4.1 Data Sources and Scope

The analytical framework used in TERRA is based on official European Union statistics on international trade in goods, collected by Member States using standardized methods, and shared through the Eurostat COMEXT database.Footnote ³ These data provide a consistent, reliable basis for tracking trade dynamics across EU countries, ensuring comparability over time and between trading partners.

COMEXT provides highly disaggregated monthly data on international trade relationships. This includes information on trade values (in Euros), quantities (in kilograms), product classifications, partner countries and territories, trade flows (imports and exports), modes of transport, and types of transaction.

This detailed dataset is extremely valuable for analysing short-term disruptions and long-term structural changes in international trade.

Within TERRA, two main COMEXT datasets are employed:

• • The PRODUCT dataset, providing monthly and annual records of trade flows between EU Member States and their international partners, reported in terms of value and quantity and based on internationally standardized product classifications, including the Combined Nomenclature (CN), the Standard International Trade Classification (SITC), and the Classification of Products by Activity (CPA).Footnote ⁴ This dataset covers both intra-EU and extra-EU trade, thereby allowing a comprehensive assessment of European trade relations.

• • The TRANSPORT_NSTR dataset, providing detailed records of extra-EU trade flows disaggregated by mode of transport and classified according to the Standard Goods Classification for Transport Statistics (NSTR). Its hierarchical structure supports multilevel analysis, ranging from broad product aggregates to highly granular categories. This dataset currently refers only to extra-EU trade, as the reporting of transport mode for intra-EU flows is optional and therefore not systematically collected.

The features and coverage of the PRODUCT and TRANSPORT_NSTR datasets shape the analyses and visualizations that can be performed in TERRA. These two datasets differ in coverage and classification. The PRODUCT dataset details trade values and quantities for both intra-EU (EU–EU) and extra-EU (EU–extra-EU) flows, using CPA-based product categories. Conversely, the TRANSPORT_NSTR dataset relies on the NSTR classification and focuses primarily on extra-EU trade with a detailed breakdown by mode of transport. Reporting intra-EU trade by mode of transport in TRANSPORT_NSTR is optional, leading to inconsistencies.

These structural differences affect network representation and analysis. PRODUCT data provide a comprehensive overview of EU trade relationships, whereas TRANSPORT_NSTR offers a more granular perspective on logistics patterns, albeit with limited intra-EU coverage. Accordingly, TERRA treats the two datasets as complementary rather than interchangeable.

To understand how TERRA’s network-based representation is built, it is first necessary to clarify the underlying structures of the two datasets. Their core schema includes a declarant country, a partner country, an indication of the trade flow (import or export), the traded product, and the quantity exchanged, with additional attributes such as trade value, month, mode of transport, and others.

To translate this tabular structure into a network representation, an explicit modelling assumption is adopted: the relationship between two trading countries is assumed to follow the direction of the traded good. This choice guarantees an unambiguous interpretation of edge direction within the network. As shown in Figure 1a, which provides a simplified example involving only two countries, the direction of the edge is from the declarant country to the partner country for exports and from the partner country to the declarant country for imports. This convention directly reflects the principle that relationships are driven by the physical movement of goods.

Figure 1a.

Simplified example of the network representation adopted in TERRA.

Figure 1a Long description

Three tables and corresponding network diagrams illustrating import, export and average data between IT and DE. The first table, labeled ′Import (Comext data)′, lists ′Declarant′, ′Part ner′, ′Flow′ and ′Qty′. IT declares to DE with a flow of ′I′ and a quantity of 100. DE declares to IT with a flow of ′I′ and a quantity of 80. The network diagram shows IT and DE with arrows indicating flows of 100 and 80. The second table, labeled ′Export (Comext data)′, shows IT declaring to DE with a flow of ′E′ and a quantity of 50 and DE declaring to IT with a flow of ′E′ and a quantity of 30. The corresponding network diagram illustrates these flows. The third table, labeled ′Average (calculated data)′, shows IT to DE with a flow of ′I/E′ and a calculated quantity of 65 and DE to IT with a flow of ′I/E′ and a calculated quantity of 60. The network diagram reflects these average flows with calculated values shown as (50 plus 80) divided by 2 equals 65 and (30 plus 100) divided by 2 equals 60.

Notes: Export declarations generate edges from the declarant country to the partner country, while import declarations generate edges in the opposite direction. When both declarations are available for the same bilateral relationship, an additional derived flow (Average) is computed as the arithmetic mean of the corresponding import and export values and used as the reference edge weight in the network.

Figure 1b.

Graphical representation of TRANSPORT_NSTR and PRODUCT data flows.

Figure 1b Long description

Two column headings appear at the top, ′PRODUCT′ on the left and ′TRANSPORT NSTR′ on the right. Under ′PRODUCT′ the subtitle reads ′CPA 2.1 classification without transport info′ and under ′TRANSPORT NSTR′ the subtitle reads ′NSTR classification with transport info′. Along the far left side, three row labels read ′Import′, ′Export′ and ′Average′. In the first row, the Product diagram shows two dashed ovals, each surrounding a small set of circular nodes, with the text ′EU′ near the left cluster and ′Extra EU′ near the right cluster; several solid lines connect nodes within each dashed oval and at least one line runs between the two dashed ovals. In the same row, the Transport Hubs diagram repeats the same visible text labels ′EU′ and ′Extra EU′ with two dashed ovals around node clusters and solid lines connecting nodes within clusters and between the two clusters. In the second row labeled ′Expport′, the Product diagram again contains the labels ′EU′ and ′Extra EU′ beside two dashed ovals enclosing node clusters, with solid lines linking multiple nodes inside each oval and at least one line linking across the gap between the two ovals; the Transport NSTR diagram in this row repeats the same two dashed ovals and the same labels ′EU′ and ′Extra EU′, with a similar pattern of solid connecting lines among the nodes. In the third row labeled ′Average′, the Product diagram shows the same two dashed ovals and the same labels ′EU′ and ′Extra EU′, with a denser set of solid lines among the nodes and multiple lines spanning between the two dashed ovals; the Transport NSTR diagram in this row also shows ′EU′ and ′Extra EU′ with two dashed ovals around node clusters and several solid lines connecting nodes within and between the clusters. No axis line, tick marks, numeric values, or units are visible anywhere in the figure.

