comes from the consistency of the country’s behavior in terms of fossil energy investments and trade transactions. There are three categories of such countries: the first category is countries with large fossil energy reserves and the economic strength to invest in other countries or favorable investment policies to attract investment from other countries, which include the United States and Canada in North America; Brazil in South America; Britain, the Netherlands, and Russia in Europe; India and the United Arab Emirates in Asia; Australia in Oceania; and South Africa in Africa. The distribution of these countries is characterized by the fact that they are all coastal countries with easy access to sea transport. The second category is that fossil energy storage and demand are at the average level globally, and the number of energy investment transactions is relatively average. The representatives of this category are Sri Lanka and the Philippines. The third category is the small number of fossil energy trading and investment transactions; Cornwall and others represent such countries.

There is also a negative correlation between critical indicators due to the unequal position of economies in the international market for fossil energy investment and fossil energy trade. In one case, the economy is essential in the energy investment market. However, it fails to take a significant position in the energy trade market. The most common examples are Bermuda, the Cayman Islands, and the Virgin Islands, all of which are coastal economies but not rich in fossil energy reserves or demand. However, they have adapted their investment policies to attract large numbers of investors to meet domestic tax and fiscal needs. Alternatively, economies have a more significant position in the energy trade market but have failed to take a significant position in the energy investment market, most typically in Korea and Greece.

As the basic structural unit of the network, motifs can reflect the connection mode of network nodes. The correlation between the two networks can be obtained from the mesoscopic perspective by correlating the frequencies of the same motifs in the international energy “investment–trade” networks. Using the Pearson correlation test, the indicators used in this paper are the number of times each of the 13 modes appears in the two networks. The results are shown in Table 3. According to the test results, in 2018, the correlation coefficient was 0.799, which is significant at the level of 0.01. In 2022, the correlation coefficient was 0.758, significant at the level of 0.00. These data show a significant positive correlation between the frequencies of the same motifs in the international energy “investment–trade” networks.

The significant motifs reflect the transaction characteristics of the economies and the international energy “investment–trade” networks as they invest or trade with their neighboring economies. The significant motifs present the international energy “investment–trade” networks in 2018 are shown in Table 4, and Table 5 shows the significant motifs present in the international energy “investment–trade” networks in 2022.

The motifs that play an important role in both networks are M 7 , M 4 , M 9 , and M 6 . M 7 is the most statistically significant motif of the two networks in 2018. Its Z-score is the largest in both networks, representing the most typical local connection mode between countries involved in energy investment and trade networks. At the same time, its p-value is 0 in both networks, indicating that it represents a local connection mode unique to energy investment and trade networks compared with random networks. In the trade network, it represents bilateral trade between two economies and simultaneously provides export trade to the same economy. In the investment network, it represents two mutually investing economies that tend to look for the same economy for equity investment. M 4 represents that the three economies have stable and interdependent investment or trade relationships. M 9 , in the trade network, represents an economy acting as an intermediary country that imports energy products from one economy and exports them to another; whereas in the investment network, it represents an economy that receives investment from one economy while making equity investments in the other. M 6 , in the trade network, represents two economies that trade with each other, which tend to receive export trade from the same economy, and in the investment network represents two economies that invest in each other, which prefer to receive equity investment from the same economy.

The significant motifs unique to the energy trade network were M 8 , M 11 , and M 12 in 2018. M 8 represents a significant economy exporting fossil fuels to two different economies. This motif usually occurs when the major economy has enormous energy reserves. If there is import and export trade between the two economies, the three economies become connected as M 6 ; if one of these two economies also exports fossil fuels to the central economy, then the three economies will become connected as M 11 . M 12 indicates that a central economy imports fossil fuels from the other two economies and exports fossil fuels to one of them.

In 2022, the motifs that hold a significant position in both networks are M 4 and M 6 . Comparing the indicators of the critical motifs in these two networks, we can see that the Z-score ranking of M 9 , M 11 , and M 12 in the energy trade network has increased, while the frequency and p-value rankings remain unchanged. Furthermore, all three rankings contain a conductive trading approach in their structure. This condition reflects the impact of the Russo-Ukrainian War on energy trade: the Russo-Ukrainian War directly triggered the energy crisis in Europe, which made it difficult for European countries to import fossil energy directly from Russia, and the main form of energy trade changed to the other countries as energy transit points to import energy from Russia for re-export to European countries. M 7 and M 9 are no longer the critical motifs in the energy investment network. This suggests that in 2022, after the COVID-19 pandemic and the Russo-Ukrainian War, energy investments between countries become more cautious, and investors are less likely to make conductive investments, preferring familiar companies to invest in.

The motifs in the international energy trade and investment networks can reflect the transactional characteristics of the economies in these two networks when investing or trading. The motifs can also reflect the correlation between the local structure of energy trade and energy investment relationships. This correlation can be expressed in two ways: first, the conditional probability that the energy investment edges can be formed between the economies that constitute the significant motifs of the energy trade network; second, the conditional probability of forming the significant motifs of the energy investment network among the economies that constitute the significant motifs of the trade network.

Table 6 shows the conditional probability of connecting edges in the energy investment network among the economies forming the significant motifs in the trade network in 2018. Table 7 shows the conditional probability of connecting edges in the energy investment network among the economies forming the significant motifs in the trade network in 2022. Comparing the data of these 2 years shows that the probability of mutual energy investments between countries with energy trade decreases substantially after the COVID-19 pandemic and the Russo-Ukrainian War to only one-half of the pre-epidemic level. However, the trend of energy investments among countries with energy trade is similar.

