Digital Twins and Network Resilience in the EU ETS: Analysing Structural Shifts in Carbon Trading

Abstract

The European Union Emissions Trading System (EU ETS) and its underlying market structure play a central role in the EU’s climate policy. This study analyses how the network of trading relationships within the EU ETS has evolved from a hub-dominated architecture to one marked by structural change and the emergence of new trading dynamics. Using transaction data from Phases I–IV, we apply complex network analysis to assess changes in connectivity, centrality, and community structure. We then construct a Digital Twin of the EU ETS, integrating graph neural networks and logistic regression models to simulate the entry of new participants and predict future trading links. The results indicate shifts in network composition and connectivity, especially in Phase IV, where regulatory innovations and institutional mechanisms appear to play a key role. While our analysis focuses on structural dynamics, these patterns may have broader implications for market performance and policy effectiveness. These findings underscore the importance of monitoring the evolving trading network alongside price signals to support a resilient, efficient, and environmentally credible carbon market.

1. Introduction

The European Union Emissions Trading System (EU ETS) is the world’s largest carbon market and a central component of the EU’s climate strategy. As the EU pursues its 2050 carbon neutrality goal, the EU ETS must allocate allowances efficiently to support this transition [1]. While most analyses emphasize carbon prices, the way firms interact within the trading network also plays a key role. This structure affects access, transaction costs, and the system’s ability to adjust to shocks. A resilient network helps avoid bottlenecks, ensures smooth trading, and supports broader sustainability efforts.

In this paper, we study how trading relationships evolve over time and what this means for the EU ETS’s ability to support decarbonization. We use Digital Twin (DT) modelling and Machine Learning (ML) to simulate the entry of new participants and predict future links. DTs are virtual replicas of real-world systems that evolve with the system they mirror. In our case, they simulate how the trading network responds to regulatory and market changes, helping us test resilience and anticipate structural risks. We implement Graph Neural Networks (GNNs) [2,3] and Logistic Regression (LR) [4,5] to predict link formation. We also apply centrality metrics, modularity-based community detection [6,7], and preferential attachment models [8] to analyse how new firms form connections. Such methods allow us to assess whether the evolving network continues to support the core goals of the cap-and-trade system—namely, flexible and efficient allowance reallocation. Our analysis and methods can help policymakers evaluate whether current market conditions maintain access to trading partners, contain transaction costs, and sustain emissions reductions. Hierarchical or highly uneven network structures can disrupt this process by concentrating influence or reducing the number of viable counterparties [9]. These effects may raise the cost of compliance and limit the flexibility needed for efficient trading. Monitoring the network can help anticipate frictions that affect both economic and environmental outcomes.

Our study contributes to a growing literature on the structure of the EU ETS. Earlier work examined the system’s architecture by modelling trading as a complex network. Borghesi and Flori [10], for example, used centrality measures to identify key national registries and showed how person-holding accounts shaped network formation. Liu et al. [11] documented growth patterns and the scale-free nature of the trading network. Our methodology extends these studies by applying DTs and GNNs to simulate structural transitions and predict the entry of new participants and connections. It adds a forward-looking dimension to the analysis and links network evolution to regulatory design and system resilience.

We find that the EU ETS has shifted from a hub-dominated structure to one shaped by evolving connectivity patterns and broader institutional participation. While some trading clusters remain stable, others reconfigure as firms and rules change. These shifts affect how allowances circulate and may influence transaction costs or access to trading partners. Structural variation across phases can also interact with market constraints, such as price floors or ceilings, which may weaken price signals and reduce cost-effectiveness. Over time, this may slow compliance and delay low-carbon investments [12,13]. Our findings highlight the need to monitor the trading network itself—not just prices—to preserve the system’s effectiveness and long-term sustainability.

The rest of this paper is organized as follows. Section 2 reviews the related literature. Section 3 provides an overview of the EU ETS. Section 4 describes the methodological framework. Section 5 presents the dataset. Section 6 discusses the results. Section 7 outlines policy implications.

2. Literature Review

Studies on the EU ETS have examined a range of topics, including emissions reductions, firm-level impacts, innovation, and the structure of trading relationships. We organize this review around these themes to highlight how our work contributes to and extends existing research. Several papers assess whether the EU ETS has successfully reduced emissions [14,15,16]. Bayer and Aklin [17] showed that the system helped avoid around 1.2 billion tons of CO₂ from 2008 to 2016, even when allowance prices were relatively low. They argued that firms responded not only to current prices but also to the expectation of future tightening, emphasizing the role of policy credibility.

Firm-level studies offer mixed results. According to Joltreau and Sommerfeld [18], most firms in Phases I and II did not experience major changes in competitiveness. This outcome is attributed to permit over-allocation, cost pass-through to consumers, and the relatively low share of energy costs in many sectors. The authors also note that windfall profits further reduced competitive pressure. Regarding innovation, Martin et al. [19] and Teixidó et al. [20] found that the EU ETS encouraged low-carbon innovation, though results were uneven. Free allocation discouraged early investments, and adoption often lagged behind innovation. A lack of micro-level data makes it difficult to assess how incentives evolved in Phase III.