Furthermore, since countries prepare trade declarations independently, discrepancies might arise in reported flows. Specifically, an export declaration from one country may not match the corresponding import declaration from its trading partner due to differences in valuation methods, timing, coverage, or reporting practices. To address these discrepancies, TERRA defines an additional derived trade flow, called average, which is created by combining available import and export declarations. Instead of selecting one declaration over the other, the network representation includes both flows and assigns each directed edge a weight equal to the average of the import and export-based measurements.

In this approach, import and export remain the original reported flows, while average shows a reconciled bilateral estimate of trade intensity between two countries and serves as the reference flow for network-based analysis in TERRA. This modelling choice provides a more comprehensive and stable view of trade relationships while preserving the directionality of goods’ physical movement.

Figure 1b provides a schematic overview of the network representations built in TERRA using the PRODUCT and TRANSPORT_NSTR datasets. In both cases, countries are modelled as nodes, and trade relationships are represented as directed edges with edge weights indicating the exchange strength based on the selected flow type (import, export, or average).

The left panel displays the network based on PRODUCT data, including both intra-EU and extra-EU trade, and is organized by product classifications. This representation offers a comprehensive overview of European trade relationships, including exchanges within the EU single market.

The right panel shows the network built from TRANSPORT_NSTR data, which focuses on extra-EU trade and provides detailed information by distinguishing flows according to mode of transport. Since transport reporting for intra-EU trade is optional, this representation is limited to EU–extra-EU exchanges.

By comparing the two panels, Figure 1b shows how PRODUCT and TRANSPORT_NSTR offer different but related analytical views within TERRA: the former focusing on trade structure across products and partners, and the latter illustrating the logistical aspect of extra-EU trade flows.

4.2 Network Indicators

Building on the data structures described above, TERRA represents international trade as a weighted directed network, where nodes correspond to countries and directed edges indicate trade flows between them. Edge weights show the strength of exchange, measured in monetary terms (Euros) and based on COMEXT data. This modelling approach enables the analysis of trade relationships using standard tools from social network analysis (Wasserman and Faust, Reference Wasserman and Faust1994). The same analytical framework is applied to PRODUCT and TRANSPORT_NSTR data. In all cases, networks are built for a specific time and product category. Figure 2 illustrates an example of a trade network generated with TERRA for textile exports in January 2024, based on TRANSPORT_NSTR data.

Figure 2.

Trade network graph of textile product exports in January 2024.

Note: Edge thickness and colour are proportional to trade values (quantile-based), providing an immediate visual encoding of trade intensity.

For clarity, the visualization uses a percentile-based filter to display only the most relevant connections. This filtering does not affect the computation of network indicators. Each intra-EU exchange is documented as both an export and an import, enabling TERRA to analyse trade flows by direction or through an average measure. For visualization, the relative positions of countries within the network are computed using a force-directed layout based on the Spring Layout algorithm (Fruchterman and Reingold, Reference Fruchterman and Reingold1991). Although the absolute spatial placement of nodes has no intrinsic analytical meaning, this representation helps identify countries that occupy central positions or serve as bridges within the network. Edge thickness and colour are used to encode trade intensity when the network is sufficiently sparse, based on a quantile-based classification of edge weights; in denser configurations, a uniform styling is adopted to preserve readability.

Alongside the visualization, TERRA computes a set of network indicators to characterize both the overall structure of trade networks and the role of individual countries within them. Network density shows how connected the system is. It compares the number of trade links that actually exist with the number that could exist, providing a synthetic indication of overall interconnectedness. Density is defined as follows

(1)\begin{equation}D = \frac{L}{{N\left( {N - 1} \right)}}\end{equation}

where $L$ is the number of observed edges, $N$ is the number of nodes in the network, and $N\left( {N - 1} \right)$ is the maximum number of possible directed edges. The indicator ranges from 0 (no trade links) to 1 (a fully connected network). In Figure 2, its value is 0.05, indicating a sparse network in which only a small fraction of potential bilateral trade links is present.

At the node level, TERRA calculates a set of centrality measures, namely in-degree, out-degree, closeness, betweenness, and distinctiveness (Fronzetti Colladon and Naldi, Reference Fronzetti Colladon and Naldi2020; Wasserman and Faust, Reference Wasserman and Faust1994). To reflect the economic importance of trade relationships, these metrics are also calculated in weighted form, using trade values in Euros as weights for the connections.

In-degree centrality measures the number of a country’s import partners, capturing the node’s level of connectivity while ignoring the strength or intensity of those connections (2a). Its weighted version (2b) quantifies the total value of imports for a given good and time period. Formally, for a given country $i$, the weighted in-degree is given by

(2a)\begin{equation}{C_{in}}\left( i \right) = \sum\nolimits_j {{a_{ji}}} \end{equation}

(2b)\begin{equation}{C^w}_{in}\left( i \right) = \sum\nolimits_j {{w_{ji}}} \end{equation}

where $a_{ji}$ is 1 if there is a directed edge from node j to node i, and $w_{ji}$ is the weight of the edge connecting country $j$ to $i$.

Similarly, out-degree centrality (3a) measures the number of export partners, and its weighted version (3b) captures the total value of exports for a given good and time period

(3a)\begin{equation}{C_{out}}\left( i \right) = \mathop \sum \limits_j {a_{ij}}\end{equation}

(3b)\begin{equation}{C^w}_{out}\left( i \right) = {\sum\nolimits_j w _{ij}}\end{equation}

In our context, low in-degree centrality suggests that a country relies on a small number of suppliers, making it more exposed to supply disruptions, price shocks, or geopolitical tensions affecting those specific partners.

