Shock Propagation and the Geometry of International Trade: The US–China Trade Bipolarity in the Light of Network Science

Abstract

What is the impact of geopolitics on the geometry of global trade? What is the key structural role that led to the emergence of the US–China trade bipolarity? Here, we study the geometry of international trade, taking into account not only the direct but also the indirect trade relations. We consider the self-weight of each country as an indicator of its intrinsic robustness to exogenous shocks. We assess the vulnerability of a country to potential demand or supply shocks based on the entropy (diversification) of its trade flows. By considering the indirect trade relations, we found that the key structural role that led to the emergence of the US–China trade bipolarity is that of the intermediary hub that acts as a “bridge” between different trade clusters. The US and China occupied key network positions of high betweenness centrality as early as 2010. As international trade was increasingly dependent on only these two intermediary trade hubs, this fact led to geopolitical tensions such as the US–China trade war. Therefore, betweenness centrality could serve as a structural indicator, forewarning of possible upcoming geopolitical tensions. The US–China trade bipolarity is also strongly present in self-weights, where a race in terms of their intrinsic robustness to exogenous shocks is more than evident. It is also interesting that the US and China are not only the top shock spreaders but also the most susceptible to shocks. However, China can act more as a shock spreader than a shock receiver, while for the USA, the opposite is true. Regarding the impact of geopolitics, we found that the Russia–Ukraine conflict forced Ukraine to diversify both its exports and imports, aiming to lower its vulnerability to possible shocks. Finally, we found that international trade is becoming increasingly oligopolistic, even when indirect trade relationships are taken into account, thus indicating that a “Deep Oligopoly” has formed.

1. Introduction

International trade can be represented as a network where the countries are connected through trade flows of goods, services, and financial flows [1,2]. This network is dynamic due to ever-changing economic conditions, unexpected crises, geopolitical tensions, or other political reasons, such as trade agreements and tariffs that can either enhance or hinder the trade flows between the involved countries [3,4]. Interactions among these factors create a complex international market, where even a “tiny spark” in one area can trigger ripple effects across the entire trade network [5,6,7]. In particular, in the case of an unexpected shock, the impact may be even greater. We specify the nature of economic shocks as follows. An economic shock can be either a supply shock or a demand shock caused by several factors. For example, a decline in consumption and investments can lead to demand shocks, as in the case of the global financial crisis (2008) [8,9]. A decline in the inventory of some products can disrupt production, leading to supply shocks, as in the case of the Japan earthquake and tsunami (2011) [10]. Trade policies can lead to demand shocks, as in the case of the annexation of Crimea by Russia (2014) [11], the trade barriers related to Brexit (2016) [12], or the US–China trade war [13]. Geopolitical tensions can lead to supply shocks, as in the case of the Russia–Ukraine gas conflict (2009) [14]. We should highlight the fact that, in general, shocks may be exogenous. This means that the initial cause that triggered the shock is outside the economy. Examples would include a pandemic or an extreme weather effect [15]. Taking into account all the above, the motivation of this research is to answer the following four questions:

• Q1: Which countries occupy network positions characterized by a high spreadability of a shock to other countries? In other words, which countries have the greatest potential to spread a shock to other countries?
• Q2: Which countries occupy network positions characterized by a high susceptibility to shocks coming from other countries? In other words, which countries can easily be “infected” by shocks originating from other countries?
• Q3: Which countries are intrinsically robust to exogenous shocks due to their own high domestic production?
• Q4: How well do countries diversify the risk of a demand or supply shock?

To address the above four questions, we analyze the structure of the International Trade Network (ITN) using concepts from Network Science. The analysis is carried out at two hierarchical levels, namely (a) at the micro level, where we compute the centrality of each country (node) [16], and (b) at the macro level, where we compute the centralization of the entire network as well as its average path length and total trade flow [17]. The main contribution of our work is that we effectively take into account not only the direct but also the indirect trade relationships to address questions Q1 and Q2 (Section 2.3.4 and Section 2.3.5). In addition, to address question Q3, we consider for the first time the self-weights of the countries as an indicator of their intrinsic robustness to exogenous shocks (Section 2.3.6). Furthermore, we use the concept of entropy [18] to assess the diversification of the distribution of trade flows [19,20]. In this way, we address question Q4 by providing a quantitative assessment of the vulnerability of countries to possible demand or supply shocks (Section 2.3.3).

The analysis of network geometry offers two main advantages over conventional analysis in international trade. First, it offers a holistic view of the entire trade system. Unlike traditional methods that focus on individual trade relationships, network analysis examines the trade system “as a whole”, focusing on how countries, ports, and regions are interconnected [5]. This contrasts with conventional analysis, which often examines isolated trade relationships. Second, it can identify the key countries of the trade system. By using centrality indicators, network analysis identifies critical trade hubs or vulnerable trade partners, the disruption of which can have a ripple effect across the entire trade system [6,21]. This “X-ray” of the entire trade system can reveal, through centralities, valuable information about the vulnerable points of the trade system. This cannot be achieved with conventional analysis.

Network Science can also enhance predictive models for trade disruptions by analyzing trade as an interconnected system of nodes (countries) and links (trade flows). More specifically, centrality indicators are used to identify key trade hubs, providing critical information for assessing vulnerabilities and the impact of potential disruptions. Dynamic network modeling allows the simulation of cascading failures within trade networks, effectively incorporating the desired trade policy scenarios (“what-if” analysis) and taking into account all inherent heterogeneities. Network Science can also reveal alternative routes, improving resilience [22]. By incorporating machine learning, predictive models can reveal hidden patterns and assess the expected economic impact of disruptions, offering valuable insights into proactive decision-making and better mitigation strategies to safeguard the stability of the ITN.

In this work, the period from 2006 to 2018 is investigated. This period includes significant economic and geopolitical events, such as for example, the global financial crisis of 2008, the global fall in commodity prices of 2015, the Brexit referendum in 2016, and the USA–China trade war in 2018. We present in

Table 1. Significant events.

Year	Event
2008	Global Financial Crisis [8,9]
2010	Eurozone Sovereign Debt Crisis [23,24,25]
2014	Annexation of Crimea by Russia (Russia–Ukraine War) and Sanctions [11]
2015	Global Fall in Commodity Prices [26,27]
2015	Chinese Stock Market Crash [28,29]
2016	Brexit Referendum [12]
2018	The USA–China Trade War [13,30]

the significant economic and geopolitical events that may have affected international trade by changing the geometry of global trade flows. For more details, we refer to the relevant references found in Table 1.

In recent years, the USA–China relationship has been influenced by the following key trade shocks, which led to further strengthening of their economic competition and global influence. The USA–China Trade War (2018) involved heavy tariffs and retaliatory measures, which negatively affected global value chains and led to the diversification of trade partnerships. The COVID-19 pandemic (2020) further stressed these tensions by exposing the vulnerabilities of global value chains (trade lockdowns) and increasing the demand for supply chain resilience. The Russia–Ukraine war (2022) indirectly influenced USA–China trade relations, as the Western sanctions imposed on Russia led Australia and Japan to strengthen their economic ties with Russia, while the US faced difficulties in maintaining its strategic alliances.

This paper aims to provide a crystal-clear mathematical framework for assessing the propagation of shocks in international trade through the application of appropriately modified tools of Graph Theory. We emphasize the fact that these tools are presented in a way that allows for (a) direct interpretation in the context of international trade as well as (b) easy application and extension to other related contexts. Hence, we hope that this paper advances the existing related literature on the topic.