Some studies focus on the network structure of trading. Karpf et al. [9] found that the EU ETS exhibited a core-periphery structure, with a few dominant actors and many peripheral firms. This configuration led to wider bid-ask spreads and reduced access to liquidity for smaller participants, potentially increasing transaction costs and reducing transparency. Their analysis, however, focused on static network features. We extend this by examining how the network evolves over time. Other studies leverage network properties to improve price forecasting. Xu et al. [21] combine network features with extreme learning machines, while Xu and Wang [22] apply visibility graphs to extract structural patterns from carbon price time series. Both papers demonstrate that network-based indicators can increase predictive accuracy, but neither investigates the underlying structure of trading relationships. Recent work explores how the EU ETS trading network changes over time. Flori [23] show that the network responds to shocks in energy commodity markets, with central players in the energy sector influencing the system’s reaction. Flori and Spelta [24] analyse biases in trading patterns, showing that firms tend to trade with partners from the same country or sector. This behaviour limits cross-border flexibility and may reduce market efficiency and resilience.

Our study builds on these findings by integrating DT modelling and ML to simulate the evolution of trading relationships. We examine how the network responds to regulatory shifts and what these structural transitions mean for market resilience. While previous studies emphasize static patterns or price dynamics, our approach introduces a forward-looking, structural perspective to the analysis of the EU ETS.

3. European Union Emissions Trading System

Covering around 40% of the EU’s total greenhouse gas emissions, the European Union Emissions Trading System (EU ETS) stands as the largest and first multinational carbon market [25]. It applies to around 10,000 power stations, industrial facilities, and intra-EU flights, making it the primary policy tool for reducing emissions in the region [26]. The EU ETS operates under a cap-and-trade mechanism, which places a strict upper limit (cap) on total emissions from covered sectors. Within this framework, entities receive or purchase emission allowances, each granting the right to emit one tonne of carbon dioxide equivalent [27]. Since the total number of allowances decreases over time, the system creates a financial incentive for firms to reduce emissions while enabling flexibility in compliance through market-based trading [28].

The EU ETS originates from the 1997 Kyoto Protocol, the first international treaty to establish legally binding emissions reduction targets for industrialized nations. To meet these obligations, the European Commission initiated discussions on emissions trading as a cost-effective policy tool. In March 2000, the Green Paper on Greenhouse Gas Emissions Trading laid the groundwork for the system, identifying fundamental design elements and inviting stakeholder input [29]. This consultation process shaped the final regulatory framework, balancing economic efficiency with environmental effectiveness [30]. The EU formally launched the ETS in 2005, structuring it into distinct compliance periods, or phases, to allow for progressive refinement of the market (see [31] for a critical review of the EU ETS evolution during Phases I–IV).

The first phase (2005–2007) served as a pilot period, establishing an initial carbon price, facilitating emissions trading across the EU, and developing the necessary monitoring, reporting, and verification (MRV) infrastructure. Due to limited historical emissions data, allocation caps were based on estimates, leading to an oversupply of allowances. This surplus caused carbon prices to collapse to zero by 2007, as unused allowances could not be carried over to the second phase [32]. Despite these shortcomings, Phase I provided essential lessons for improving future phases.

Phase II (2008–2012) introduced stricter emissions limits, reducing the cap by approximately 6.5% below 2005 levels. Three additional countries—Iceland, Liechtenstein, and Norway—joined the system, and the scope expanded to cover nitrous oxide (N₂O) emissions from nitric acid production. Free allocation of allowances declined slightly to around 90%, with some countries introducing auctions. Regulators set a penalty of EUR 100 per excess tonne of CO₂ emissions to enforce compliance. Firms could also offset emissions by purchasing international credits, totalizing approximately 1.4 billion tonnes of CO₂ emissions. A major structural change was the transition to a centralized Union Registry, replacing national registries for allowance tracking, alongside the introduction of the European Union Transaction Log (EUTL) to monitor compliance [33]. The aviation sector joined the ETS in 2012, though authorities temporarily suspended enforcement for flights to and from non-European countries. While Phase II benefited from more accurate emissions data, the 2008 financial crisis unexpectedly reduced industrial activity, leading to a surplus of allowances and a prolonged period of low carbon prices [34].

Recognizing the inefficiencies of earlier phases, Phase III (2013–2020) brought significant reforms aimed at improving market stability and effectiveness. To ensure uniformity across member states, the EU replaced national emission caps with a single, EU-wide cap. The allocation of allowances shifted from predominantly free allocation to auctioning as the default method, reducing market distortions. The ETS adopted harmonized rules for the remaining free allocations, giving priority to sectors vulnerable to carbon leakage. Additional sectors and greenhouse gases were brought under regulation, while a reserve of 300 million allowances (NER 300) was set aside to finance renewable energy innovation and carbon capture and storage (CCS) projects. These adjustments increased price stability and encouraged investment in low-carbon technologies [35]. Studies suggest that these reforms reduced emissions without negatively impacting economic competitiveness [36].

