In this section, we examine the evolution of emissions trading in the EU ETS.
Section 6.1 summarizes transaction patterns, showing a concentrated trading structure where a few installations dominate activity (the EU ETS Directive 2003/87/EC (
https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX:32003L0087) defines an installation as a stationary technical unit where one or more Annex I activities are carried out and any associated activities directly connected to that site). Trading is unevenly distributed, with industrialized regions serving as key hubs.
Section 6.2 analyses the EU ETS network across Phases I–IV, revealing a shift in connectivity and structural organization over time. Community detection captures trading cluster dynamics, while centrality measures track the changing influence of participants.
Section 6.3 employs DTs to simulate network evolution, modelling node additions, edge rewiring, and structural shifts. These simulations identify emerging trading relationships and market participants. Finally,
Section 6.4 integrates ML models (GNNs and LR) within the DT framework to predict future network configurations. While LR reinforces established hubs, GNNs capture emerging connections, enhancing our understanding of market structure and regulatory impacts.
6.1. Descriptive Statistics
This subsection explores transaction patterns and installation activity within the EU ETS. By summarizing the data, we identify relevant trends in trading frequency, installation participation, and transaction volumes.
Figure 1 shows the spatial distribution of installations and transaction densities across Europe. Trading activity is highly concentrated in industrialized regions, with notable clusters in the United Kingdom, Germany, France, and the Benelux area. Major urban and economic centres—such as London, Paris, and Berlin—exhibit significant transaction volumes. In contrast, trading density diminishes in Northern and Eastern Europe, with sparser activity in rural regions and along the system’s geographic periphery. The observed distribution sheds light on the central role of industrial hubs in emissions trading. While the EU ETS covers a broad geographic range, transactions are unevenly distributed, reflecting economic activity and regulatory engagement. Installations appear more frequently in regions with established industrial bases, reinforcing the network’s core trading relationships.
Table 1 summarizes the descriptive statistics of installation participation. Across 16,898 installations, the average installation engaged in 236 transactions, with a median of 185. The interquartile range (IQR) spanned from 92 to 305 transactions, indicating moderate variability.
Figure 2 provides a visual representation of these patterns. The top panel reveals that most installations engage in relatively few transactions, with a long right-skewed tail indicating the presence of highly active participants. While some installations appear only once, the most active installation recorded 1840 transactions. The middle panel shows the boxplot of transaction counts, where we can observe extreme outliers, i.e., installations with over 625 transactions. This underscores the imbalance between highly active participants and those engaging sporadically. Finally, the bottom panel of
Figure 2 illustrates the distribution of transaction volumes in tonnes of allowances. The histogram confirms a highly skewed distribution, where most transactions involve relatively small quantities, while a small number of trades account for exceptionally large volumes. This pattern suggests that a few installations play a dominant role in market activity, either due to their regulatory obligations or strategic trading behaviour.
Figure 3 further emphasizes market concentration, displaying the installations with the highest transaction counts. Three installations in Great Britain (GB_321, GB_381, and GB_154) top the list, reinforcing the country’s prominent role in emissions trading. Poland (PL) follows closely, with multiple installations ranking among the most active. Germany (DE), Norway (NO), and Hungary (HU) also feature prominently. The treemap reveals a concentrated trading structure, where a small number of installations drive a significant portion of the market’s activity. (Each rectangle in the treemap represents an installation, with size proportional to its number of transactions in the EU ETS from 2005 to 2023. Labels follow the format
CC_ID, where
CC is the ISO country code and
ID is an anonymized identifier. The “other” category aggregates all remaining installations with low transaction volume.) A minor segment labelled “other” represents installations with much lower transaction counts, illustrating a stark contrast between frequent and infrequent participants.
Figure 4 presents trading volumes across the four phases of the EU ETS. Phase I (2005–2007) exhibited a steady but modest increase in trading activity, serving as a test period for market mechanisms. Phase II (2008–2012) saw a significant jump in volume, peaking in 2008 as regulatory frameworks stabilized. Volumes remained high but fluctuated, reflecting economic conditions and market adjustments. Phase III (2013–2020) recorded the highest trading volumes, particularly in 2015 and 2016, when regulatory changes and policy shifts likely influenced trading behaviour. After 2016, a gradual decline occurred, possibly due to market saturation, regulatory constraints, or allowance supply adjustments. Phase IV (2021–2023) introduced structural reforms that led to a sharp reduction in trading volumes. Stricter emissions caps and adjustments in allocation mechanisms contributed to this decline, reflecting the evolving nature of the EU ETS.