The economies involving M 4 have the highest probability of linkage, which means that if there is an import and export trade among the three economies A, B, and C, then the probability of investment relationship between them is more significant. The probability of having an investment relationship between the BC economies in M 7 , the BC economies in M 11 , the AB economies in M 12 , and the AB economies in M 6 is higher, which suggests that economies with import/export trade are also prone to investment relationships. The corresponding economy in M 9 has a small probability of connecting edges, and its structure is the conducted transaction between the three economies. This condition shows that when one economy acts as an intermediary in a one-way trade between two other economies, the probability of investment occurring between these three economies is not much different from that between ordinary economies in the investment network.

Figure 7 shows the conditional probability of connecting significant motifs in the energy investment network among the economies that form the significant motifs in the trade network. As can be seen from the figure, the proportion of energy trading partners forming key modalities of energy investment among themselves after the COVID-19 pandemic and the Russo-Ukrainian War is about three-quarters lower than before COVID-19 and the Russo-Ukrainian War.

In 2018, the economies that constitute M 4 in the international energy trading network tend to form M 6 in the energy investment network. This means that if there are bilateral trade relations between the three economies, the investment patterns within these three economies are more inclined to have one economy as the main investor to invest in the remaining two economies, and the two invested economies will trade with each other in investment. In 2022, however, the economies constituting M 4 in the international energy trade network are most inclined to form M 4 in the energy investment network. This condition reflects the tendency of the three economies to invest in each other if they can trade with each other. This change confirms the previous statement that “energy investors have become cautious in their investments, preferring to invest in familiar companies.”

In 2018, only M 4 , M 6 , M 7 , and M 11 in the trade network can constitute significant motifs in the investment network, while M 8 , M 9 , and M 12 do not constitute significant motifs in the investment network. This condition suggests that only trade patterns that include bilateral trade relations can form a representative local structure in investment relations. However, in 2022, only M 4 in the trade network will form the critical motifs in the investment network. This shows that after COVID-19 and the Russo-Ukrainian War, only the energy trade model with a very close cooperative relationship can form a representative partial structure in the investment relationship.

The motifs can also express the correlation between the local structure of international energy investment and trade. It consists of two components: first, the conditional probability that the energy trade edges can be formed between the economies that constitute the significant motifs of the energy investment network; second, the conditional probability of forming the significant motifs of the energy trade network among the economies that constitute the significant motifs of the investment network.

The conditional probability of connecting edges in the energy trade network between economies that constitute the critical motifs in the energy investment network in 2018 is shown in Table 8. The conditional probability of connecting edges in the energy trade network between economies that constitute the critical motifs in the energy investment network in 2022 is shown in Table 9. Comparing these data, we can observe that the probability of energy trade between economies with an investment motif of M 6 decreases substantially to only one-half of the pre-epidemic level. However, the probability of energy trade between economies with an investment pattern of M 6 has increased. This suggests that the energy crisis caused by the epidemic and the war has led to a more conservative energy trade strategy, preferring trade cooperation between economies with equal and close investment relationships.

In 2018, the economies involving M 4 had the highest probability of linkage, which means that if there is mutual investment among the three economies A, B, and C, the probability of trade relationship between them is about 0.754. In 2022, this probability increased to 0.854. In 2018, the probability of having a trade relationship between the BC economies in M 7 and the AB economies in M 6 was higher. In 2022, the AB economies in M 6 were also more likely to have trade relations relative to AC and BC. This suggests that economies with mutual investment are also prone to trade relationships. In 2018, the probability of trade relations between AB of M 9 was smaller, while AB economies, which are economies with no investment relations in the investment network, were also less likely to have trade relations in the trade network (0.338). However, it is greater than the graph density of the trade network (0.083), which indicates that the three economies that constitute the significant motifs of the investment network, even if there is no investment relationship between them, will be more inclined to have trade relations than the ordinary economies in the trade network.

Figure 8 shows the conditional probability of connecting significant motifs in the energy investment network among the economies that form the significant motifs in the trade network. From the two figures, Figures 8A, B, it can be seen that if the local structure among the three economies in the energy investment network can form the significant motifs of the investment network, the three economies tend to form the trade interaction relationship between them in the trade network, that is, the connection form of M 4 . This bias is even more pronounced when the link between the three economies in the investment network is also M 4 . This condition indicates that the three economies that can form representative local investment relations in the investment network are more likely to have bilateral trade relations between the three economies in the trade network.

In addition, in 2018, M 9 was more inclined to form the linkage form of M 7 , which means that the three economies requiring investment transmission are more inclined to form bilateral trade patterns in which two economies export fossil energy to the other economy simultaneously.

Comparing the significant motifs in the investment network with the same patterns in the trade network, we can find the following:

First, economies involved in significant motifs in the investment network ( M 4 , M 6 , M 7 , and M 9 ) have a higher probability of trade linkages. In contrast, economies involved in the same pattern in the trade network do not have the same probability of linkages, even though they tend to be more closely linked than the average economy in the investment network. This condition shows that two countries with investment relations are more inclined to establish trade relations, while two countries with trade relations are less likely to establish investment relations as compared to the former.

Second, M 4 of the two networks is the mode with the highest probability in which the three countries are connected, indicating that the three economies with bilateral investment relations are more likely to conduct import and export trade. The three economies with bilateral trade relationships are also more likely to have investment relationships with each other.

Third, after COVID-19 and the Russo-Ukrainian War, economies have become more cautious in their energy investment and trade activities. This caution is reflected in a significant reduction in investment volume and a preference for trade between economies with equal and close investment ties.