Phase IV (2021–2035) aligns with the EU’s broader climate strategy under the European Green Deal and the Fit for 55 legislative package. The overarching objective is to achieve climate neutrality by 2050, with an intermediate goal of reducing net greenhouse gas emissions by at least 55% by 2030. This phase implements several structural adjustments, including a steeper annual reduction in the emissions cap to accelerate decarbonization, a revised allocation system ensuring a gradual transition from free allocation to full auctioning, and an expansion of the Market Stability Reserve (MSR) to address allowance surplus and improve price resilience [37]. Additionally, Phase IV introduces carbon pricing mechanisms for previously uncovered sectors, such as shipping and road transport. Transaction costs remain an ongoing concern, as they may impact liquidity and market efficiency in future phases [28]. By integrating these reforms, the EU ETS aims to improve market efficiency while providing a robust framework for achieving long-term emissions reductions.

4. Methodology

This section outlines the methodological framework we used to analyse the structure, stability, and evolution of the EU ETS trading network. In Section 4.1, we describe how we intend to represent the EU ETS as a complex network. Section 4.2 introduces the DT framework, which allows us to simulate the system’s evolution by incorporating historical trading data and modelling structural changes under different regulatory scenarios. In Section 4.3, we extend this approach by integrating ML techniques into the DT framework to improve the prediction of future trading relationships.

4.1. Complex Network Representation of the EU ETS

We model the European Union Emissions Trading System (EU ETS) as a complex network to analyse its structural characteristics and trading relationships. In this framework, grounded in graph theory, nodes represent countries, and directed edges capture the flow of emissions allowances between them [38]. We assign weights to the edges based on the volume of allowances transferred, enabling a quantitative evaluation of trading intensity and patterns. This network-based approach goes beyond the analysis of isolated transactions by capturing the broader structure of allowance exchanges. Countries with high connectivity occupy central positions in the network, shaping liquidity and potentially influencing price dynamics. By examining the network across different phases of the ETS, we track structural shifts driven by regulatory reforms or external shocks.

To identify which countries are more central and how these roles change over time, we introduce centrality and network density measures indicators in Section 4.1.1 and Section 4.1.2, respectively. These metrics also help assess the degree of market integration. In Section 4.1.3, we present the Louvain method for community detection, a widely used algorithm to identify trading clusters. This approach allows us to evaluate how trading relationships evolve and whether cohesive subgroups emerge or dissolve throughout the system’s development.

4.1.1. Centrality Measures

Centrality measures quantify the relative importance of nodes, revealing influential players and their roles in the emissions market. In a directed network, two distinct degree centralities exist: in-degree and out-degree. We define in-degree centrality $C_D^{in}\left(v\right)$ as $C_D^{in}\left(v\right)={\displaystyle \frac{k_v^{in}}{n-1}}$, where $k_v^{in}$ represents the number of incoming edges to node v. Conversely, we define out-degree centrality $C_D^{out}\left(v\right)$ as $C_D^{out}\left(v\right)={\displaystyle \frac{k_v^{out}}{n-1}}$, where $k_v^{out}$ represents the number of outgoing edges from node v. Here, n represents the total number of nodes in the network. A node’s in-degree centrality measures the number of distinct entities transferring resources or allowances to it, while the out-degree centrality represents the number of distinct entities receiving resources or allowances from it.

The degree distribution $P\left(k\right)$ describes the likelihood of randomly selecting a node with a specific degree in a network. Directed networks have two distinct degree distributions: the in-degree distribution

$$P\left(k^{in}\right)={\displaystyle \frac{\mathrm{Number} \mathrm{of} \mathrm{nodes} \mathrm{with} \mathrm{in}\text{-}\mathrm{degree} k^{in}}{n}},$$

(1)

representing nodes with incoming edges, and the out-degree distribution

$$P\left(k^{out}\right)={\displaystyle \frac{\mathrm{Number} \mathrm{of} \mathrm{nodes} \mathrm{with} \mathrm{out}\text{-}\mathrm{degree} k^{out}}{n}},$$

(2)

representing nodes with outgoing edges. Analysing these distributions helps identify if a small group of countries dominates trading activity or if participation spreads evenly. Skewed distributions indicate market concentration, while flatter distributions reflect broader participation.

4.1.2. Network Density

Network density measures how interconnected the system is by comparing the observed number of edges to the total possible connections. For a directed network, we calculate the density D as:

$$D={\displaystyle \frac{m}{n(n-1)}},$$

(3)

where m is the number of edges. A higher density indicates a more active trading environment with greater market integration. Tracking density changes across EU ETS phases identifies whether trading relationships have become more concentrated or diversified over time.