The paper is structured as follows. In Section 2.1, we present the data used, while in Section 2.2, we model international trade as a weighted, directed network with self-weights. In Section 2.3, we present the indicators that characterize the countries (at the micro level), while in Section 2.4, we present the indicators that characterize the entire ITN (at the macro level). In Section 3.1 and Section 3.2, we present the results for the countries as well as for the entire ITN correspondingly. In Section 4, we summarize the main findings and conclusions of the current work as well as some possible extensions left for future work.

2. Methodology

2.1. Data

We used data from the UN Comtrade database [31] and HS2 product classification. These data consist of annual, country-level, bilateral trade flows aggregated over all sectors. The dataset includes 138 countries for the period from 2006 to 2018. The countries included in this study are listed in Appendix A.

2.2. Modeling International Trade as a Network

Representation is the key to understanding any phenomenon. New representations can help us solve previously unsolvable problems or raise new questions. Network Science provides the most appropriate mathematical framework for representing complex interdependencies [17,32]. Modern trade flows are characterized by increasing complexity and heterogeneity. Therefore, modeling international trade as a network is the most appropriate method for analyzing trade flows [33,34]. Network indicators can effectively characterize the structure of international trade at both the microscopic and macroscopic levels, allowing valuable insights to be revealed.

Networks consist of nodes and links. Nodes $i=\mathrm{1,2},\dots ,N$ represent countries and links represent the trade flows between them. The links are weighted and directed. The weights are denoted by$w_{i\to j}\left(t\right)$ indicating the directed trade flow $i\to j$ from country $i$ to country $j$ in year$t$. Self-weights$w_{ii}\left(t\right)$ indicate domestic production minus the exports of country $i$ in year$t$. For simplicity, we omitted the time parameter$t=2006,\dots ,2018$, i.e., $w_{i\to j}\left(t\right)=w_{i\to j}$ and$w_{ii}\left(t\right)=w_{ii}$. Weights and self-weights are non-negative, taking values in the interval $[0,+\infty )$ measured in millions of constant dollars (USD). In

Table 2. The weight matrix $W\left(t\right)$.

Matrix Elements	Notation	Interpretation in the Context of International Trade
Off-diagonal	$w_{i\to j}$	Trade flow from country $i$ to country $j$
Diagonal self-weights	$w_{ii}$	Domestic production minus exports of country $i$

, the elements of the weight matrix$W\left(t\right)$ are summarized. In Figure 1, we provide the visualization of an ITN with 5 countries (a toy model) with weighted and directed links as well as self-weights, corresponding to the arbitrarily selected weight matrix:

$$W=\left[\begin{array}{ccccc}{w}_{11}& w_{1\to 2}& w_{1\to 3}& w_{1\to 4}& w_{1\to 5}\\ w_{2\to 1}& w_{22}& w_{2\to 3}& w_{2\to 4}& w_{2\to 5}\\ w_{3\to 1}& w_{3\to 2}& w_{33}& w_{3\to 4}& w_{3\to 5}\\ w_{4\to 1}& w_{4\to 2}& w_{4\to 3}& w_{44}& w_{4\to 5}\\ w_{5\to 1}& w_{5\to 2}& w_{5\to 3}& w_{5\to 4}& w_{55}\end{array}\right]=\left[\begin{array}{ccccc}3& 23& 12& 5& 6\\ 15& 5& 3& 23& 9\\ 12& 3& 6& 8& 21\\ 16& 21& 4& 7& 12\\ 2& 5& 61& 5& 6\end{array}\right]$$

2.3. Indicators for the Countries (Analysis at the Micro Level)

At the micro level, the following indicators are used namely degree, balance of trade, entropy, closeness, and betweenness. Each of these indicators can effectively capture the different roles a country can play in the ITN. These indicators, commonly referred to as centralities in Graph Theory, address the following question: How important is a country in the ITN? [16]. The term “important” has a wide range of different interpretations, leading to different mathematical formulas to correctly assess the desired role of a country in the ITN. In addition to the above, the self-weights of the countries are also discussed.

We present below in detail the mathematical formula for each indicator as well as its interpretation in the context of international trade. This way of presenting the indicators is particularly useful for the reader to understand and interpret the results correctly, avoiding possible misinterpretations. For simplicity, when we refer to an indicator, we mean its weighted version; for example, degree means weighted degree.

2.3.1. Degree

The most fundamental network indicator of a country is its degree. This is distinguished as degree-out for exports and degree-in for imports. Degree-out ${deg}_i^{out}$ is the sum of the export trade flows of country$i$, while degree-in ${deg}_i^{in}$ is the sum of the import trade flows. From a computational point of view, ${deg}_i^{out}$ is the sum of the $i$-th row of the weight matrix$W\left(t\right)$, excluding the diagonal element. Similarly, ${deg}_i^{in}$ is the sum of the $i$-th column, excluding the diagonal element. According to the relevant literature, the degree of a country assesses its trade dominance (relative position) [19,20]. A high value of ${deg}_i^{out}$ indicates a dominant exporter, while a high value of ${deg}_i^{in}$ indicates a dominant importer. A dominant exporter has a high spreadability of a shock to its direct trade partners, while a dominant importer has a high susceptibility to a shock originating from its direct trade partners [20]. In

Table 3. Degree.

Name	Mathematical Formula	Interpretation in the Context of International Trade
Degree-Out	${deg}_i^{out}={\displaystyle \sum _{\begin{array}{c}j=1\\ j\ne i\end{array}}^N}{w}_{i\to j}$	The sum of exports from country$i$. A high value indicates a dominant exporter. A dominant exporter has a high spreadability of a shock to its direct trade partners.
Degree-In	${deg}_i^{in}={\displaystyle \sum _{\begin{array}{c}j=1\\ j\ne i\end{array}}^N}{w}_{j\to i}$	The sum of imports to country$i$. A high value indicates a dominant importer. A dominant importer has a high susceptibility to a shock originating from its direct trade partners.

, we present the relevant mathematical formulas for degree as well as the corresponding interpretation in the context of international trade.

2.3.2. Balance of Trade

The balance of trade${bal}_i$ of country $i$ is defined as the difference between the sum of its exports and the sum of its imports [35]. If it is positive (negative), then the country has a surplus (deficit) in terms of its trade flows. A surplus indicates a higher export dominance, while a deficit indicates a higher import dominance. Therefore, the surplus implies that the spreadability of a shock to a country’s direct trade partners is higher compared to this country’s susceptibility to a shock originating from its direct trade partners. On the contrary, the deficit implies the reverse. In

Table 4. Balance of trade.

Name	Mathematical Formula	Interpretation in the Context of International Trade
Balance of Trade	${bal}_i={deg}_i^{out}-{deg}_i^{in}$	If it is positive (negative), then the country$i$ has a trade surplus (deficit). A surplus implies that the spreadability of a shock to its direct trade partners is higher compared to the susceptibility to a shock originating from its direct trade partners. Deficit implies the reverse.

, we present the relevant mathematical formula for the balance of trade as well as its corresponding interpretation in the context of international trade.