In the context of international trade networks, closeness centrality captures how easily a country can reach all other trading partners, either directly or through a small number of intermediaries. It is defined as

(4)\begin{equation}{C_{clo}}\left( i \right) = \frac{1}{{\sum\nolimits_{j \ne i} {d\left( {i,j} \right)} }}\end{equation}

where $d\left( {i,j} \right)$ denotes the length of the shortest trade path between country $i$ and country $j$ (Wasserman and Faust, Reference Wasserman and Faust1994). Higher closeness centrality indicates that a country is, on average, only a few trade steps away from all others. In import–export terms, this reflects a more central position in the global trading system, allowing the country to access markets and suppliers more efficiently and to adjust more rapidly to changes in trade patterns. Countries with hub-like roles typically exhibit higher closeness values, as they are embedded in dense trade corridors that shorten distances to the rest of the network (De Benedictis et al., Reference De Benedictis, Nenci, Santoni, Tajoli and Vicarelli2014).

Betweenness centrality measures the extent to which a country acts as an intermediary in trade relationships, capturing its brokerage power within the network. It is defined as

(5)\begin{equation}{C_{bet}}\left( i \right) = \sum\nolimits_{j \ne i \ne k} {\frac{{{\sigma _{jk}}\left( i \right)}}{{{\sigma _{jk}}}}} \end{equation}

where ${\sigma _{jk}}$ is the total number of shortest paths between countries $j$ and $k,$ while ${\sigma _{jk}}\left( i \right)$ is the number of those paths that pass through $i$. In a trade context, this metric highlights countries that play a pivotal role in connecting otherwise weakly linked regions or markets. High betweenness centrality indicates a strong intermediary position, implying greater capacity to facilitate, influence, or potentially disrupt trade flows. Such countries may serve as key transit hubs or strategic connectors, thereby exerting structural leverage over the circulation of goods across the network.

Traditional centrality measures, such as degree, assess the importance of nodes based on the number or magnitude of their direct connections, typically favouring highly connected hubs. Distinctiveness centrality captures a different dimension of importance by highlighting nodes that maintain ties with weakly connected and peripheral partners. In doing so, it emphasizes their role in linking marginal areas of the trade network and enhancing overall network cohesion. Among the five metrics proposed by Fronzetti Colladon and Naldi (Reference Fronzetti Colladon and Naldi2020), we chose weighted distinctiveness centrality

(6)\begin{equation}{C_{dis}}(i) = {\sum\nolimits_{j \ne i} w _{ij}}{\log}\frac{{n - 1}}{{k_j^\alpha }}\end{equation}

where ${k_j}$ is the degree of node $j$, ${w_{ij}}$ is the weight of the edge connecting nodes $i$ and $j$ (measured in trade value, euros), n is the total number of nodes in the network and $\alpha $ is a parameter typically set to one. Connections to highly connected nodes are penalized, while links to peripheral nodes are given greater weight. In the context of trade networks, this metric may help identify countries of strategic importance that act as intermediaries between the core and the periphery, a role that can become especially critical during periods of disruption or crisis.

A structural limitation of COMEXT data is the absence of information on trade flows between non-European countries (extra-EU to extra-EU), as the dataset is compiled from the perspective of European reporting nations. Consequently, the resulting trade network offers only a partial view of the global system, which may affect the interpretation and calculation of specific metrics, particularly those based on shortest paths or global connectivity, such as closeness, betweenness, and network density. To mitigate this limitation, TERRA allows extra-EU countries to be aggregated into a single node. This reduces potential distortions in the network structure, albeit at the cost of reduced geographical detail.

4.3 Time Series Analysis

While network analysis captures trade relations between countries at a specific point in time, TERRA highlights how these connections evolve. This longitudinal approach allows tracking changes in trade patterns, identifying shocks and subsequent adjustments, and assessing the persistence of bilateral relationships. To this end, TERRA manages a large set of time series detailing import and export flows between European countries and their trading partners, in monetary values (Euros) and physical quantities (kilograms). These series are available in absolute terms and as annual variations, allowing users to analyse both short-term fluctuations and long-term dynamics.

Within the dashboard, time series data are primarily used for exploratory and monitoring purposes. Interactive visualizations enable users to examine trends, level shifts, seasonal patterns, and other critical aspects of trade dynamics, alongside basic descriptive statistics to facilitate initial interpretation. This design emphasizes TERRA’s role as a monitoring tool rather than as a comprehensive econometric platform.

More advanced longitudinal analyses, particularly those focusing on the temporal evolution of network metrics, are supported through TERRA’s APIs and offline components. The APIs exposed by the framework allow researchers to retrieve time-indexed network indicators and to conduct customized analyses in external analytical environments. These include, for example, rotating leadership analysis (Fronzetti Colladon and Vestrelli, Reference Fronzetti Colladon and Vestrelli2025), which examines oscillations in countries’ centrality measures over time to capture shifts in trade roles and influence within the network.

These analytical capabilities are directly illustrated in the empirical applications presented in this paper. In the case studies on electricity trade during the COVID-19 pandemic and on weapons and ammunition trade during the Russia–Ukraine conflict, time series of network metrics such as degree and betweenness centrality are used to analyse how countries’ positions within trade networks evolve in response to major external shocks.

4.4 Constant Elasticity of Substitution Model

This subsection describes the structure of the Constant Elasticity of Substitution (CES) model, a standard framework in international economics widely used to analyse trade reallocation across alternative suppliers under counterfactual scenarios (Redding and Weinstein, Reference Redding and Weinstein2023). Within TERRA, this CES model is implemented exclusively in the offline analytical environmentFootnote ⁵ to perform stylized supply shock analyses and trade reallocation exercises that cannot be explored through the web-based dashboard alone (see Appendix B).