4.1.3. Community Detection via the Louvain Method

Identifying groups of countries that frequently trade allowances provides insights into market segmentation and trading clusters within directed networks. We apply the Louvain method [7] adapted for directed networks to detect communities, partitioning the network into groups of nodes with stronger internal connections than external ones. The modularity score Q measures the effectiveness of this partitioning for directed networks:

$$Q={\displaystyle \frac{1}{M}}\sum _{i,j}\left(A_{i,j}-{\displaystyle \frac{s_i^{out}{s}_j^{in}}{M}}\right)\delta (c_i,c_j),$$

(4)

where $A_{i,j}$ represents the weight of the directed edge from node i to node j, $s_i^{out}$ and $s_j^{in}$ are the total outgoing and incoming edge weights of these nodes, respectively, M denotes the total edge weight in the directed network, and $\delta (c_i,c_j)$ equals 1 if nodes i and j belong to the same community and 0 otherwise. A higher modularity score indicates clearly defined trading clusters.

The Louvain method for directed networks follows an iterative process, initially assigning each node to its own community, subsequently reassigning nodes to maximize modularity gains, and finally aggregating communities into meta-nodes before repeating these steps. This approach efficiently identifies trading blocs within the EU ETS directed network. Applying community detection across multiple ETS phases helps determine whether trading clusters remain stable or shift due to regulatory or economic changes. Persistent clusters suggest long-term trading alliances, while frequent reconfigurations indicate market responses to policy interventions or external shocks.

4.2. Digital Twins

Regulatory interventions—such as the EU ETS Market Stability Reserve (MSR)—influence how firms form connections in the trading network. The MSR automatically adjusts the supply of allowances based on surplus thresholds, which affects market expectations, liquidity, and the incentives for firms to trade. These shifts, in turn, alter the pattern of connections between participants. Although we do not explicitly model policy rules in the node connection strategy, our analysis accounts for their effects indirectly. We incorporate the structural changes observed in historical trading behaviour—much of which reflects the system-wide influence of the MSR—into the simulation framework. We use a DT approach to simulate how the EU ETS network evolves during Phase IV (beginning July 2021). DTs are virtual representations of physical systems that integrate empirical data with network models to track structural evolution, test resilience, and anticipate future scenarios [39,40]. In our case, the DT relies on observed transaction data to estimate endogenous connection patterns and forecast how trading relationships may shift under changing conditions [41].

We use three dynamic mechanisms to simulate the structural evolution of the EU ETS network within the DT framework. These mechanisms capture how the trading network adapts as new participants enter, existing relationships shift, and communities reorganize. The first mechanism models node entry and link formation via preferential attachment, where new nodes are more likely to connect with highly connected participants. This governs the creation of Twin Nodes, which enter the network and attach to existing nodes with probabilities proportional to node degree, reflecting real-world trading patterns. The degree distributions presented in Equations (1) and (2) determine the likelihood of node selection in this process. The second mechanism introduces edge rewiring and dynamic growth. In each simulation step, we use the same attachment rule to add the Dynamics Nodes, while a portion of existing edges is randomly reconfigured to simulate evolving trade preferences and shifting partnerships. The third mechanism captures community reorganization and modular evolution. Evolving Nodes connect via both degree-based and community-based attachment, where the probability of linking increases with the size of existing communities. The model detects community structure using the Louvain method and merges groups with dense interconnections, simulating sectoral integration or cross-border alliances. As in previous phases, edge rewiring continues to reflect the emergence of new trading relationships during the transition to Phase V.

We initialized the DT using transaction data from Phases I–IV, assigning node attributes such as in-degree and out-degree centrality measures and community memberships, and encoding edge properties including weight, direction, and transaction frequency. These mechanisms together allow the model to simulate the transition into Phase IV and capture anticipated changes in directed trading relationships [42,43]. The preferential attachment model, introduced by [44], describes how new nodes tend to establish directed edges towards nodes with high connectivity, following a “rich-get-richer” mechanism. In our directed network model, we describe the probability of forming a new directed edge from a new node to an existing node i by:

$$P\left(i\right)={\displaystyle \frac{k_i^{in}}{{\sum }_j{k}_j^{in}}}.$$

(5)

This mechanism reflects real-world market behaviour, where well-established participants attract new incoming trading connections. Additionally, we model directed edge formation between existing nodes based on combined in-degree and out-degree centralities, ensuring that influential nodes significantly shape the network structure. The probability of forming a directed edge from node i to node j is:

$$P(i\to j)={\displaystyle \frac{k_i^{out}+k_j^{in}}{{\sum }_{k,l}(k_k^{out}+k_l^{in})}}.$$

(6)

Incorporating directed preferential attachment into the DT framework allows a realistic evolution of directed trading relationships, preserving the influence of highly connected nodes while dynamically enabling new directed connections to emerge [45,46]. The edge rewiring mechanism modifies existing directed trade relationships by selectively replacing edges. The algorithm evaluates each edge and, with a 20% probability, removes and replaces it with a new directed connection. The reassignment ensures new edges do not create duplicate directed links or self-loops, capturing shifts in directed trading relationships as participants disengage from prior connections and establish new ones.