The descriptive analysis reveals clear patterns in transaction frequency, volume, and market structure. While the EU ETS spans thousands of installations, a subset of highly active participants drives the bulk of transactions. The skewed distribution of transaction counts and allowance volumes underscores the presence of dominant market players. A complex network approach offers deeper insights beyond these summary statistics. By modelling the EU ETS as a network of trading relationships, we can capture how installations interact, detect structural shifts, and anticipate evolving trading patterns. The next section applies network science techniques to map trading relationships and assess market dynamics.
6.2. Structural Evolution of the EU ETS Network
We constructed networks for Phases I–IV to represent emissions allowance transactions over each period.
Figure 5,
Figure 6,
Figure 7 and
Figure 8 visualize the evolving network structure, highlighting communities and centrality. We detected communities using the Louvain method. Node sizes reflect degree centrality, indicating the relative importance of each country. Different colours distinguish distinct trading communities, allowing for a clearer understanding of network segmentation.
Self-links in network representations indicate transactions where the source and target accounts belong to the same country. This occurs because emissions trading within the EU ETS involves allowance transfers between different accounts, which may be administered under the same national registry. For example, installations within the same country frequently engage in internal trades, either due to corporate ownership structures, compliance adjustments, or strategic trading decisions. These self-loops capture domestic trading activity, distinguishing it from cross-border transactions and providing insights into how emissions allowances circulate within national markets.
Figure 5 represents the split in communities of Phase I. The network was relatively dense, consisting of 25 nodes and 292 edges, yielding a network density of 0.487. The average degree was 23.36, meaning each country was, on average, linked to over 23 others. A few central nodes dominated connectivity, creating a moderately centralized structure. We detected six communities that varied in size, with the largest including five countries. The United Kingdom (GB) and France (FR) were central within their communities, while other important hubs included the Netherlands (NL), Spain (ES), and Denmark (DK). Germany (DE) and Austria (AT) competed for centrality in their cluster. Notably, Malta (MT0) appeared as a completely isolated entity, indicating its detachment from broader market interactions.
Figure 6 represents the split in communities of Phase II. It shows substantial expansion, with the network growing to 42 nodes and 727 edges. Despite this, network density declined slightly to 0.422, indicating a broader but somewhat less interconnected market. The average degree increased to 34.61, suggesting higher interaction frequency. Degree centrality became more distributed, indicating the emergence of additional hubs. The number of communities rose to eight, reflecting structural diversification. Some previously distinct groups merged, reducing modularity and increasing inter-community connections. New entrants such as Bulgaria (BG), Switzerland (CH), Iceland (IS), Liechtenstein (LI), Norway (NO), Romania (RO), and Ukraine (UA) expanded the network, further increasing complexity. Germany (DE) and the Netherlands (NL) solidified their bridging roles. Additional isolated nodes emerged, such as Cyprus (CY0) and Croatia (HR), suggesting that certain countries remained outside the primary trading clusters.
Figure 7 shows a denser network comprising 40 nodes and 810 edges. The network density increased to 0.519, with the average degree rising to 40.5. The number of communities was five, indicating a trend toward consolidation. The largest community consisted of 11 nodes, reflecting tighter integration among certain groups. The overall structure became more interconnected, with prominent subgroups forming within communities. Intra-community connections strengthened, suggesting that emissions trading relationships solidified over time. While inter-community edges remained selective, preferential attachment mechanisms drove new links toward already well-connected nodes. Countries like France (FR), the United Kingdom (GB), and Germany (DE) maintained their centrality, reinforcing their influence. Smaller clusters persisted, reflecting localized trading patterns, potentially influenced by regional regulations or strategic agreements.