In line with the Armington (Reference Armington1969) assumption, the total imports of a given country are modelled as a CES aggregate of goods supplied by different countries, treated as imperfectly substitutable varieties differentiated by country of origin. Each supplier is associated with a distribution parameter ${\alpha _i}$, capturing its relative importance in the importing country’s market. These $\alpha $ parameter values are calibrated using baseline export volumes, so that the model reproduces observed trade patterns under normal, undisturbed conditions and accurately reflects the underlying structure of international trade.

The elasticity of substitution $\varepsilon $ plays a crucial role in the model, as it governs the degree to which imports from one supplier can be replaced by imports from another. Higher values of the $\varepsilon $ elasticity imply greater substitutability across suppliers; while lower values indicate more rigid trade relationships and limited scope for adjustment following a shock

(7)\begin{equation}Q=\left(\sum\nolimits_i\alpha_iq_i^{\left(\frac{\varepsilon-1}\varepsilon\right)}\right)^{\left(\frac\varepsilon{\varepsilon-1}\right)}\end{equation}

where ${q_i}$ denotes the quantity imported from supplier $i$; ${\alpha _i}$ is the distribution parameter calibrated on baseline quantities; $\varepsilon $ is the elasticity of substitution between suppliers, and $Q$ represents the aggregate import quantity. To simulate a stylized supply shock, a given supplier $k$ is removed from the choice set, defined as the set of exporting countries that are available to the importing country as potential sources of supply. Operationally, this is implemented by setting ${q_k} = 0$, thereby excluding supplier $k$ from the CES aggregation. The CES system is revaluated, and residual demand is reallocated among remaining suppliers according to their baseline market shares, relative prices, and the elasticity of substitution. This mechanism ensures a coherent and internally consistent reallocation of trade flows following a simulated shock, providing an illustrative representation of how import patterns may adjust when a supplier becomes unavailable.

5.1 Analysis of Electricity Supply Dynamics during the COVID-19 Pandemic

The COVID-19 pandemic represents a paradigmatic example of a global systemic shock, with documented effects on production, mobility, financial markets, and international trade (Baker et al., Reference Baker, Bloom, Davis and Terry2020; Guardabascio et al., Reference Guardabascio, Brogi and Benassi2023; Verschuur et al., Reference Verschuur, Koks and Hall2021). Beyond its direct health impact, the pandemic introduced unprecedented uncertainty into commodity markets, amplified volatility, and altered investment and trading behaviour, partly through mobility restrictions and government containment measures (Etienne et al., Reference Etienne, Irwin and Garcia2015; Lawson et al., Reference Lawson, Alam and Etienne2021).

Electricity constitutes a critical and time-sensitive commodity whose trade networks require continuous balancing between supply and demand, making them particularly suitable for analysing structural resilience under stress. Previous studies have shown that, despite sharp contractions in traded volumes, core trade networks may preserve their overall connectivity during crises, while undergoing significant reallocations of central roles among countries (Kiyota, Reference Kiyota2022; Vidya et al., Reference Vidya, Mummidi and Adarsh2023).

In line with the cited literature, this case study uses TERRA to examine the impact of the COVID-19 pandemic on the European electricity trade network. More specifically, the analysis investigates whether the pandemic altered the network structure or triggered a reconfiguration of countries’ positions within it.

To obtain an initial overview of how the shock was distributed spatially and temporally, we use the interactive map, which visualizes monthly year-on-year variations in trade flows through customizable heatmaps.Footnote ⁷

Figure 3 compares April 2019 (left panel) and April 2020 (right panel), showing export changes ranging from –60% to +60%. The shift from light colours in 2019 to mostly red and orange in 2020 clearly highlights the sharp contraction in trade volumes caused by the COVID-19 pandemic.

Figure 3.

Interactive map panel of EU exports: comparison between April 2019 and April 2020.

Figure 3 Long description

Two thematic maps of Europe display monthly year-on-year export changes for April 2019 and April 2020. The legend shows a gradient from green (positive change) to red (negative change), with values ranging from 20 percent to minus 40 percent. In April 2019, most areas, including northern regions like Sweden and Finland, show minimal change near 0 percent. By April 2020, southern countries such as Italy, Spain and France exhibit significant declines, with changes between minus 10 percent and minus 40 percent. Northern Europe shows less negative impact. The maps are oriented with north at the top, illustrating a shift towards more negative export changes in 2020 compared to 2019.

At the same time, the interactive map highlights heterogeneity across countries: while most EU members suffered sharp declines in exports (notably Spain, France, Italy, Romania, and Greece) in April 2020, some countries, such as Sweden, Finland, and Denmark, experienced comparatively milder contractions. This reflects differences in industrial structure and trade composition, consistent with recent studies documenting that economies less dependent on manufacturing exports were relatively more resilient during the first wave of COVID-19 (Verschuur et al., Reference Verschuur, Koks and Hall2021; Vidya et al., Reference Vidya, Mummidi and Adarsh2023), and underscores one of TERRA’s strengths in making such cross-country differences immediately visible.

To determine whether this decline also affected the structure of trade relations, we examine the product category Electricity, transmission, and distribution services. Figure 4 illustrates the trade networks after merging extra-EU partners and averaging flows. The results indicate that network density decreased only slightly from 0.20 in April 2019 to 0.19 in April 2020 (–5%), suggesting that most trade links persisted despite a significant drop in volumes. Although the overall topology stayed stable, country-specific indicators reveal notable shifts. For instance, Italy’s betweenness centrality decreased from 0.21 to 0.12, and its normalized degree dropped from 0.11 to 0.06, indicating a relative decline in its importance within the network.

Figure 4.