The community reorganization mechanism adjusts the network structure based on internal edge density. First, the Louvain method detects initial communities. The algorithm then measures the density of inter-community connections and identifies clusters with strong cross-links. When the density exceeds a predefined threshold, the model merges the communities, simulating commercial integration as previously distinct groups consolidate through intensified trading relationships. Beyond structural modelling, DTs enable scenario analysis by simulating network responses to policy changes, economic shifts, and regulatory adjustments. Policymakers can test alternative allocation schemes, assess the impact of adding new industrial sectors, or evaluate how interventions affect trading relationships. For example, restricting transactions involving major hubs could expose vulnerabilities in network connectivity and help identify potential systemic risks [47,48,49].

Market participants can also use DTs to refine trading strategies, anticipate price fluctuations, and detect anomalies in transaction patterns. By synchronizing with real-time data, the DT enhances transparency, supports risk mitigation, and strengthens informed decision-making [50,51]. Ultimately, integrating DTs with complex network analysis improves our ability to forecast developments in the EU ETS. This framework provides a structured tool for anticipating new trading relationships, ensuring regulatory compliance, and designing more adaptive and effective climate policies [52].

4.3. Combining Digital Twins with Machine Learning

ML extends the predictive capabilities of DTs, allowing for more precise simulations of network evolution and improving the ability to anticipate structural changes. By learning patterns from past EU ETS phases, ML models identify essential factors influencing edge formation and evolving connectivity dynamics. This integration strengthens the capacity to forecast new trading relationships and detect shifts in the emissions trading system. The modelling process consisted of multiple stages. Historical data from Phases I–IV served as both training and validation sets, incorporating key features such as node degree centrality, edge weights, directional flows, and community properties, including modularity and node density. These features capture structural and behavioural aspects of the EU ETS network, providing a foundation for predicting future link formations. The core objective was to model and predict new edge formations using supervised learning, reflecting how economic, regulatory, and network-driven forces shape the evolution of trading relationships.

To achieve this, we implemented two predictive approaches: GNN and LR. GNNs captured complex dependencies between nodes through iterative message passing, enabling a more refined representation of network structure and link probabilities. LR, in contrast, used hand-crafted structural features—such as node degree, common neighbours, and shortest path length—to estimate the likelihood of link formation. These two methods offered distinct strengths: LR tended to reinforce traditional hubs, favouring connections involving already well-connected nodes, and was thus well suited for confirming persistent trading patterns. GNNs, by contrast, were better equipped to detect emerging or less obvious connections, including those involving previously peripheral participants, due to their ability to learn higher-order patterns directly from the graph. The combination of these methods ensured a balance between interpretability and the ability to uncover novel structural changes.

Integrating DTs with ML-based predictive modelling allowed us to identify emerging trading relationships and anticipate structural adjustments in the EU ETS network. This approach applied network science principles to empirical data, providing a clearer view of market evolution in Phase IV.

4.3.1. Graph Neural Network

GNNs model graph-structured data by learning node representations through iterative message passing. This approach allows each node to incorporate information from its neighbours, gradually expanding its receptive field across multiple layers [53,54]. A GNN updates the node embedding at layer l using:

$$h_v^{(l+1)}=\sigma \left(W^{\left(l\right)}·h_v^{\left(l\right)}+\sum _{u\in \mathcal{N}\left(v\right)}{\displaystyle \frac{1}{c_{vu}}}{W}^{\left(l\right)}·h_u^{\left(l\right)}\right),$$

(7)

where $h_v^{\left(l\right)}$ represents the embedding of node (country) v at layer l, and $\mathcal{N}\left(v\right)$ denotes its set of neighbouring countries. The normalization term $c_{vu}$ is typically set as the number of neighbours or adjusted based on edge weights. The trainable weight matrix $W^{\left(l\right)}$ is updated during training, and $\sigma$ is the activation function. ReLU was used within the GNN layers, while a Sigmoid function generated link existence probabilities between nodes.

GNNs operate through three main steps: message aggregation, node state updates, and final prediction. The aggregation step collects information from neighbouring nodes:

$$m_v^{\left(l\right)}=\sum _{u\in \mathcal{N}\left(v\right)}\mathrm{MSG}\left(h_u^{\left(l\right)},h_v^{\left(l\right)}\right),$$

(8)

where $\mathrm{MSG}(·)$ is a function that processes neighbour information. The node state update follows:

$$h_v^{(l+1)}=\mathrm{UPD}\left(h_v^{\left(l\right)},m_v^{\left(l\right)}\right),$$

(9)

where $\mathrm{UPD}(·)$ incorporates new information. After multiple layers, final embeddings serve as inputs for classification tasks such as edge prediction:

$$P(y=1|X)=\mathrm{Sigmoid}\left(W^{\left(L\right)}{h}_v^{\left(L\right)}\right).$$

(10)