2.3.3. Entropy

Concerning the vulnerability to economic shocks, it is useful to measure the degree of inequality in the distribution of trade flows. This can be achieved effectively using Shannon’s Entropy [18]. The concept of entropy, which comes from physics, quantifies the average information one can obtain when observing the probability distribution of the values of some variable. If most values are more or else equally probable (high diversification or high uncertainty) then entropy is high. On the contrary, if a few values are highly probable (low diversification or low uncertainty) then entropy is low. According to the relevant literature, the entropy of a country’s trade flows assesses its trade diversification with implications for its vulnerability to economic shocks [19,20]. This is distinguished as entropy-out for exports and entropy-in for imports. Entropy-out ${\mathcal{S}}_i^{out}$ assesses the diversification of export trade flows from country$i$ while entropy-in ${\mathcal{S}}_i^{in}$ assesses the diversification of import trade flows to country$i$. A high value of ${\mathcal{S}}_i^{out}$ indicates a diversified exporter while a high value of ${\mathcal{S}}_i^{in}$ indicates a diversified importer. As trade diversification increases, the vulnerability to supply/demand shocks decreases. Higher trade diversification ensures that there are multiple alternative trade flows, which are sufficient to prevent catastrophic scenarios. A diversified exporter has a lower vulnerability to demand shocks in the case where a direct export flow is disrupted. A diversified importer has a lower vulnerability to supply shocks in the case where a direct import flow is disrupted. In

Table 5. Entropy.

Name	Mathematical Formula	Interpretation in the Context of International Trade
Export Distribution	$p_{i\to j}^{out}={\displaystyle \frac{w_{i\to j}}{{\sum }_{\begin{array}{c}m=1\\ m\ne i\end{array}}^N{w}_{i\to m}}}={\displaystyle \frac{w_{i\to j}}{{deg}_i^{out}}}$	The probability distribution of export trade flows $w_{i\to j}$ from country $i$.
Import Distribution	$p_{j\to i}^{in}={\displaystyle \frac{w_{j\to i}}{{\sum }_{\begin{array}{c}m=1\\ m\ne i\end{array}}^N{w}_{m\to i}}}={\displaystyle \frac{w_{j\to i}}{{deg}_i^{in}}}$	The probability distribution of import trade flows $w_{j\to i}$ to country $i$.
Entropy-Out	${\mathcal{S}}_i^{out}=-{\displaystyle \sum _{\begin{array}{c}j=1\\ j\ne i\end{array}}^N}{p}_{i\to j}^{out}\cdot {log}_2\left(p_{i\to j}^{out}\right)$	The entropy of export trade flows $w_{i\to j}$ from country$i$. It assesses the diversification of the export trade flows$w_{i\to j}$. A high value indicates a diversified exporter. A diversified exporter has low vulnerability to demand shocks in the case where a direct export flow$w_{i\to j}$ is disrupted. Low value means that country $i$ has a portfolio of export trade flows that is mainly concentrated in certain trade partners.
Entropy-In	${\mathcal{S}}_i^{in}=-{\displaystyle \sum _{\begin{array}{c}j=1\\ j\ne i\end{array}}^N}{p}_{j\to i}^{in}\cdot {log}_2\left(p_{j\to i}^{in}\right)$	The entropy of import trade flows $w_{j\to i}$ to country$i$. It assesses the diversification of the import trade flows$w_{j\to i}$. A high value indicates a diversified importer. A diversified importer has low vulnerability to supply shocks in the case where a direct import flow$w_{j\to i}$ is disrupted. Low value means that country $i$ has a portfolio of import trade flows that is mainly concentrated in certain trade partners.

, we present the relevant mathematical formulas for the entropy of a country’s trade flows as well as its corresponding interpretation in the context of international trade. We note that the data used in this work, i.e., the trade flows$w_{i\to j}$, correspond to networks with no isolated countries. This means the following: for every year$t$ examined, there is no country with zero exports$\left({deg}_i^{out}=0\right)$ or zero imports$\left({deg}_i^{in}=0\right)$. In the case where some of the probabilities$p_{i\to j}^{out}$ and$p_{j\to i}^{in}$ of Table 5 are zero, the corresponding terms in the entropy formulae are also zero, namely: $0·{log}_2\left(0\right)=0$, following the well-known Theorem of Information Theory (Theorem 17.7.7 in [36]). We illustrate in Figure 2 representative scenarios to clarify the distinction between trade dominance (degree) versus trade diversification (entropy).

2.3.4. Closeness

In terms of shock propagation, it is necessary to address the following question: how close is a country to all other countries? For this purpose, we use the concept of closeness [16], which is distinguished into closeness-out for exports and closeness-in for imports. Previously discussed indicators, namely the degree, the balance of trade, and the entropy, consider only direct trade flows. It is also necessary to consider indirect trade flows with distant countries that have longer distances. Closeness-out ${close}_i^{out}$ assesses the spreadability of a shock to the whole network, considering not only direct but also indirect trade relationships. Similarly, closeness-in ${close}_i^{in}$ assesses the susceptibility to a shock originating from the whole network, considering not only direct but also indirect trade relationships. The main goal is to detect which countries have high closeness, or equivalently, short distances from all other countries. The distance $d_{i\to j}$ from country $i$ to country$j$ is defined as the length of the shortest directed path (geodesic) from country $i$ to country $j$. This is the lowest possible sum of weights which corresponds to a directed path from country $i$ to country $j$ [37]. If there is no such path, then the corresponding distance $d_{i\to j}$ is infinite and the corresponding directed network is not strongly connected. We note that the data used in this work, i.e., the trade flows$w_{i\to j}$, correspond only to strongly connected networks for every year$t$ examined. As the weights indicate the trade flows between the countries, the lowest possible sum of weights corresponds to a directed path with low trade dependence. This means that the shortest directed path corresponds to a trade line with low shock spreadability/conductance. This is of course problematic as Dijkstra’s algorithm for identifying the shortest directed paths cannot capture the desired critical trade lines which are characterized by high trade dependence and, therefore, high shock spreadability/conductance. The solution to this problem is to map the large trade flows $w_{i\to j}$ to low weights $r_{i\to j}$ indicating the resistance to shock propagation. This can be implemented by using any decreasing function. Such transformations of network weights are usual in the relevant literature [37,38]. For each year$t$, we identify the largest trade flow $w_{max}$ observed in the network, namely: $w_{max}=\underset{i\ne j}{\mathit{max}}\left\{w_{i\to j}\right\}$. We denote by $\mathcal{l}$ the ceiling of ${\log }_{10}\left(w_{max}\right)$, namely: $\mathcal{l}=⌈{\log }_{10}\left(w_{max}\right)⌉$ where $w_{max}\ge 1$. The ceiling function $⌈x⌉$ returns the smallest integer greater than or equal to $x$, for example, $⌈2.1⌉=3$, $⌈2.9⌉=3$, $⌈3⌉=3$. In

Table 6. The decreasing step function which maps high trade flows weights $w_{i\to j}$ to low shock resistance weights$r_{i\to j}$.

IF	THEN
$w_{i\to j}\in \left({10}^{\mathcal{l}-1}\right. , \left.{10}^{\mathcal{l}}\right]$	$r_{i\to j}=1$
$w_{i\to j}\in \left({10}^{\mathcal{l}-2}\right. , \left.{10}^{\mathcal{l}-1}\right]$	$r_{i\to j}=2$
$⋮$	$⋮$
$w_{i\to j}\in \left({10}^1\right. , \left.{10}^2\right]=\left(10\right. , \left.100\right]$	$r_{i\to j}=\mathcal{l}-1$
$w_{i\to j}\in \left({10}^0\right. , \left.{10}^1\right]=\left(1\right. , \left.10\right]$	$r_{i\to j}=\mathcal{l}$
$w_{i\to j}\in \left(0\right. , \left.{10}^0\right]=\left(0\right. , \left.1\right]$	$r_{i\to j}=\mathcal{l}+1$
$w_{i\to j}=0$	$r_{i\to j}=0$

, we present the decreasing step function that we used to map the large trade flows $w_{i\to j}$ to low resistance weights $r_{i\to j}$. Of course, if there is no connection, i.e., $w_{i\to j}=0$, then the corresponding resistance weight is also set equal to zero, i.e., $r_{i\to j}=0$. Considering the transformation of weights (Table 6), the revised shortest directed path corresponds now to the lowest possible sum of resistance weights $r_{i\to j},$ which, in turn, corresponds to a directed path with the highest trade dependence. This means that the revised shortest directed path (the path of least resistance for shock propagation) corresponds now to the trade line with the highest shock spreadability/conductance. Dijkstra’s algorithm for identifying the shortest directed paths solves now a minimization problem over networks with the resistance weights $r_{i\to j}$. We present a representative scenario (see Figure 3, taking into account Table 6 and

Table 7. Lengths of all directed paths of Figure 3. Although the directed path $A\to 2\to 3\to B$ involves two intermediary countries (country 2 and country 3), it is the revised shortest directed path (i.e., the path of least resistance for shock propagation), which corresponds to the most critical trade line with the highest shock spreadability/conductance. The key point here is that the impact of additional intermediary countries is relatively lower compared to the trade dependence (i.e., the volume of trade flow) between them.