Graph EU–World: prevalent trade network (60%) on ‘Electricity, transmission and distribution services’.

Figure 4 Long description

Two network diagrams and a table. The first diagram, labeled April 2019, shows connections between European countries with arrows indicating direction. The second diagram, labeled April 2020, displays similar connections with some changes in direction and density. The table on the right lists metrics for Italy in 2019 and 2020. Columns are Metric, 2019 and 2020. Row 1: Density 0.20, 0.19. Row 2: W. Degree 0.11, 0.06. Row 3: inDegree 9, 9. Row 4: W. inDegree 0.09, 0.04. Row 5: Out Degree 8, 8. Row 6: W. Out Degree 0.02, 0.02. Row 7: Closeness 0.00, 0.00. Row 8: Betweenness 0.21, 0.12. Row 9: Distinctiveness 0.02, 0.01.

Notes: Comparison between April 2019 and April 2020.

This suggests that, despite stable overall connectivity, dominant countries adjusted their strategies, leading to a reallocation of central positions.

To better capture how these shifts evolved, we move from the static comparison in Figure 4 to a dynamic perspective, examining the monthly time series of betweenness centrality for each EU country, employing the same network construction parameters as outlined before (extra-EU data collapsed, flows averaged, and metrics derived from the complete graph). Figure 5 reports the monthly evolution of betweenness centrality for the main European countries, ranked in descending order according to this metric. Together, these countries account for approximately 70% of the total betweenness centrality of the monthly electricity trade network (including the aggregated extra-EU node). Despite moderate fluctuations in network density between 0.19 and 0.20, France, Italy, and Slovakia experienced a decline in centrality during the peak of the pandemic. By contrast, Poland’s centrality remained broadly stable, while Hungary temporarily gained prominence between June and September 2020. Germany consistently retained high centrality, confirming its key role in the network. The distinct yet stable centrality profiles of Germany and France further illustrate differentiated functional roles within the European electricity trade network.

Figure 5.

Monthly betweenness centrality for electricity, transmission and distribution services of major EU countries.

Figure 5 Long description

A multi-line graph plots seven series across a timeline from 2019.08 to 2020.12 on the x-axis. The left y-axis ranges from 0 to 0.6 and corresponds to the betweenness metric series for DE, FR, HU, SK, PL and IT. The right y-axis ranges from 0.18 to 0.21 and corresponds to the density series. Density fluctuates across the period, starting near 0.19 in August 2019, rising over 0.20 around February 2020 and recovering toward 0.20 by December 2020. Regarding the betweenness centrality DE rises to a peak of approximately 0.5 around February 2020 and then declines toward 0.3 by December 2020. FR experienced a noticeable decline in centrality (peaking in November 2019 with 0.4 and staying below 0.3 in the following months), suggesting a temporary reduction in their position within the network. In contrast, Poland maintained a broadly stable level of centrality throughout this period, while Hungary experienced a temporary increase, gaining prominence between June and September 2020 before returning to its previous position.

Notes: lines, left axis based on betweenness values; histogram, right axis network density. The version including the aggregated extra-EU node is reported in Appendix A (Figure A1).

Overall, Figure 5 indicates that, although the collapse in absolute trade volumes involved only marginal changes in network density, the distribution of bridging roles among countries shifted markedly under stress. This contrast between reduced trade volumes and stable connectivity aligns with recent findings indicating that major trade networks maintained their structural integrity throughout the pandemic (Kiyota, Reference Kiyota2022; Vidya et al., Reference Vidya, Mummidi and Adarsh2023). These results indicate that, despite severe global disruptions, the electricity trade network preserved its overall connectivity, while the relative positions of key countries were substantially reshaped.

To demonstrate the scenario analysis feature, we simulate the failure of some connections to visualize network dynamics both graphically and through quantitative metrics. The tool supports removing connections to evaluate the impact of market shocks. Figure 6 shows a network-based exploratory scenario for electricity trade in April 2020 during the COVID-19 pandemic. The left panel reproduces the observed trade network discussed in Figure 4, while the right panel illustrates an edge-removal exercise representing a hypothetical trade disruption involving Slovakia, chosen because of its high betweenness centrality.

Figure 6.

Graph EU–World: edge-removal scenario showing the dominant graph at 60%.

Figure 6 Long description

Two network diagrams and a table. The first diagram, labeled April 2020 Real situation, shows trade connections among EU countries with flags representing each country. The second diagram, labeled April 2020 Simulation, displays a similar network with adjusted connections. Both diagrams include countries like DE, FR, IT and others, connected by lines indicating trade relationships. The table on the right compares Real and Scenario values for trade prevalence among various entities: Extra EU, DE, SK, FR, PL, HU and IT. Values are given as decimals, such as Extra EU with 0.64 for Real and 0.70 for Scenario, DE with 0.52 for Real and 0.53 for Scenario and others. SK has a value of 0.18 for Real and NA for Scenario. The table visually represents these values with shaded bars next to each numeric value.

Notes: Network visualizations illustrate changes in trade connectivity following the shock. The table on the right-hand side of the network plots reports the corresponding numerical values of the betweenness centrality, supporting the interpretation of the visual results.

Comparing the two graphs, it shows that, despite the removal of the connections involving Slovakia, the overall network structure remains relatively stable: Germany, France, and the aggregated extra-EU node exhibit high and broadly stable centrality, with only marginal variations, while significant rearrangements occur among intermediary nodes, with Poland and Italy gaining centrality and Hungary losing relevance. Furthermore, the graph highlights Belgium’s growing prominence, as evidenced by the addition of two new export edges in the dominant graph (towards the Netherlands and extra-EU). This exploratory scenario illustrates the usefulness of network-based scenario analysis tools for assessing potential ripple effects of supply disruptions.