4.3.2. Logistic Regression

LR [4,5] served as a complementary predictive method, offering a simpler yet effective approach for classifying new link formations. The model estimated the probability that an edge exists between two nodes based on structural features such as degree centrality, common neighbours, and preferential attachment. The probability of edge formation is as follows:

$$P(y=1|X)={\displaystyle \frac{1}{1+e^{-({\beta }_0+{\sum }_{i=1}^3{\beta }_i{x}_i)}}},$$

(11)

where $x_1$ represents node degree, $x_2$ captures the number of shared neighbours, and $x_3$ models the preferential attachment mechanism we find. Positive examples are derived from existing edges, while negative examples are randomly sampled non-edges. Negative sampling ensures the model learns to distinguish real connections from randomly generated node pairs. To optimize model performance, we split the dataset into 80% training and 20% testing, using cross-validation to prevent overfitting. The final model classifies node pairs based on a probability threshold, typically set at 0.5:

$$\widehat{y}=\left\{\begin{array}{ccc}1\hfill & \mathrm{if}& P(y=1|X)\ge 0.5\hfill \\ 0\hfill & \mathrm{if}& P(y=1|X)<0.5\hfill \end{array}\right.$$

(12)

4.3.3. Evaluation Metrics

To assess the predictive accuracy of our models, we employed several widely used classification metrics [55]. Given that our objective was to predict the formation of new trading relationships in the EU ETS, it was essential to evaluate how well the model distinguished between actual and predicted edges. One of the primary tools for model evaluation is the Receiver Operating Characteristic (ROC) curve, which illustrates the trade-off between the true positive rate (sensitivity) and the false positive rate at different classification thresholds. The Area Under the Curve (AUC) quantifies the model’s ability to differentiate between edges (existing or future links) and non-edges (absence of a trading relationship). A higher AUC indicates a stronger predictive capability, as the model effectively ranks true edges higher than false ones.

Since the dataset was inherently imbalanced—new edges were relatively rare compared to non-edges—standard accuracy alone was not a reliable measure of performance. Instead, we employed precision, recall, and F1-score to provide a more nuanced evaluation. Precision measures the proportion of predicted edges that are actual edges. A high precision value indicates that the model makes fewer false positive predictions, meaning it does not mistakenly classify non-existent links as valid trading relationships. This is particularly important in regulatory and market analyses, where incorrectly predicting a link could lead to misleading conclusions about emerging trading structures. Recall (or sensitivity) measures the proportion of actual edges that the model correctly identifies. High recall means we capture most existing or emerging trading relationships, even if we allow some false positives. This metric is indispensable when the priority is to identify as many potential link formations as possible, even at the risk of occasional misclassification. F1-score is the harmonic mean of precision and recall, balancing both concerns. It provides a single measure of model performance when there is a trade-off between precision and recall. This is particularly relevant in our context, as overlooking a potential trading relationship (false negative) and incorrectly predicting an edge (false positive) have different implications for market analysis.

Given the complexity of emissions trading networks, an ideal model should achieve a balance between high precision and high recall, ensuring that predicted trading relationships are both accurate and comprehensive. We report these metrics to evaluate the robustness of our predictions.

5. Data

We used transaction and account data from the European Union Transaction Log (EUTL) (https://ec.europa.eu/clima/ets/welcome.do?languageCode=en (accessed on 10 June 2025)), which records all transfers of emissions allowances within the EU ETS (the routines to extract the data sources are available at https://github.com/jabrell/eutl_scraper). The dataset contained 1,997,165 records, including details on transaction IDs, transaction dates, transferring and acquiring account IDs, and the volume of allowances exchanged. Additionally, account-level data provided information on the account holder, account type, and the country where the account was registered. We present a detailed dictionary of these variables in

Table A1. Dictionary of variables for transaction and account data. The registry_id codes correspond to those presented in Table A2.

Variable	Description
Transaction variables
transactionID	ID of the transaction in which the transaction block took place
transferringAccount id	Identifier of the account that transferred the permits
acquiringAccount id	Identifier of the account that acquired permits
amount	Number of units transferred
Account variables
id	Unique account identifier
name	Name of account
registry id	Two-letter ISO code for registry

and

Table A2. Country codes and descriptions.

Code	Description	Code	Description
AT	Austria	AU	Australia
BE	Belgium	BG	Bulgaria
CDM	Clean Development Mechanism	CH	Switzerland
CY (CY0)	Cyprus	CZ	Czech Republic
DE	Germany	DK	Denmark
EC	European Commission	EE	Estonia
ES	Spain	EU	European Union
FI	Finland	FR	France
GB	United Kingdom	GR	Greece
HR	Croatia	HU	Hungary
IE	Ireland	IS	Iceland
IT	Italy	JP	Japan
LI	Liechtenstein	LT	Lithuania
LU	Luxembourg	LV	Latvia
MT (MT0)	Malta	NL	Netherlands
NO	Norway	NZ	New Zealand
PL	Poland	PT	Portugal
RO	Romania	RU	Russian Federation
SE	Sweden	SI	Slovenia
SK	Slovakia	UA	Ukraine
XI	Northern Ireland

(Appendix A).