Directed Path	Length of the Directed Path Based on:
	Trade Flow Weights ${\mathit{w}}_{\mathit{i}\to \mathit{j}}$	Shock Resistance Weights ${\mathit{r}}_{\mathit{i}\to \mathit{j}}$
$A\to B$	$w_{A\to B}=80$	$r_{A\to B}=4$
$A\to 1\to B$	$w_{A\to 1}+w_{1\to B}=$ $1200+2500=3700$	$r_{A\to 1}+r_{1\to B}=2+2=4$
$A\to 2\to 3\to B$	$w_{A\to 2}+w_{2\to 3}+w_{3\to B}=$ $\mathrm{11,000}+\mathrm{17,000}+\mathrm{80,000}=$ $\mathrm{108,000}$	$r_{A\to 2}+r_{2\to 3}+r_{3\to B}=1+1+1=3$

) to clarify the transformation of trade flow weights $w_{i\to j}$ to shock resistance weights $r_{i\to j}$.

In this paper, for closeness, we computed the harmonic closeness [39] instead of Freeman’s closeness [16]. Harmonic closeness is defined as the sum of the inverted distances $d_{i\to j}$, while Freeman’s closeness is defined as the inverted sum of the distances $d_{i\to j}$. Therefore, harmonic closeness ensures reliable results in the case where the network is not strongly connected [39]. However, the main reason for using harmonic closeness instead of Freeman’s closeness is that it has been recently used to simulate cascading failures and stress testing, such as the propagation of some forms of economic shock, with excellent results [40,41,42]. In

Table 8. Closeness.

Name	Mathematical Formula	Interpretation in the Context of International Trade
Distance	$d_{i\to j}=min\left\{r_{i\to m_1}+\cdots +r_{m_n\to j}\right\}$	The lowest possible sum of resistance weights from country $i$ to country$j$, where $m_1, \dots ,m_n$ are the intermediary countries (indirect trade partners). A low value of distance $d_{i\to j}$ indicates a low resistance to shock propagation from country $i$ (source) to country$j$ (target). This implies a high spreadability of shock from $i$ to$j$, or equivalently, a high susceptibility of $j$ to the shock originating from $i$.
Closeness-Out	${close}_i^{out}={\displaystyle \sum _{\begin{array}{c}j=1\\ j\ne i\end{array}}^N}{\displaystyle \frac{1}{d_{i\to j}}}$	The sum of inverted export distances $d_{i\to j}$ from country $i$. A high value indicates a close exporter. A close exporter has a high spreadability of a shock to the whole network, considering not only direct but also indirect trade relationships.
Closeness-In	${close}_i^{in}={\displaystyle \sum _{\begin{array}{c}j=1\\ j\ne i\end{array}}^N}{\displaystyle \frac{1}{d_{j\to i}}}$	The sum of inverted import distances $d_{j\to i}$ to country$i$. A high value indicates a close importer. A close importer has a high susceptibility to a shock originating from the whole network, considering not only direct but also indirect trade relationships.

, we present the relevant mathematical formulae for closeness (or, more precisely, harmonic closeness) as well as the corresponding interpretation in the context of international trade.

2.3.5. Betweenness

It is of great interest to detect which countries are the intermediary hubs in the ITN. The reason for this is the fact that these countries act as bridges that favor the further propagation of shocks from one region of the network to another. Betweenness ${bet}_i$ is defined as the sum of proportions of all shortest directed paths (geodesics) of the form $m\to \left(i\right)\to n$ between the pairs of two distinct countries $m$ and $n$, with $m\ne i$ and $n\ne i$ and $m\ne n$, that pass through the intermediary country $i$ [16]. We note that the shortest directed paths are identified based on shock resistance weights $r_{i\to j}$, following the same transformation of network weights (Table 6), as we did for the calculation of closeness. In

Table 9. Betweenness.

Name	Mathematical Formula	Interpretation in the Context of International Trade
Betweenness	${bet}_i={\displaystyle \sum _{\begin{array}{c}m=1\\ m\ne i\end{array}}^N}\left({\displaystyle \sum _{\begin{array}{c}n=1\\ n\ne i\\ n\ne m\end{array}}^N}{\displaystyle \frac{\left|{Geod}_{m\to \left(i\right)\to n}\right|}{\left|{Geod}_{m\to n}\right|}}\right)$	$\left|{Geod}_{m\to \left(i\right)\to n}\right|$ is the number of shortest directed paths (geodesics) $m\to \left(i\right)\to n$ from country $m$ to country$n$ that pass through the intermediary country$i$. $\left|{Geod}_{m\to n}\right|$ is the number of all shortest directed paths (geodesics) $m\to n$ from country $m$ to country$n$. A high value means that country$i$ plays the role of an intermediary hub, acting as a bridge that favors the further propagation of shocks to other trade clusters or regions of the ITN.

, we present the relevant mathematical formula for betweenness as well as the corresponding interpretation in the context of international trade. We note that the betweenness is not distinguished into exports (out) and imports (in) like the other indicators discussed previously.

2.3.6. Self-Weights

A novelty of this paper is that the self-weights $w_{ii}$ of the countries are discussed. Self-weight$w_{ii}$ indicates domestic production minus the exports of country $i$. That is, the value of goods and services produced and consumed domestically in country $i$ is considered (Section 2.2). Therefore, self-weight$w_{ii}$ can serve as an indicator of the intrinsic robustness of country $i$ in the event of an exogenous shock. More specifically:

• A high value of $w_{ii}$ due to relatively high domestic production indicates the high intrinsic robustness of country $i$ in the event of an exogenous shock (self-reliant country). Holding everything else constant (ceteris paribus), an exogenous shock which infects country $i$ will not largely affect its domestic market due to its own high production.
• A low value of $w_{ii}$ due to relatively low domestic production indicates a low intrinsic robustness of country $i$ in the event of an exogenous shock. Holding everything else constant (ceteris paribus), an exogenous shock which infects country $i$ will largely affect its domestic market due to its high dependence on foreign markets.

2.4. Indicators for the International Trade Network (Analysis at the Macro Level)

At the macro level, the following indicators are used, namely total trade flow, average path length, and centralization. We present below in detail the mathematical formula for each indicator as well as its interpretation in the context of international trade. This way of presenting the indicators is particularly useful for the reader to understand and interpret the results correctly, avoiding possible misinterpretations.

2.4.1. Total Trade Flow

The total trade flow $TTF$ of the network is the sum of all trade flows $w_{i\to j}$. A high value of $TTF$ indicates a high trade dependence among all countries, i.e., the countries are highly dependent on each other. This fact may contribute to a wider spread of shocks throughout the network, affecting more countries. In

Table 10. Total trade flow.

