Elliptic2: AML Graph Benchmark on Bitcoin

• Elliptic2 is a graph-based machine learning benchmark designed for anti-money laundering research on Bitcoin.
• It models Bitcoin address clusters as nodes and aggregates transactions as directed edges over 121,810 labeled subgraphs with notable class imbalance.
• The dataset supports evaluation of graph neural networks using detailed subgraph extraction, advanced evaluation protocols, and implementations such as GLASS.

Elliptic2 is a large-scale, publicly available graph-based machine learning benchmark for anti-money laundering (AML) research on the Bitcoin blockchain. Designed for high-fidelity subgraph representation learning, Elliptic2 models Bitcoin address clusters (“entities”) as nodes and aggregate transactions as directed edges in a massive background graph. The dataset provides 121,810 extracted subgraphs with licit and suspicious labels, supporting principled evaluation of graph neural network (GNN) approaches for the identification of money laundering structures. Elliptic2’s construction logic, feature modalities, evaluation protocols, and insights into laundering behaviors have made it a standard in the intersection of blockchain analytics and machine learning (Song et al., 2024, Bellei et al., 2024).

1. Graph Modeling and Dataset Structure

Elliptic2 abstracts the Bitcoin blockchain as a directed graph $G = (V, E)$, in which:

• $V$ represents "entities" (address-clusters), where each node corresponds to a set of Bitcoin addresses heuristically controlled by a single real-world actor.
• $E \subset V \times V$ denotes directed edges, with edge $(u,v)$ indicating one or more Bitcoin transactions sent from entity $u$ to $v$ across the observed history (Song et al., 2024).

The adjacency matrix $A \in \{0,1\}^{|V| \times |V|}$ encodes presence or absence of directed transaction-aggregates. There is no time-step segmentation; all edges aggregate transactions over the dataset's scope (one-year interval in the principal release) (Bellei et al., 2024).

2. Scale, Features, and Data Schema

Scale and Composition

The background graph comprises:

• $|V| = 49,299,864$ clusters (nodes)
• $|E| = 196,215,606$ directed edges This places Elliptic2 at the upper end of real-world graph datasets in both AML and general graph ML contexts (Song et al., 2024, Bellei et al., 2024).

Feature Modalities

Each node $v$ carries a feature vector $V$0 ($V$1 in the primary release). Features derive from blockchain primitives and entity heuristics, capturing:

• Cluster size (address count)
• Transaction counts (in/out), volumes (total BTC sent/received)
• Degree statistics, temporal activity range (first/last timestamp)
• Statistical flow descriptors (mean, variance over sliding windows)
• Entity type markers (exchange, miner, service) Continuous quantities are discretized into $V$2 bins: $V$3, with no further normalization (Bellei et al., 2024).

Edge features (95 dimensions) encode aggregate transaction properties (volume, fee, timestamp, interarrival time) and are binned or ordinalized to maintain privacy and scalability.

Data Format

Elliptic2 is released as:

• edge_list.csv: $V$4
• node_features.csv: $V$5
• subgraphs.json: $V$6 "id": $V$7, "nodes": [...], "label": 0/1 $V$8 Loading pipelines support pandas, NetworkX, and PyTorch-Geometric; Python reference code is provided (Bellei et al., 2024).

3. Subgraph Extraction, Label Definition, and Class Balance

Subgraph Construction

Subgraphs $V$9 are extracted around flows detected between illicit and licit entities. Key terminology:

• “Sources”: nodes with zero in-degree in $E \subset V \times V$0
• “Sinks”: nodes with zero out-degree in $E \subset V \times V$1
• “Senders” $E \subset V \times V$2: nodes external to $E \subset V \times V$3 with edges into source(s)
• “Receivers” $E \subset V \times V$4: nodes outside $E \subset V \times V$5 pointed to by sink(s)

Subgraph extraction:

1. Seeds labeled nodes (licit/illicit), expands by up to $E \subset V \times V$6 hops using breadth- or depth-limited traversal.
2. Stops expansion if another labeled node is reached.
3. Retains connected components of consistently labeled paths.
4. A subgraph is "suspicious" if senders include illicit nodes and receivers are all licit; "licit" if both are licit (Song et al., 2024, Bellei et al., 2024).