The EUTL dataset distinguishes between the registry administering an account and the country where it operates. An entity can register an account in a different country due to factors such as regulatory requirements, fiscal advantages, or the need to access specific exchange platforms that mandate registry compliance [10]. However, Annex XIV(4) of Regulation 389/2013 states that the EUTL publishes transaction records only on May 1 of the third year following the transaction date (see the Commission Regulation (EU) No389/2013 (https://eur-lex.europa.eu/eli/reg/2013/389/oj) for further details). This delayed disclosure affects the timeliness of market analysis.

A fundamental limitation of this dataset is its focus on transfers rather than direct market trades, leaving out critical transaction details such as trade execution prices. This issue occurs because allowance transactions often take place in futures markets, where agreements settle at a later date, and the final transferred amount may not reflect intra-day price variations. Without observed trading prices, assessing supply and demand dynamics at specific points in time becomes difficult, limiting the ability to evaluate market efficiency and price formation mechanisms.

Another challenge is the loss of direct counterparty information. Because intermediaries, such as clearinghouses, clear many transactions, the dataset does not reveal the original buyer–seller relationships. This complicates network analysis, as the actual trading structure cannot be fully reconstructed. Furthermore, this means that our reconstructed network may underestimate the centrality of key participants, since our data may include records between intermediary accounts instead of direct links. In other words, some hidden nodes, particularly intermediary hubs, may not be identifiable, potentially biasing centrality and community detection results.

The dataset also reveals a recurring spike in transaction volume every December, reflecting regulatory deadlines and the settlement of futures contracts. These annual surges underscore the discrepancy between observed transfers and actual market trades, reinforcing the need for more granular data, such as real-time trade records and transaction prices, to improve market analysis. In the absence of complete transaction-level data, network modelling offers an alternative approach to infer interactions between market participants. Historical patterns can help reconstruct missing relationships, allowing for a more detailed examination of market structure and dynamics. However, the dataset’s limitations underscore the need for access to more detailed records to fully capture trading behaviour within the EU ETS.

6. Results

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. Descriptive statistics of the number of transactions per installation.

	Obs	Mean	Std. Dev.	Min	25%	50%	75%	Max
Transactions	16,898	235.79	218.51	1	92.5	185	305.5	1840

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. Community transitions of countries across Phases I–IV.

	Community
Country	Phase I	Phase II	Phase III	Phase IV
AT	5	2	4	3
AU	-	5	2	-
BE	2	4	5	8
BG	-	3	3	21
CDM	-	4	5	-
CH	-	2	4	-
CY	-	5	3	7
CY0	1	6	-	-
CZ	2	3	2	21
DE	5	1	5	21
DK	4	3	1	16
EE	4	2	4	20
ES	3	4	3	2
EU	-	5	3	20
FI	4	2	4	17
FR	1	1	2	19
GB	1	5	2	20
GR	1	1	3	15
HR	-	8	1	18
HU	2	3	2	21
IE	5	5	4	10
IS	-	5	1	-
IT	3	5	1	14
JP	-	3	2	-
LI	-	2	5	-
LT	4	1	4	4
LU	1	4	5	1
LV	4	2	4	11
MT	-	5	3	21
MT0	6	7	-	-
NL	2	1	2	6
NO	-	4	4	-
NZ	-	1	2	-
PL	2	2	4	13
PT	3	5	3	9
RO	-	2	3	12
RU	-	1	5	-
SE	5	4	4	20
SI	5	1	1	5
SK	2	2	2	10
UA	-	4	4	-
XI	-	5	2	-

(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. Ranking of centrality.