Name	Mathematical Formula	Interpretation in the Context of International Trade
Total Trade Flow	$TTF={\displaystyle \sum _{\begin{array}{c}i=1\end{array}}^N}\left({\displaystyle \sum _{\begin{array}{c}j=1\\ j\ne i\end{array}}^N}{w}_{i\to j}\right)$	The sum of all trade flows$w_{i\to j}$. It assesses the trade dependence among all countries, indicating the density of the ITN. A higher value may contribute to a wider spread of shocks throughout the network.

, we present the relevant mathematical formula for the total trade flow as well as the corresponding interpretation in the context of international trade.

2.4.2. Average Path Length

The average path length $APL$ of the network is the average of all distances $d_{i\to j}$ [17]. Lower values of $APL$ indicate the existence of trade lines that act as shortcuts in the network. In this way, the countries are closer to each other and, thus, the degree of separation among them is lower. This fact may contribute to the further propagation of shocks from one region of the network to another. We note that the distances $d_{i\to j}$ are identified and computed based on shock resistance weights $r_{i\to j}$, following the same transformation of network weights (Table 6) as we did for the computation of closeness and betweenness. In

Table 11. Average path length.

Name	Mathematical Formula	Interpretation in the Context of International Trade
Average Path Length	$APL={\displaystyle \frac{{\sum }_{\begin{array}{c}i=1\end{array}}^N\left({\sum }_{\begin{array}{c}j=1\\ j\ne i\end{array}}^N{d}_{i\to j}\right)}{N·\left(N-1\right)}}$	Average of all distances $d_{i\to j}$. It assesses the average trade distance between two countries, indicating the existence or non-existence of trade lines that act as “shortcuts” in the ITN. A lower value indicates that the countries are closer to each other. This fact may contribute to the further propagation of shocks from one region of the network to another.

, we present the relevant mathematical formula for the average path length as well as the corresponding interpretation in the context of international trade.

2.4.3. Centralization

The centralization of the network assesses how central the most central country $\xi$ of the entire network is in relation to all other countries $i$ [16]. If there are only a few countries in the network, which are much more central compared to the other countries, then the network is considered centralized, and thus, centralization is high. Centralization is the sum of the differences between the maximum value observed, i.e., the value of country $\xi$, and the values of all other countries $i$. In centralization, the reference value is the maximum value observed, while on the contrary, for the standard deviation for example, the reference value is the arithmetic mean. There are several mathematical formulae for centralization depending on the selected indicator examined. In

Table 12. Centralization.

Name	Mathematical Formula	Interpretation in the Context of International Trade
Degree-Out Centralization	${\mathbb{D}}^{out}={\displaystyle \sum _{i=1}^N}\left({deg}_{\xi }^{out}-{deg}_i^{out}\right)$ where ${deg}_{\xi }^{out}=\underset{i=1,\dots ,N}{\max }\left\{{deg}_i^{out}\right\}$	It assesses how dominant the most dominant exporter $\xi$ is in relation to all other countries $i$. A high value means that there are only a few countries that have a much higher spreadability of shock to their direct trade partners compared to the other countries.
Degree-In Centralization	${\mathbb{D}}^{in}={\displaystyle \sum _{i=1}^N}\left({deg}_{\xi }^{in}-{deg}_i^{in}\right)$ where ${deg}_{\xi }^{in}=\underset{i=1,\dots ,N}{\max }\left\{{deg}_i^{in}\right\}$	It assesses how dominant the most dominant importer $\xi$ is in relation to all other countries $i$. A high value means that there are only a few countries that have a much higher susceptibility to a shock originating from their direct trade partners compared to the other countries.
Entropy-Out Centralization	${\mathbb{S}}^{out}={\displaystyle \sum _{i=1}^N}\left({\mathcal{S}}_{\xi }^{out}-{\mathcal{S}}_i^{out}\right)$ where ${\mathcal{S}}_{\xi }^{out}=\underset{i=1,\dots ,N}{\max }\left\{{\mathcal{S}}_i^{out}\right\}$	It assesses how diversified the most diversified exporter $\xi$ is in relation to all other countries$i$. A high value means that there are only a few countries that have a much lower vulnerability to demand shocks (in the case where a direct export flow $w_{i\to j}$ is disrupted) compared to the other countries.
Entropy-In Centralization	${\mathbb{S}}^{in}={\displaystyle \sum _{i=1}^N}\left({\mathcal{S}}_{\xi }^{in}-{\mathcal{S}}_i^{in}\right)$ where ${\mathcal{S}}_{\xi }^{in}=\underset{i=1,\dots ,N}{\max }\left\{{\mathcal{S}}_i^{in}\right\}$	It assesses how diversified the most diversified importer$\xi$ is in relation to all other countries$i$. A high value means that there are only a few countries that have a much lower vulnerability to supply shocks (in the case where a direct import flow$w_{j\to i}$ is disrupted) compared to the other countries.
Closeness-Out Centralization	${\mathbb{C}}^{out}={\displaystyle \sum _{i=1}^N}\left({close}_{\xi }^{out}-{close}_i^{out}\right)$ where ${close}_{\xi }^{out}=\underset{i=1,\dots ,N}{\max }\left\{{close}_i^{out}\right\}$	It assesses how close the closest exporter $\xi$ is in relation to all other countries $i$. A high value means that there are only a few countries that have much higher spreadability of a shock to the whole network (considering not only direct but also indirect trade relationships) compared to the other countries.
Closeness-In Centralization	${\mathbb{C}}^{in}={\displaystyle \sum _{i=1}^N}\left({close}_{\xi }^{in}-{close}_i^{in}\right)$ where ${close}_{\xi }^{in}=\underset{i=1,\dots ,N}{\max }\left\{{close}_i^{in}\right\}$	It assesses how close the closest importer $\xi$ is in relation to all other countries $i$. A high value means that there are only a few countries that have much higher susceptibility to a shock originating from the whole network (considering not only direct but also indirect trade relationships) compared to the other countries.
Betweenness Centralization	$\mathbb{B}={\displaystyle \sum _{i=1}^N}\left({bet}_{\xi }-{bet}_i\right)$ where ${bet}_{\xi }=\underset{i=1,\dots ,N}{\max }\left\{{bet}_i\right\}$	It assesses how intermediary the most intermediary country $\xi$ is in relation to all other countries $i$. A high value means that there are only a few countries that clearly play the role of an intermediary hub (acting as a bridge between different trade clusters) compared to the other countries.
Gross Sales (Self-Weights) Centralization	$\mathbb{W}={\displaystyle \sum _{i=1}^N}\left(w_{\xi \xi }-w_{ii}\right)$ where $w_{\xi \xi }=\underset{i=1,\dots ,N}{\max }\left\{w_{ii}\right\}$	It assesses how self-reliant the most self-reliant country $\xi$ is in relation to all other countries $i$. A high value means that there are only a few countries that have much higher intrinsic robustness to exogenous shocks compared to the other countries.

, we present the relevant mathematical formula of centralization for degree, entropy, closeness, betweenness, and self-weights, as well as the corresponding interpretation in the context of international trade. Note that we did not use the normalized version of centralization, i.e., the denominator was omitted [16,43]. In this way, the results were captured in a clearer way. In the present work, omitting the denominator was not a problem for the comparison of the results. The reason for this is that the number of countries (nodes) was always the same, namely$N=138$, for all the years examined from $t=2006$ to$t=2018$. Thus, the denominator was the same for all years.