Label Assignment and Imbalance

Out of 121,810 labeled subgraphs:

• Licit: $E \subset V \times V$7 119,092 (97.8%)
• Suspicious: $E \subset V \times V$8 2,718 (2.2%) Labeling is grounded in proprietary on-chain/off-chain attribution; the dataset reflects an extreme class imbalance (Song et al., 2024).

Subgraph Class	Count	Proportion
Licit	119,092	97.8%
Suspicious	2,718	2.2%

A plausible implication is that evaluation under class imbalance necessitates metrics such as PR-AUC and F1 (positive = suspicious).

4. Benchmarking Tasks, Splits, and Evaluation Protocols

Benchmark Splits

The labeled subgraphs are randomly partitioned into 80% training, 10% validation, and 10% test sets (Song et al., 2024, Bellei et al., 2024).

Primary Tasks

1. Subgraph Classification: Predict $E \subset V \times V$9 (“licit” vs. "suspicious") given subgraph $(u,v)$0 and features.
2. Subgraph Discovery: Efficiently propose and rank candidate suspicious subgraphs without prior knowledge of $(u,v)$1.

Evaluation Metrics

• Subgraph classification:
  • PR-AUC (precision-recall area under curve)
  • F1-score (micro-averaged, suspicious is positive)
• Subgraph discovery:
  • Hit Ratio@k (HR@k)
  • NDCG@k (Normalized Discounted Cumulative Gain)
  • These metrics directly address the dataset's class imbalance and ranking-focused downstream applications (Song et al., 2024).

Result Summary

GLASS, a subgraph GNN leveraging the full background graph with a binary membership feature, achieves state-of-the-art performance (F1 = 0.933, PR-AUC = 0.208, ROC-AUC = 0.889), surpassing baselines such as GNN-Seg and Sub2Vec (Bellei et al., 2024).

5. Reference Implementations and Workflow

The released software stack enables scalable experimentation leveraging:

• PyTorch-Geometric with custom data loaders
• Subgraph sampling techniques (e.g., leveraging SALIENT/SALIENT++ for multi-machine batch sampling)
• Support for both baseline (“GNN-Seg”) and advanced (“GLASS”) subgraph GNN paradigms
• Feature embeddings via integer-indexed tables, in-graph neighborhood sampling, and mini-batching workflows (Bellei et al., 2024)

This architecture is designed for efficient, out-of-core training on large graphs and supports extensibility to alternative subgraph/minibatch extraction schemes.

6. Forensic Insights and Domain-Specific Structures

Analysis of model-flagged subgraphs on Elliptic2 has provided empirical evidence of recurring money-laundering patterns, notably:

• Peeling chains: characterized by sequential, small-value transactions sweeping toward regulated exchanges.
• Nested services: routes via unregulated intermediaries yielding distinctive “Y-shape” connectivity signatures.

Post-hoc exchange validation found that 26.9% of recipient accounts in flagged subgraphs were tied to laundering, compared to a $(u,v)$20.1% baseline in the general account population (Bellei et al., 2024).

A plausible implication is that subgraph “shape” analysis can surface previously undetected laundering strategies.

7. Extensions, Limitations, and Prospects

While Elliptic2 targets Bitcoin, the core pipeline—address clustering, path extraction, subgraph labeling—generalizes to other transactional blockchains (e.g., Ethereum) and even interbank transfer networks. Limitations include dependence on partial ground truth and the absence of explicit temporal segmentation in the released edge data. Ongoing opportunities exist to refine extraction routines, extend entity heuristics, and apply the benchmark to alternative networks where subgraph signatures are indicative of layering, structuring, or integration in illegitimate flows (Bellei et al., 2024, Song et al., 2024).