Figure 8 illustrates a stark structural shift in Phase IV. The number of nodes declined to 29, while the number of edges dropped dramatically to 58, resulting in a sparse network density of 0.071. The average degree plummeted to 4.0, indicating reduced connectivity and a more dispersed network structure. The network divided into 21 communities, most of which contained only one or two nodes, pointing to a shift toward more localized or isolated trading interactions. Notably, the “EU” node emerged as a dominant entity, suggesting that many participants now consolidated transactions under a centralized European registry. This development likely reflects regulatory revisions and the adoption of common platforms such as the Union Registry and auctioning mechanisms. The observed structural reconfiguration may be shaped by institutional reforms and external shocks, including changes in allowance distribution and the disruptive effects of the COVID-19 pandemic. Overall, the network analysis revealed a progression from a sparse structure in Phase I to a more interconnected market in Phases II and III, followed by a distinct reorganization in Phase IV. This final phase reflected changes linked to emerging EU-level mechanisms and evolving regulatory frameworks, which continue to reshape the structure and function of the market.
Table A3 (
Appendix A) presents the community transitions of countries across Phases I to IV. Each country was assigned a community ID for each phase, allowing us to track structural changes in the network over time. Some countries, such as Lithuania (LI) and Slovenia (SI), remained within the same communities across multiple phases, indicating stable roles in the emissions trading network. Conversely, countries like France (FR), the United Kingdom (GB), and Germany (DE) shifted across different communities, reflecting dynamic participation and evolving market interactions. Some countries, such as Cyprus (CY0) and Malta (MT0), appeared in earlier phases but became disconnected in later ones. The entry of new participants, such as Croatia (HR) in Phase II, points out the network’s expansion. Community evolution also reveals the role of influential participants. Larger communities, such as those including Germany (DE), the United Kingdom (GB), and France (FR), suggest their bridging function in the market. Smaller, isolated communities, such as Malta (MT0), indicate limited interaction with the broader network. Over time, the network exhibited both structural consolidation and diversification, with some communities merging into larger clusters—such as Poland (PL) and Bulgaria (BG) in Phase IV—while others split or reorganized. Such transformations may be attributed to evolving regulations, shifting economic conditions, and the EU ETS’s continuous adaptation to market dynamics.
Table A4 (
Appendix A) ranks the most relevant influencers based on degree centrality across all phases. This ranking helps identify countries that maintained strong connectivity or lost influence over time. Early phases reveal a centralized network, where a few nodes dominate connectivity. As the system evolves, influence becomes more distributed among participants, reflecting changes in network organization. In Phases I and II, countries such as France (FR), the Netherlands (NL), and the United Kingdom (GB) exhibit high degree centrality, acting as dominant hubs. However, in later phases, their influence declines, and new hubs emerge. These evolving trends highlight a shift in network structure, as some participants lose central roles and others become more prominent. The merging and splitting of communities illustrate shifting relationships and market priorities. Established hubs retain influence, but their dominance diminishes as the network undergoes structural reconfiguration.
Figure 9 illustrates the evolution of degree centrality trends across phases. In this figure, we tracked the degree centrality of five top influencers over time to reveal structural shifts in the network. A degree centrality close to two suggests that a country maintains direct trading relationships with nearly every other country in the network, highlighting its role as a highly connected participant. This level of centrality reflects a position of strong market integration, where the country either facilitates transactions between others or dominates trading activity. The early phases (I–II) show a centralized system, while later phases (III–IV) reflect a transition in network configuration, with declining centrality for traditional hubs. Countries such as the United Kingdom (GB) display a steady rise in centrality, peaking in Phase III before a sharp decline in Phase IV. The Netherlands (NL) and Germany (DE) follow similar patterns, maintaining stable centrality in early phases before experiencing a drop in Phase IV. France (FR) starts with high degree centrality in Phase I but declines steadily across all phases, with a pronounced drop in Phase IV. Denmark (DK) consistently ranks lower than the other top nodes, with a gradual decline culminating in Phase IV’s sharp drop.
The observed trends provide valuable insights into the network’s evolution. Early phases exhibit high connectivity among a few dominant nodes, forming a relatively centralized structure. As the system matures, influence becomes more distributed across emerging connections and new participants. By Phase IV, the structure reflects a notable reconfiguration, likely shaped by regulatory developments and the introduction of EU-level mechanisms that influence trading patterns. The decline of previously dominant hubs suggests a redistribution of roles, reinforcing the dynamic nature of the EU ETS trading system. It is worth noting that some of the observed changes in Phase IV may be partially influenced by the presence of regulatory intermediaries, which can obscure direct trading relationships between participants. While this adds complexity to interpreting recent structural shifts, our network-based methodology remains applicable even in systems shaped by institutional layers or aggregated data. This adaptability is particularly important when modelling forward-looking scenarios, where regulatory architecture and trading platforms may continue to evolve. Overall, these findings demonstrate a structural transformation of the emissions trading network towards a more institutionally complex system.