3. Results

3.1. Results for the Countries

We present below the results for the countries (micro level) in terms of the indicators presented in Section 2.3. Regarding degree-out (Table 3), we observe from Figure 4a that China, the USA, and Germany are the three most dominant exporters. The distances between them have increased over time, with China being a significantly more dominant exporter compared to Germany since 2010. China’s leading role in exports is related to (a) its position in global manufacturing, producing a variety of products with low costs, (b) its trade agreements, and (c) its general export-oriented mentality, consistently supported by the government. The leading role of the USA in exports can be attributed to its high-value-added goods and services, namely manufacturing, pharmaceuticals, aerospace, financial services, etc. Regarding degree-in (Table 3), we observe from Figure 4b that the USA is by far the most dominant importer, while China experienced a significant increase in its import dominance from 2006 to 2018. The leading position of the USA in imports can be attributed to (a) its high domestic demand, (b) high disposable income, (c) high GDP, (d) its consumer-driven market, and (e) its participation in global value chains with a high demand for intermediate products. For China, the high level of imports is sustained by the need for raw materials and intermediate goods to support its export-driven manufacturing economy, meeting the domestic demand for a large population.

Remark 1. 

Shock spreaders are also shock-susceptible. China, the USA, and Germany are at the top as exporters (Figure 4a) as well as importers (Figure 4b). Therefore, we may conclude that high shock spreadability comes with high shock susceptibility, as assessed based on their direct trade relationships (Table 3). The countries that follow in the ranks—namely Japan, the UK, and France—are also present as dominant exporters (Figure 4a) as well as dominant importers (Figure 4b). Hence, our conclusion is further supported. It is also worth mentioning that the impact of global crises, namely the global financial crisis of 2008 [44] and, to a lesser extent, the global fall in commodity prices of 2015 [45], is evident with sudden drops in exports (Figure 4a) and imports (Figure 4b).

Remark 2. 

China can act more as a shock spreader than a shock receiver, while for the USA, the opposite is true. Regarding the balance of trade (Table 4), we observe from Figure 4c that China has by far the largest trade surplus. Therefore, a shock originating in China can much more easily spread to its direct trade partners rather than the opposite. In other words, China can act more as a shock spreader than a shock receiver. The same is also true for Germany and Japan, which significantly increased their trade surplus from 2006 to 2018. On the other hand, Russia reduced its trade surplus to nearly zero during these years. The surplus of China is constantly and by far the highest because of its export-oriented trade policies. From 2006, Germany increased its surplus because of the high demand for German exports, coupled with constrained imports resulting from limited wage growth and domestic consumption. On the contrary, Russia reduced its surplus because of declining oil prices and economic constraints, which resulted in a decline in the demand and the value of its exports. A key reason for Russia’s decrease in the surplus is the sanctions that were imposed on Russia by numerous countries around the world after the 2014 annexation of the Crimean Peninsula. Regarding trade deficit (Table 4), we observe from Figure 4d that the USA and Hong Kong have the highest deficit. Hence, we conclude that while China can act more as a shock spreader than a shock receiver, for the USA, the opposite is true. The deficit of the USA was by far the highest in 2006, and from then, it drastically decreased to half until the global financial crisis of 2008 due to the depreciation of the US dollar, which led to higher import costs and an increased demand for exports. More specifically, the USA was less reliant on imported oil, and the US dollar was weaker during the early 2000s after the introduction of the Euro. This situation boosted exports. Also, tight credit after the global financial crisis of 2008 led consumers to spend much less. Hong Kong had the opposite trend, increasing its trade deficit from the global financial crisis of 2008. In terms of exports, the disruptions in Asia–Pacific trade decreased the export flows of Hong Kong, given its role as a re-export hub. In terms of imports, increased public spending to support the economy led to higher imports. India also increased its trade deficit in 2006. In terms of exports, the high tariffs policy and the depreciation of its currency, the rupee, led India to experience slower export growth. In terms of imports, India increased its dependence on electronic goods, and the rising global oil prices increased value of its imports.

Remark 3. 

Russia, India, and Germany have consistently the lowest vulnerability to possible shocks. Regarding entropy (Table 5), we found that two BRICS countries, Russia and India, as well as Germany, are consistently the most diversified countries in terms of exports (Figure 5a) and imports (Figure 5b). This fact suggests that these countries manage to have low vulnerability to possible demand or supply shocks. This has been achieved thanks to specific trade policies. For example, Russia established long-term supply contracts for its energy exports, while India is involved in trade alliances that aim to mitigate geopolitical risks. Greece is also an interesting case, as from Figure 5a, we observe that it has been significantly shielded against possible demand shocks during all these years by dramatically increasing its export diversification, eventually reaching the level of Russia. This was achieved due to the implementation of export-oriented reforms (e.g., the simplification of export procedures and reduction in bureaucratic barriers) and the transition toward higher-value exports (e.g., technology, renewable energy, and pharmaceuticals). Regarding China and the USA, we can observe from Figure 5a that China started like Greece with low diversification as an exporter in 2006, and from then, it managed to eventually reach the level of the USA in 2018. On the other hand, the USA has not increased its export diversification since 2006. Regarding imports, we observe from Figure 5b that China overtook the USA’s import diversification after the global financial crisis of 2008, increasing this gap until 2018.

Remark 4. 

High susceptibility does not necessarily imply high vulnerability. Germany, in addition to its trade dominance (high degree, Figure 4a,b), is also highly diversified (high entropy, Figure 5). Hence, we conclude that trade dominance may be achieved through high diversification. An interesting implication of this is that Germany’s high susceptibility (high degree-in, Figure 4b) does not lead to high vulnerability to supply shocks (high entropy-in, Figure 5b). In other words, high susceptibility does not necessarily imply high vulnerability. Indeed, susceptibility is about being infected, while vulnerability is about being fragile. The above conclusion is further supported by China, which is highly susceptible to shocks (high degree-in, Figure 4b), especially after 2011, but at the same time not vulnerable to supply shocks (high entropy-in, Figure 5b).

Remark 5. 

Trade dominance and trade diversification do not necessarily go together. By comparing Figure 4a,b (degree) with Figure 5 (entropy), we conclude that, in general, the most dominant countries are not always the most diversified, and conversely, the most diversified countries are not always the most dominant. We remind the reader that in Figure 2, we provide a useful visualization of four representative scenarios to clarify the distinction between trade dominance (degree, Table 3) versus trade diversification (Entropy, Table 5).

Remark 6. 

The Russia–Ukraine conflict forced Ukraine to diversify both its exports and imports, aiming to lower its vulnerability to possible shocks. From the start of the Russia–Ukraine conflict in 2013–2014, due to the annexation of Crimea by Russia [46], Ukraine significantly increased its diversification as an exporter (Figure 5a), while on the other hand, the export diversification of Russia remained almost the same. One key reason for Ukraine’s increase in export diversification was the implementation of the EU–Ukraine Association Agreement, which includes the Deep and Comprehensive Free Trade Area (DCFTA) [47]. Similarly, in terms of imports, Ukraine already significantly increased its diversification before 2013–2014 (Figure 5b), while on the other hand, Russia experienced a decrease after 2015. Ukraine’s increase in import diversification was due to the above agreement, which reduced tariffs and aligned Ukrainian standards with EU norms. Therefore, we may conclude that the Russia–Ukraine conflict forced Ukraine to diversify both its exports and imports, aiming to lower its vulnerability to possible demand or supply shocks.

Remark 7. 