5.2 Weapons and Ammunition during the Russia–Ukraine Conflict

The Russia–Ukraine war represents a major geopolitical shock with profound implications for global trade, particularly in strategically sensitive sectors related to security and defence. Beyond its humanitarian and political consequences, the conflict triggered abrupt disruptions in arms production, logistics, and international supply routes, while accelerating rearmament policies and reshaping defence procurement strategies across Europe (Zhuravka et al., Reference Zhuravka, Botvinov, Parshyna, Makarenko and Nebaba2021; Wang et al., Reference Wang, Chen and Song2023).

Weapons and ammunition constitute a highly concentrated and regulated trade segment, characterized by limited substitutability, strong geopolitical constraints, and pronounced network hierarchies. These features make arms trade networks particularly suitable for analysing whether geopolitical shocks undermine network cohesion or instead induce a reallocation and concentration of strategic brokerage roles under heightened political risk.

Building on this literature, this case study applies the TERRA framework to examine how the European weapons and ammunition trade network responded to the Russia–Ukraine conflict. The analysis investigates whether the shock preserved overall network connectivity while simultaneously triggering a reconfiguration and concentration of countries’ brokerage positions and substitution patterns within European arms supply chains.

The analysis is organized as follows. Subsection 5.2.1 presents evidence from the dashboard, illustrating changes in trade flows and network positions during the conflict using network and time series indicators. Subsection 5.2.2 introduces the counterfactual supply shock scenario and uses the Constant Elasticity of Substitution (CES) framework described in Section 4.4 to model trade reallocation among suppliers. Subsection 5.2.3 discusses the results of the counterfactual analyses and their implications.

5.2.1 Stability and Reallocation of Brokerage Roles

This subsection examines the evolution of the European weapons and ammunition trade network before and after the outbreak of the Russia–Ukraine war. To this aim, Figure 7 presents a comparative analysis of the trade network across three key periods: October 2021 (pre-war), February 2022 (short-term post-war), and October 2022 (medium-term post-war). The focus is on the dominant trade exchanges, which account for 60% of total flows, excluding the aggregated extra-EU node.

Figure 7.

EU–World network for the trade of weapons and ammunition at 60% prevalence (average flows), October 2021–February 2022–October 2022.

Figure 7 Long description

Three directed network diagrams display trade relationships among EU countries for weapons and ammunition across three time snapshots: October 2021, February 2022 and October 2022. Each node in the network is represented by a country flag and directed edges indicate trade flow from exporter to importer. No axis labels or units are present, as these are network graphs. A density value is shown above each diagram. In October 2021, the network density is 0.07. Multiple directed connections are visible among a large number of country nodes arranged in a circular layout. The United States flag node appears centrally connected with several outgoing and incoming edges. In February 2022, the network density remains at 0.07. The number of visible nodes appears reduced compared to October 2021 and directed edges are concentrated among a smaller set of country nodes. The United Kingdom flag node appears as a prominent hub with multiple connections. In October 2022, the network density decreases to 0.06. Fewer directed edges are visible overall and the network appears less dense than in the two earlier snapshots. Below the three diagrams, two tables present numeric values for seven countries: Poland (PL), Germany (DE), Italy (IT), Spain (ES), Czech Republic (CZ), France (FR) and the Netherlands (NL). The first table covers October 2021 and February 2022. For October 2021, the row labeled W. Degree shows values of 0.11 for Poland, 0.22 for Germany, 0.22 for Italy, 0.14 for Spain, 0.11 for Czech Republic, 0.06 for France and 0.06 for Netherlands. The row labeled W. Out Deg shows 0.02 for Poland, 0.15 for Germany, 0.18 for Italy, 0.11 for Spain, 0.08 for Czech Republic, 0.02 for France and 0.02 for Netherlands. For February 2022, W. Degree values are 0.11 for Poland, 0.21 for Germany, 0.19 for Italy, 0.16 for Spain, 0.08 for Czech Republic, 0.07 for France and 0.05 for Netherlands. W. Out Deg values for February 2022 are 0.01 for Poland, 0.14 for Germany, 0.16 for Italy, 0.13 for Spain, 0.06 for Czech Republic, 0.02 for France and 0.02 for Netherlands. The second table covers October 2022. W. Degree values are 0.38 for Poland, 0.15 for Germany, 0.14 for Italy, 0.08 for Spain, 0.06 for Czech Republic, 0.05 for France and 0.03 for Netherlands. W. Out Deg values are 0.20 for Poland, 0.08 for Germany, 0.12 for Italy, 0.05 for Spain, 0.05 for Czech Republic, 0.02 for France and 0.01 for Netherlands. W. Degree represents the weighted total of trade connections for each country and W. Out Deg represents the weighted outgoing connections, indicating export activity. In October 2022, Poland shows the highest W. Degree at 0.38 and the highest W. Out Deg at 0.20 among all listed countries.

Notes: The figure presents the network structure and selected centrality metrics. Tables below the network plots report the corresponding numerical values of weighted degree and weighted out degree centrality for the main countries.

Under geopolitical stress, the European arms trade network displays a stable topological structure while reallocating brokerage roles among a select group of countries. Network density remained constant at 0.07 in both October 2021 and February 2022 but decreased to 0.06 (a 14% decline) by October 2022, indicating a modest structural contraction. Despite this general stability, significant reallocations of brokerage roles are evident. Ukraine joined the dominant network at the beginning of the conflict and remained a part of it thereafter. Germany, Italy, and Spain were the most important exporters during the pre-war and short-term post-war periods. However, by October 2022, Poland had emerged as the leading exporter, despite its limited number of outgoing connections.

This suggests an increasing concentration of trade flows around a few strategic suppliers. Italy also maintained a central role, highlighting its ongoing significance in the European arms trade.