6.3. Simulating Structural Change with Digital Twins
To analyse the potential structural evolution of the EU ETS network, we constructed a DT for Phase IV and simulated dynamic changes in node and edge configurations.
Figure 10 presents the initial state of the DT, replicating the existing Phase IV network while introducing five new nodes. We labelled the Twin Nodesas
, where
. These nodes represent hypothetical new participants entering the emissions trading system, which could correspond to new countries joining the market or installations from a specific sector being integrated. The network consisted of 34 nodes, including the 5 additions, and 68 edges, resulting in an average degree of 4.0. This metric indicates that each node, on average, maintained the same level of connectivity observed in Phase IV.
The next step simulated network evolution by applying the three dynamic mechanisms introduced in
Section 4.2: (i) preferential attachment, where new nodes are more likely to connect to highly connected participants; (ii) edge rewiring, which randomly reassigns a subset of existing connections to reflect changes in trading relationships; and (iii) community reorganization, where the algorithm merges clusters with high inter-community density to simulate commercial integration. These mechanisms collectively drove the structural transformation of the network, capturing both incremental adjustments and more substantial shifts in trading behaviour.
Following these modifications, the updated DT (
Figure 10) displayed increased network complexity. The simulation introduced new Dynamic Nodes, labelled as Dyn.Node_j_i, which represented temporary states of nodes that evolved over multiple iterations. These nodes were adjusted based on trading activity, regulatory influences, or network constraints, mirroring the gradual adaptation of real-world market participants. The refined network expanded to 40 nodes, including newly incorporated participants, and 80 edges, reflecting the evolution of trade relationships. Community structures also underwent significant changes, increasing to eight distinct trading clusters, with an average of 5.71 nodes per community. This reflected a reorganization of trading relationships and the formation of more specialized subgroups within the emissions trading system.
Figure 11 illustrates the final stage of network evolution, highlighting long-term transformations in node roles and structural configurations. In addition to the Twin Nodes and Dynamical Nodes, the model introduced the Evolving Nodes, labelled as Evol.Node_i, representing nodes that had undergone cumulative adaptations over successive iterations. These nodes tracked gradual shifts in connectivity and influence, reflecting how certain participants transitioned from peripheral to central positions in the trading network. For instance, an installation or country with increasing trade volume may emerge as a dominant hub over time. The final network state comprised 43 nodes, incorporating three additional participants projected for Phase V. The number of edges increased to 86 due to newly formed and rewired connections, reflecting the dynamic nature of emissions trading. Despite minor shifts in community structure, the network stabilized into eight communities, with an average of 7.17 nodes per cluster. This suggests an ongoing process of structural consolidation, where trading communities become more integrated through new connections and reorganization.
These results show how the EU ETS trading network can change as the market grows and regulations evolve. By using a DT to simulate these dynamics, we are able to explore how new connections form, how trading relationships shift, and how communities reorganize over time. This approach helps us identify patterns that may shape the future of the carbon market—an issue we take up in the next section, where we integrate ML to improve predictions about these structural changes.
6.4. The Future of the European Carbon Market
In this section, we use ML models integrated with DTs to generate predictions about the future structure and behaviour of the European carbon market. This integration increases the model’s ability to simulate structural changes, track network evolution, and optimize connectivity. By leveraging ML techniques, we improve the accuracy of predictions related to edge formation and trading dynamics within the EU ETS. We explore GNNs for link prediction, alongside classical ML models such as LR. These models perform well when edge prediction features are carefully engineered to capture both structural and transactional characteristics.
We constructed the input graph using data from Phases I–IV, incorporating nodes, edges, and relevant attributes, such as the volume of traded allowances between countries. The GNN model was trained on this dataset to predict new connections expected to form in Phase IV. The process involved defining node embeddings, training the model, and evaluating its predictive performance. To train and evaluate the ML model, we split the dataset into training and testing subsets (we use the
train_test_split() https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.train_test_split.html function from Scikit-Learn
https://scikit-learn.org/stable/). The training set comprised 80% of the data, while the remaining 20% were reserved for testing. Specifically, we applied this to the edge index, ensuring a balanced distribution of edges across training and test sets. This approach allowed the model to learn structural patterns from the training data while evaluating its generalization on unseen edges. By maintaining an 80/20 split, we stroke a balance between providing sufficient data for training and preserving enough examples for robust performance assessment.