China, the USA, and Germany are shock spreaders and shock-susceptible, even when indirect trade relationships are considered (“close exporters” and “close importers”). Regarding closeness (Table 8), we observe by comparing Figure 6 (closeness) with Figure 4a,b (degree) that China, the USA, and Germany are shock spreaders (dominant exporters) and shock susceptible (dominant importers), even when indirect trade relationships are considered. The countries that follow in the ranks—namely Japan and the UK—are also present, not only in Figure 6 (closeness) but also in Figure 4a,b (degree). Therefore, we may conclude that high shock spreadability comes with high shock susceptibility, as assessed based on not only direct (degree, Table 3) but also indirect (closeness, Table 8) trade relationships. This finding generalizes the previous result (Remark 1) which was limited by considering only direct trade relationships. The reason behind this finding is that the top countries such as China, the USA, and Germany, as well as the countries that follow in the ranks—namely Japan and the UK—have direct trade relationships with almost all the countries considered in the network. Furthermore, the strength of these direct trade relationships is not negligible in the sense that trade dependence, i.e., the volume of trade flow between the countries, is noticeable. Therefore, the impact of indirect trade relationships when calculating closeness is weak. That is why the same countries, except for France, are present with similar pattern in time in Figure 6 (closeness) and in Figure 4a,b (degree).

Remark 8. 

China has become the most critical “bridge” in the International Trade Network, forming a trade bipolarity with the US. Regarding betweenness (Table 9), we observe from Figure 7a that China has significantly strengthened its role as an intermediary hub, acting as a “bridge” between different trade clusters in the ITN. This happened because China managed to increase its bilateral trade agreements with other regions, continents and markets of the ITN [48]. On the other hand, the USA lost its leading role as a critical “bridge” in the ITN, which it maintained until 2013. This was due to the absence of significant EU-ASIA trade agreements and its growing protectionism. We emphasize the following two points, regarding the “bridge” role of countries in the trade network: First, China was favored from the global financial crisis of 2008, while on the contrary, the US and Germany had clear damage. Germany fell to third place, while China rose to second place. Second, the US and China were the only countries that acquired a much stronger “bridge” role in the network compared to the other countries. This led to the formation of a clear US–China bipolarity in terms of the role of the intermediary hub in the trade network. It is interesting to note that the large gap between the USA and China in 2006 closed in just 8 years, namely in 2014–2015, when the global fall in commodity prices took place. In 2017, after the global commodity prices fall and the Chinese stock market crash, China became the most critical “bridge”. However, despite the USA’s decline, it is still one of the most important crossroads in the ITN. In general, China and the USA are by far the top two countries of high betweenness that most favor the further propagation of shocks to other trade clusters, regions, and markets of the ITN. The increased reliance on just these two countries as critical trade intermediaries subsequently led to geopolitical tensions, such as the USA–China trade war [49]. Based on the above, we conclude that betweenness could serve as a leading indicator, forewarning of potential upcoming geopolitical tensions. The forewarning role of betweenness has also been confirmed in the context of terrorism [50,51,52,53].

Remark 9. 

The USA has constantly and by far the highest intrinsic robustness to exogenous shocks, with China closing the gap quickly. Regarding self-weights (Section 2.3.6), we observe from Figure 7b that the intrinsic robustness of the USA to exogenous shocks was only temporarily affected by the global financial crisis of 2008, indicating that the USA is constantly and by far the most self-reliant country. As for China, its intrinsic robustness to exogenous shocks has risen continuously since 2006. More specifically, China managed to climb to the second most self-reliant country as early as 2010. The main reason for this is that China has become the world’s top manufacturer in recent years. We would like to highlight the fact that the rising intrinsic robustness of China was unaffected by the global financial crisis of 2008. While China is quickly closing the gap with the USA, on the other hand, Japan and Germany, as well as other countries, are struggling to maintain their intrinsic level of robustness to exogenous shocks. The USA and China hold the upper hand, while the rest of the countries follow at a distance. As the US–China trade bipolarity is also emphatically present for betweenness (Figure 7a), we conclude that an underlying causal relationship between the intrinsic robustness (self-weight) of a country and its network position (betweenness) may exist. In other words, countries with high intrinsic robustness may serve as driving nodes that occupy key network positions and, thus, control international trade flows. Of course, a deeper investigation of this hypothesis is needed, which is left for the future, as it is not in the scope of this paper.

3.2. Results for the International Trade Network

The results in Section 3.1 offer valuable insights, revealing the trade dynamics of each country in relation to other countries. However, to have a comprehensive view of international trade, it is also necessary to examine the dynamics of the entire ITN. Therefore, we present the results for the entire network below (at the macro level) in terms of the indicators presented in Section 2.4.

Remark 10. 

The impact of global crises is evident in the total trade flow as well as in the average distance between the countries. We observe from Figure 8a that during global crises, namely the global financial crisis of 2008 and the fall in global commodity prices of 2015, the total trade flow (Table 10) of the entire network decreased dramatically. This means that the trade dependence among the countries decreased as countries tried to mitigate the further spread of shocks. The corresponding pattern is observed in Figure 8b for the average path length (Table 11). More specifically, during these two global crises, we observe that the average distance between the countries increased significantly as countries tried to increase their distance from “infected” countries. Considering all the above points, by observing Figure 8, we may conclude the following: from a macroscopic perspective, both macro indicators, namely the total trade flow and the average path length, indicated a strong “reaction” of the entire network to these two global crises, as it tried to maintain its functionality and mitigate the further spread of shocks. Starting from the micro level, the countries revised their trade dependence with the other countries and increased their distance from the “infected” countries. This micro-behavior led to several macro-effects, such as the decline in the total trade flow, which means that the ITN became sparser, as well as the rise of the average distance between the countries. Such a phenomenon can be explained by the principles of risk management and economic externalities. When a shock hits one country, other countries may impose trade restrictions to avoid possible spillover effects. This reduction in trade dependence is a strong indicator that countries struggle to minimize systemic risk. This demonstrates the adaptability of the economic system, where trade routes are lengthened in response to shocks as a form of self-protection to maintain international trade stability.

Remark 11. 

The average distance in international trade is shrinking, boosting globalization. Despite the increase in the average path length during global crises (Remark 10), we observe from Figure 8b that the trend from 2006 to 2018 is downward, boosting globalization. The average distance in international trade has shrunk due to many reasons, including the rise in e-commerce and digital transactions, making international trade easier. Another major reason that contributed to this “death of distance” in international trade is the advancement of modern transportation, with logistics enabling faster and more cost-effective delivery. In general, technological advances in transportation and communication bridge distant geographical locations, enhancing economic integration.

Remark 12. 

International trade is becoming increasingly oligopolistic. The impact of global crises, namely the global financial crisis of 2008 and, to a lesser extent, the fall in global commodity prices of 2015, is evident in the centralization of degree (Figure 9a) in both exports and imports. However, the trend after the global financial crisis of 2008 was upward, with degree-out centralization converging to degree-in centralization. This means that the inequality of export dominance increases, converging to the inequality of import dominance. In other words, the highest values of shock spreadability are concentrated in fewer and fewer countries-sellers of the ITN (Table 12). This finding is consistent with Figure 4a, where only three countries—namely China, the USA, and Germany—are the leading sellers, forming an increasingly oligopolistic structure in the ITN. This growing oligopolistic structure, which characterizes the ITN, can be explained by economies of scale. More specifically, large economies can develop strong production capabilities, diversified trade flows, and acquire strategic roles in global value chains [19]. These factors allow leading economies to strengthen their leading positions during crises and attract disproportionate trade flows. This behavior is like preferential attachment, which implements the aphorism “the rich get richer”, forming a cumulative advantage [54].

Remark 13. 