Overall, the evidence from Figure 7 indicates that, despite limited changes in aggregate connectivity, the arms trade network underwent a marked reallocation of central exporting roles following the outbreak of the war. The evidence points to a network that remains structurally connected while becoming increasingly concentrated around a small set of strategic suppliers. This pattern is consistent with theoretical contributions showing that networked economies may preserve aggregate connectivity while becoming increasingly sensitive to shocks affecting a small set of highly central nodes (Acemoglu et al., Reference Acemoglu, Carvalho, Ozdaglar and Tahbaz‐Salehi2012; Carvalho, Reference Carvalho2014).

Beyond the topological structure of the dominant network, Figure 7 provides an immediate visual encoding of trade intensities through edge thickness and colour. Darker and thicker edges identify the main export corridors that concentrate the largest volumes of arms and ammunition trade. In October 2021, the intensity of outgoing links from Germany, Italy, and Spain highlights their dominant supplier role within the network. In February 2022, shortly after the outbreak of the conflict, the visual pattern became more heterogeneous, indicating a partial redistribution of trade intensities across a broader set of exporters. By October 2022, the emergence of Poland as a leading supplier is clearly reflected not only in its network position but also in the strong darkened links directed towards Ukraine, signalling a marked concentration of trade volumes along a limited number of strategic corridors.

To complete the analysis, we examine the temporal evolution of countries’ roles using a time series of centrality metrics.Footnote ⁸ These dynamics illustrate how geopolitical stress translates into a reallocation of brokerage roles within an increasingly concentrated network structure. Figure 8 reports the degree centrality time series for the main EU countries. Together, the selected countries account for approximately 70–80% of total monthly degree, confirming their central role in the network. Temporal variations in degree centrality illustrate patterns of reallocation of brokerage roles over time.

Figure 8.

Monthly degree centrality of major EU countries (excluding extra-EU) for weapons and ammunition trade, 2021–2022.

Figure 8 Long description

The line graph displays monthly degree centrality values of major EU countries for weapons and ammunition trade from 2021 to 2022. The horizontal axis represents time from January 2021 to December 2022, while the vertical axis shows betweenness centrality values ranging from 0 to 0.5. Multiple lines represent different countries, with Germany showing a significant increase in betweenness centrality, peaking around 0.5 in mid-2022. Italy and other countries have fluctuating values, with Italy reaching peaks between 0.15 and 0.3 in specific months. The legend at the bottom identifies each country′s line by color.

Note: The version including the aggregated extra-EU node is reported in Appendix A (Figure A2).

The results show shifting leadership dynamics. Consistent with Zhuravka et al. (Reference Zhuravka, Botvinov, Parshyna, Makarenko and Nebaba2021), Poland gains dominance in 2022, particularly in May and July. Slovakia rose sharply between March and April 2022, with its degree centrality increasing from below 0.05 to a peak of 0.20, before stabilizing at lower levels (between 0.05 and 0.10) in the post-war period. Similarly, Bulgaria exhibits a marked increase, peaking at 0.20 in May 2022. Germany and Italy remain key players throughout the period, with occasional monthly peaks, while Spain exhibits a declining trend, decreasing from pre-war levels around 0.20 to approximately 0.10 thereafter.

While degree centrality captures changes in direct trade connections, betweenness centrality allows us to identify the countries that act as strategic intermediaries within the reconfigured network. We therefore examine betweenness centrality to capture brokerage positions within the arms trade network. As shown in Figure 9, Germany emerges as the most dominant broker, with betweenness centrality values ranging from 0.20 to 0.40 before the conflict and from 0.10 to 0.30 in the post-conflict period. Italy ranks second in betweenness centrality, confirming its significant role in exchanges, with peaks between 0.15 and 0.30 in specific months, including October 2021, April 2022, July 2022, and September 2022. While these fluctuations coincide with the key phases of the conflict, further analysis would be required to disentangle war-related effects from other influencing factors.

Figure 9.

Monthly betweenness centrality of major EU countries (excluding extra-EU) for weapons and ammunition trade, 2021–2022.

Figure 9 Long description

The multi-line graph compares trends from July 2021 to December 2022 across seven DE, IT, PL, CZ, NL, ES, FR, SK. The horizontal axis represents time in months and years, while the vertical axis shows values ranging from 0 to 0.6. Each line represents different countries, distinguished by color and style. Key observations include: DE shows a peak around October 2021 at approximately 0.4. IT is relatively stable during the first half of the period but experiences a marked increase in July 2022, reaching approximately 0.31, followed by another peak in September. PL remains relatively stable, generally fluctuating between 0.05 and 0.1. NL and ES display stronger short-term fluctuations, with ES reaching a notable peak in late 2021. Overall, the figure highlights substantial differences in both the level and dynamics of centrality across countries.

Note: The version including the aggregated extra-EU node is reported in Appendix A (Figure A3).

Other countries played episodic roles, including Spain in November 2021 and October 2022, the Czech Republic in October 2021, and the Netherlands in May 2022. By contrast, the remaining countries occupy marginal positions in terms of betweenness centrality.

This pattern is consistent with rotating leadership dynamics in trade networks, where brokerage roles shift over time rather than remaining fixed.

Overall, the evidence indicates that the arms trade network remained structurally resilient while experiencing increasing trade flow concentration and a reallocation of brokerage roles, with Poland emerging as a key exporter and Germany and Italy preserving their brokerage positions. This combination of structural resilience and national reconfiguration is consistent with findings from other trade networks exposed to major shocks (De Benedictis et al., Reference De Benedictis, Nenci, Santoni, Tajoli and Vicarelli2014; Wang et al., Reference Wang, Chen and Song2023).

5.2.3 Functional Fragility under Counterfactual Supply Shocks

We now evaluate how the concentrated network structure, presented in Section 5.2.1, responds to the removal of a dominant supplier. These mechanisms are closely related to the propagation and amplification channels identified in production network models, where shocks to highly central suppliers generate disproportionately large reallocation effects (Baqaee and Farhi, Reference Baqaee and Farhi2020).