Table 2 presents the evaluation results of the GNN model across multiple training epochs. Initially, both training and test losses were high, and the test AUC was close to 0.5, indicating performance close to random guessing. As training progressed, the test AUC stabilized between 0.71 and 0.74, showing that the model effectively generalized to unseen data. The decreasing training loss suggested improved learning of structural and transactional patterns within the network.
Figure 12 visualizes the predicted edges in Phase IV, with highlighted new connections identified by the GNN model. The EU node remained the dominant hub, with several newly predicted links directed toward or emerging from it. The model also forecasted connections involving peripheral nodes, such as Spain (ES), Portugal (PT), and Denmark (DK), suggesting an expected expansion in trading activity beyond the core participants. The ability of GNNs to leverage relational and structural properties allows them to detect edges that might not be immediately apparent with simpler models. For instance, connections between less central nodes, such as Croatia (HR) and Lithuania (LT), indicate that the model captured deeper network dependencies beyond direct trading relationships. This predictive capability offers insights into the future evolution of the network, pointing out potential shifts in trading behaviour.
Figure 13 extends the analysis by incorporating the DT framework, where predicted edges were evaluated within an evolving network structure. The simulation introduced the Twin Nodes, Dynamic Nodes, and Evolving Nodes, representing potential participants in the system. The model predicted increased connectivity involving the EU node, reinforcing its role as the central trading hub. Additionally, the simulation revealed that Slovakia (SK) and Poland (PL) were gaining new connections, possibly reflecting their growing influence in the emissions trading market. The inclusion of dynamically generated nodes suggests that the GNN model could generalize beyond existing structures, forecasting interactions even for newly introduced participants. By integrating DTs with ML-based link prediction, we obtained a more dynamic and adaptive representation of the EU ETS. The model not only predicted structural changes but also emphasized emerging patterns that may influence regulatory decisions and market behaviour in future trading phases.
Table 3 presents the evaluation metrics for the LR model in predicting new edges. The model achieved an AUC score of 0.95, indicating strong classification performance. The precision of 0.9333 means that 93.33% of predicted edges corresponded to actual edges, demonstrating a high level of reliability. With a recall of 1.0, the model successfully identified all relevant edges, ensuring no potential connections were overlooked. The F1-score of 0.9655 reflected a well-balanced trade-off between precision and recall.
The ROC curve in
Figure 14 visualizes the model’s classification performance. The AUC of 0.95 confirms that the LR model effectively distinguished between existing and non-existing edges. The curve remains close to the top-left corner, reinforcing the model’s high sensitivity and specificity.
Figure 15 illustrates the predicted edges in Phase IV. The red lines highlight new connections forecasted by the model. Most predicted edges cluster around Bulgaria (BG), Czech Republic (CZ), Hungary (HU), and Germany (DE), indicating emerging trading links between these regions. Additional connections, such as those between Ireland (IE) and Slovakia (SK), suggest evolving market relationships. The EU node remains central, reinforcing its dominant position in the network.
Figure 16 extends this analysis to the DT framework, incorporating the Twin Nodes, Dynamic Nodes, and Evolving Nodes, representing forecasted participants and structural changes in the market. The red edges indicate predicted connections, with a notable concentration around the EU node. This suggests the EU’s continued role as a trading hub while new nodes integrated into the network. The predicted connections revealed expanding trading relationships, particularly involving countries like Cyprus (CY), Sweden (SE), Denmark (DK), and Finland (FI). The LR model emphasized connections between already well-established nodes, reinforcing existing trading hubs. In contrast, the GNN model predicted a broader distribution of edges, identifying connections between peripheral nodes. This difference suggests that while LR effectively captured strong trading relationships, GNNs may offer insights into emerging market structures. Overall, the LR model delivered high accuracy and recall, making it reliable for predicting structural changes within the EU ETS network. However, its tendency to reinforce central hubs rather than explore new link formations highlights the complementary role of GNNs in network evolution analysis.