The inequality in trade diversification is not conditioned by the inequality in trade dominance. Unlike the degree centralization (Figure 9a), the entropy centralization (Figure 9b) of the network was not influenced significantly by the global financial crisis of 2008 or the fall in global commodity prices of 2015. From 2006 to 2012, the entropy-out centralization decreased, converging to the entropy-in centralization, while from 2012, the gap between them grew again (Figure 9b). This is a completely different pattern compared to degree centralization, where degree-out centralization converged to degree-in centralization after the global financial crisis of 2008. All the above imply that the inequality in trade diversification (Figure 9b) is not conditioned by the inequality in trade dominance (Figure 9a). More specifically, countries adopt symmetric trade policies in import–export intensity (Figure 9a) but asymmetric trade policies in import–export diversification (Figure 9b).

Remark 14. 

International trade is becoming increasingly oligopolistic, even when indirect trade relationships are considered (“Deep Oligopoly”). We observe from Figure 9c that closeness-out centralization increases, especially after 2013. This means that the inequality of countries in terms of their shock spreadability to the whole network increases (Table 12). In other words, the highest values of shock spreadability to the whole network are concentrated in fewer and fewer countries-sellers of the network (Table 12). Therefore, international trade becomes increasingly oligopolistic, even when indirect trade relationships are considered. This growing “Deep Oligopoly” is consistent with Figure 6a, where only three countries—namely China, the USA, and Germany—are the leading shock propagators to the whole network (Table 8). This finding generalizes Remark 12, which was limited by considering only direct trade relationships. On the other hand, closeness-in centralization decreases, especially after the global financial crisis of 2008 (Figure 9c). This fact implies that the inequality of countries in terms of their susceptibility to a shock originating from the whole network decreases (Table 12). This may be understandable as a “reaction” of the whole network to this economic shock occurred as it tried to maintain its functionality and mitigate the further spread of shocks (Remark 10). More specifically, no country wanted to be too close to other countries due to the fear of being “infected”.

Remark 15. 

International trade is increasingly dependent on just two critical “bridges”, namely China and the USA. We observe from Figure 10a that betweenness centralization decreases up to 2015 and then increases again. This means the following: from 2006 to 2015, the distribution of betweenness values across countries became less and less unequal, while from 2015 to 2018, the highest values of betweenness were concentrated in fewer countries again. This finding is consistent with Figure 7a, where in 2006, only the USA was the most critical “bridge” in the ITN. From 2006 to 2015, China significantly strengthened its role as an intermediary hub, resulting in a less unequal distribution of betweenness values across countries. From 2015 to 2018, China and the USA were by far the top two countries with the highest values of betweenness compared to the other countries.

Remark 16. 

After a significant decline due to the 2008 global financial crisis, the inequality of countries’ intrinsic robustness to exogenous shocks is increasing rapidly, with the USA and China being by far the most self-reliant countries. We observe from Figure 10b that the impact of the global financial crisis of 2008 is evident in the centralization of self-weights. However, the trend after the global financial crisis of 2008 was strongly upward. This means that the inequality of countries’ intrinsic robustness to exogenous shocks is increasing rapidly (Table 12). This finding is consistent with Figure 7b, as the highest self-weights were concentrated in only two countries—namely the USA and China—with all other countries being far behind.

4. Conclusions

We modeled and studied international trade from 2006 to 2018 as a weighted, directed network with self-weights. The nodes represent countries, and the directed weights represent the trade flows between them. We consider the self-weight of each country as an indicator of its intrinsic robustness to exogenous shocks.

By considering the indirect trade relations, we found that the main structural role that led to the emergence of the US–China trade bipolarity is that of the intermediary hub that acts as a “bridge” between different trade clusters. The US and China occupied key network positions of high betweenness centrality as early as 2010 (Figure 7a, Remark 8). The US was the leading intermediary hub from the first years of our analysis, while China was established as a key player after some years. As international trade became increasingly dependent on only these two intermediary trade hubs, this fact led to geopolitical tensions such as the US–China trade war. Therefore, betweenness centrality could serve as a structural indicator, forewarning of possible upcoming geopolitical tensions. The fall of previously dominant EU countries, such as Germany, further contributed to the emergence of the US–China trade bipolarity. The same is also true for emerging economies, such as India, because they did not rise in the ranks during the time period under consideration. By considering the self-weights, we found again a strong US–China bipolarity, as a race in terms of their intrinsic robustness to exogenous shocks, is more than evident (Figure 7b, Remark 9). It is also interesting that the US and China are not only the top shock spreaders but also the most susceptible to shocks (Remarks 1 and 7). However, China can act more as a shock spreader than a shock receiver, while for the USA, the opposite is true (Remark 2). Regarding the Russia–Ukraine conflict, we found that Ukraine was forced to diversify both its exports and imports, aiming to lower its vulnerability to possible shocks (Remark 6). This is a new finding that highlights the impact of geopolitics on the geometry of global trade. Finally, we found that international trade is becoming increasingly oligopolistic, even when indirect trade relationships are taken into account, thus indicating that a “deep oligopoly” has formed (Figure 9c, Remark 14).

We would like to emphasize the two main novelties of our methodology, distinguishing our approach from other existing network-based trade studies. First, closeness and betweenness are computed based on shock resistance weights $r_{i\to j}$ which are identified based on a novel decreasing step function that maps large trade flows $w_{i\to j}$ to low resistance weights $r_{i\to j}$ (Section 2.3.4 and Section 2.3.5). The advantage of this step function is that the weights $r_{i\to j}$ are clearly distinguishable, even for large values of $w_{i\to j}$. This high discrimination capability for large values of $w_{i\to j}$ cannot be achieved with conventional transformations, such as the ${\displaystyle \frac{1}{w_{i\to j}}}$ [49,55]. We highlight that it is the use of our novel decreasing step function that led us to reveal the new interesting results for betweenness (Figure 7a, Remark 8) and closeness (Figure 9c, Remark 14). Second, to the best of our knowledge, this is the first time that the self-weights of countries have been discussed as an indicator of their intrinsic robustness to exogenous shocks with new interesting results (Figure 7b, Remark 9).

Network Science can offer new perspectives and practical implications in trade policies, risk mitigation strategies, and international negotiations. Regarding trade policies, the network position of each country can effectively inform policymakers about the key strengths and weaknesses of each country, as well as the potential opportunities and threats as they arise from the dependencies of each country on other direct or indirect trade partners. This network-based SWOT analysis reveals critical information that must be taken into account when formulating informed decisions on complex tariff policies and trade agreements. More specifically, in this work, the key structural role of betweenness (Figure 7a, Remark 8) and self-weights (Figure 7b, Remark 9) was revealed. This novel finding may lead policymakers to design policies that aim to improve the position of desired countries with respect to these key structural indicators. Such trade policies may mitigate the emergent US–China trade bipolarity. This is a clear, practical implication of our findings, taking into account the high ranking of the US and China for betweenness and self-weights. Regarding risk mitigation strategies, entropy is a useful tool that can effectively inform whether a country is highly dependent on specific trade partners. Entropy can provide information on which trade flows should be further diversified to achieve lower vulnerability to potential demand or supply shocks. Regarding international negotiations, the analysis of the structure of the ITN can effectively inform about the systemic impact of trade policies or tariffs on interstate alliances and trade agreements.

Regarding future work, it would be valuable to examine whether there is a causal relationship between the self-weights of countries and their network positions (e.g., degree or betweenness). In other words, is production the cause of a country’s position in the network or vice versa? This causal relationship can be detected using Granger Causality or Transfer Entropy. In addition, a dynamic agent-based model is also needed to simulate selected “what-if” scenarios for shock propagation and changes to network structure (network co-evolution, [56,57]), taking into account the self-weights (production) of the countries.