This subsection presents the results of the counterfactual analysis, illustrating how the removal of a key supplier reshapes trade flows in the weapons and ammunition market. We focus on the redistribution of quantities across alternative European exporters and assess substitution patterns implied by the CES framework.

We simulate the removal of Poland (PL), a significant and policy-relevant disruption, considering its pivotal role as a central logistical hub and a major contributor to European arms exports to Ukraine. This exclusion prompts a considerable reallocation of residual demand among alternative exporters, facilitating an empirical evaluation of supply elasticity, the marginal capacity of remaining suppliers, and the influence of relative prices in international competition. Furthermore, it exposes the vulnerability of a European supply chain that is excessively concentrated in a limited number of countries.

Table 1 summarizes the redistributionFootnote ⁹ patterns implied by the CES framework, highlighting a highly skewed substitution process dominated by a small set of alternative suppliers. More specifically, it shows the quantitative effects of the counterfactual removal of Poland (PL) from the group of exporters to Ukraine. As expected, the Polish share drops to zero ( $shar{e_{post}} = 0$), whereas in the pre-shock period it accounted for over 90% of total quantities ( $shar{e_{base}} = 0.906$). This generates a substantial reallocation of trade flows, which the CES model distributes across alternative suppliers according to relative prices and baseline shares.

Table 1.

CES-based counterfactual analysis results

Table 1 Long description

Rows list suppliers and columns report Value, Quantity, Price, Baseline Quantity, Post shock Quantity, change in export quantities relative to baseline, Baseline Share, and Post shock Share. Poland has Value 257,659,829, Quantity 3,285,008, Price 78.435, Baseline Quantity 3,360,721.78, Post shock Quantity 0.00, change minus 3,360,721.78, Baseline Share 0.906, and Post shock Share 0.000. Slovakia has Value 20,062,559, Quantity 206,585, Price 97.115, Baseline Quantity 170,693.76, Post shock Quantity 3,279,421.37, change 3,108,727.61, Baseline Share 0.057, and Post shock Share 0.606. Lithuania has Value 1,976,576, Quantity 33,213, Price 59.512, Baseline Quantity 44,782.58, Post shock Quantity 860,376.77, change 815,594.19, Baseline Share 0.009, and Post shock Share 0.097. Spain has Value 472,471, Quantity 56,836, Price 8.313, Baseline Quantity 549,628.38, Post shock Quantity 10,540,418.02, change 9,991,789.64, Baseline Share 0.016, and Post shock Share 0.167. Latvia has Value 460,524, Quantity 23,565, Price 19.543, Baseline Quantity 96,758.48, Post shock Quantity 1,858,953.82, change 1,762,195.34, Baseline Share 0.006, and Post shock Share 0.069. Germany, Czechia, Estonia, Denmark, Netherlands, Italy, and Belgium each show small baseline shares at 0.002 or lower and post shock shares ranging from 0.000 to 0.024, with post shock quantities 214,539.90 for Germany, 11,343.76 for Czechia, 44,861.64 for Estonia, 6,519.26 for Denmark, 3,893,992.67 for Netherlands, 98.43 for Italy, and 6,328.03 for Belgium.

Notes: Baseline and post-shock export shares and quantities for EU suppliers after the removal of Poland from the market. Quantities are measured in physical units. ${\Delta _q}$ denotes the change in export quantities relative to the baseline scenario and is computed as the difference between post-shock and baseline values.

The redistribution is highly skewed: Slovakia absorbs 61% of post-shock quantities ( $shar{e_{post}} \approx 0.606$), while Spain, Latvia, and Lithuania account for most of the remaining adjustment. In more detail, Spain increases its market share to around 17% ( $shar{e_{post}} \approx 0.167$) despite having a limited presence prior to the shock. Latvia and Lithuania also experience substantial relative gains, together reaching approximately 16–17% of post-shock quantities. Meanwhile, the Netherlands expands significantly, reaching around 3.9 million units, driven by highly competitive pricing.

These results, shown in the following Figure 10, indicate that post-shock substitution is highly concentrated rather than diffused across the network, reinforcing the evidence of functional fragility identified in the network analysis.

Figure 10.

Comparison of baseline and post-shock export quantities by EU supplier in the counterfactual analysis.

Figure 10 Long description

Horizontal bar chart comparing ‘Quantity’ and ‘New Quantity’ across 11 European countries, listed on the y-axis from ES, NL, SK, PL, LV, LT, DE, EE, CZ, DK, to IT. The x-axis shows values from 0 to 12,000,000. ES shows the largest New Quantity value, at roughly 10,500,000, followed by the NL at about 3,800,000 and SK at about 3,200,000. PL is the only country where the original Quantity bar (in blue) is dominant, at roughly 3,200,000, with little to no New Quantity value shown. LV and LT show moderate New Quantity values of about 1,800,000 and 900,000 respectively. DE shows a small New Quantity value, while EE, CZ, DK, and IT show minimal to negligible values for both metrics.

These results suggest that stable aggregate connectivity may coexist with growing functional fragility. System-wide adjustment increasingly depends on a limited number of highly central suppliers. In line with production network theory, these highly connected suppliers serve as critical bottlenecks for aggregate adjustment (Acemoglu et al., Reference Acemoglu, Carvalho, Ozdaglar and Tahbaz‐Salehi2012; Carvalho, Reference Carvalho2014; Baqaee and Farhi, Reference Baqaee and Farhi2020).

From a policy standpoint, these results highlight the importance of diversification strategies and coordinated capacity-building measures aimed at reducing excessive dependence on a small set of exporters. Enhancing production flexibility and expanding the set of suppliers would mitigate the amplification mechanisms identified above, thereby enhancing the resilience of European defence supply chains against geopolitical disruptions.