Country	Phase I	Country	Phase II	Country	Phase III	Country	Phase IV
FR	1.88	GB	1.78	GB	1.95	EU	1.00
NL	1.88	DE	1.59	DE	1.90	DE	0.21
GB	1.79	FR	1.59	NL	1.90	BG	0.18
DK	1.71	NL	1.59	IT	1.74	SK	0.14
DE	1.58	DK	1.54	ES	1.69	IE	0.14
AT	1.46	IT	1.39	EU	1.69	HU	0.14
ES	1.25	CH	1.34	FR	1.69	CZ	0.14
CZ	1.17	PL	1.32	CH	1.44	SI	0.11
FI	1.17	ES	1.27	PL	1.41	RO	0.11
IT	1.08	AT	1.22	CZ	1.33	PT	0.11
BE	1.04	BE	1.22	BE	1.31	PL	0.11
PL	0.88	CZ	1.20	BG	1.31	NL	0.11
SE	0.88	SE	1.20	NO	1.28	LV	0.11
SK	0.83	SK	1.17	AT	1.26	LU	0.11
HU	0.79	FI	1.10	SE	1.26	LT	0.11
IE	0.79	LI	1.10	SI	1.23	IT	0.11
LT	0.79	NO	1.07	DK	1.13	HR	0.11
EE	0.75	RO	1.07	FI	1.13	GR	0.11
LV	0.71	EE	1.05	IE	1.08	FR	0.11
PT	0.63	BG	0.98	MT	1.05	FI	0.11
GR	0.42	HU	0.93	RO	1.05	ES	0.11
SI	0.38	IE	0.93	SK	1.03	EE	0.11
LU	0.25	SI	0.90	EE	0.90	DK	0.11
CY0	0.17	EU	0.80	HU	0.90	CY	0.11
MT0	0.08	PT	0.78	LT	0.85	BE	0.11
-	-	LV	0.76	PT	0.85	AT	0.11
-	-	GR	0.73	GR	0.79	MT	0.07
-	-	LT	0.73	LU	0.77	SE	0.04
-	-	JP	0.68	LV	0.77	GB	0.04
-	-	LU	0.66	JP	0.64	-	-
-	-	CDM	0.39	CY	0.59	-	-
-	-	NZ	0.34	HR	0.59	-	-
-	-	UA	0.24	IS	0.59	-	-
-	-	CY	0.17	CDM	0.44	-	-
-	-	XI	0.15	NZ	0.38	-	-
-	-	RU	0.12	XI	0.38	-	-
-	-	IS	0.10	AU	0.36	-	-
-	-	MT	0.10	RU	0.36	-	-
-	-	AU	0.05	LI	0.28	-	-
-	-	CY0	0.05	UA	0.26	-	-
-	-	HR	0.05	-	-	-	-
-	-	MT0	0.05	-	-	-	-

(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 $Twin.Node\_i$, where $i\in \{1,\dots ,s\}$. 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. Evaluation of GNN model performance for edge prediction.

Epoch	Train Loss	Test Loss	Test AUC
0	0.6982	0.7146	0.5357
10	0.6164	0.6599	0.6214
20	0.5017	0.6749	0.7357
30	0.4178	0.6940	0.7071
40	0.3888	0.7094	0.7286
50	0.3687	0.6787	0.7357

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. Evaluation metrics for edge prediction using Logistic Regression.

AUC Score	Precision	Recall	F1-Score
0.9500	0.9333	1.0000	0.9655

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.

7. Conclusions

This paper applied DT modelling, complex network analysis, and ML to study the structural evolution of trading relationships in the European Union Emissions Trading System (EU ETS). Using detailed transaction data, we documented a shift from a hub-dominated network to a more structurally reconfigured system. Our results showed that while some trading clusters persisted, others reorganized in response to regulatory adjustments and firm behaviour. Additionally, we made a novel contribution by combining DT simulations with ML models—specifically Graph Neural Networks and LR—to analyse how carbon trading networks evolved under shifting conditions. While earlier research explored static properties or price-based dynamics, our forward-looking approach emphasized structural resilience and coordination challenges that are often overlooked in price-based analyses. By forecasting future link formation, we assessed whether the EU ETS trading network could absorb increased market activity.

Incorporating sustainability metrics and explicitly modelling environmental outcomes alongside economic performance would strengthen the predictive power of these analyses, supporting policymakers in designing robust market structures that reliably promote environmental sustainability. Building on this framework, future research could extend DT simulations by incorporating firm-level behavioural assumptions—such as compliance strategies or risk preferences—to better capture the microfoundations of trading dynamics. Additional work could also integrate environmental and economic performance metrics more explicitly into the modelling environment. Future extensions could also incorporate key regulatory elements (MSR thresholds, for example) directly into the node connection strategy, enabling simulations to reflect the impact of policy interventions on network formation. Another promising avenue involves addressing the issue of hidden hub nodes caused by intermediary clearinghouses in transaction data. Supplementary datasets or methods to disaggregate these relationships could improve network reconstruction and the accuracy of centrality-based diagnostics. Applying this approach to other emissions trading systems or emerging cross-border carbon markets could offer comparative insights into the structural resilience and efficiency of different market designs. These results suggest that regulatory oversight should go beyond price monitoring to include the structure of trading relationships. Incorporating network diagnostics into market surveillance could help identify early signs of structural stress and guide targeted interventions. Ultimately, reinforcing market structure resilience contributes directly to the broader goal of achieving sustainable emissions reductions and maintaining momentum toward Europe’s climate neutrality targets.

Our modelling exercise has some limitations. First, the transaction data record quota transfers but do not include price or bilateral trade details, limiting our ability to fully reconstruct market-level incentives. Second, while the DT framework simulates structural evolution based on historical patterns, it does not incorporate agent-level decision-making or external shocks. Finally, the findings are specific to the EU ETS and may not generalize directly to other carbon markets without contextual adjustments. Importantly, our argument regarding the link between market structure and sustainability rested on theoretical reasoning and economic intuition, not direct empirical measurement. We did not quantify transaction frictions or price differentials across communities in this analysis. Future work could address this by empirically examining micro-level frictions—such as the frequency of cross-cluster trades, transaction delays, or price dispersion—and constructing indicators to reflect the cost of trading across heterogeneous network components. Such analysis would help establish a clearer causal link between network topology and sustainability outcomes.