Bitcoin transaction networks are large scale socio- technical systems in which activities are represented through multi-hop interaction patterns. Graph Neural Networks(GNNs) have become a widely adopted tool for analyzing such systems, supporting tasks such as entity detection and transaction classification. Large-scale datasets like Elliptic have allowed for a rise in the analysis of these systems and in tasks such as fraud detection. In these settings, the amount of transactional context available to each node is determined by the neighborhood aggregation and sampling strategies, yet the interaction between these receptive fields and embedding geometry has received limited attention. In this work, we conduct a controlled comparison of Euclidean and tangent-space hyperbolic GNNs for node classification on a large Bitcoin transaction graph. By explicitly varying the neighborhood while keeping the model architecture and dimensionality fixed, we analyze the differences in two embedding spaces. We further examine optimization behavior and observe that joint selection of learning rate and curvature plays a critical role in stabilizing high-dimensional hyperbolic embeddings. Overall, our findings provide practical insights into the role of embedding geometry and neighborhood depth when modeling large-scale transaction networks, informing the deployment of hyperbolic GNNs for computational social systems.
Figures & tables
Dataset
Models
Metrics
Geometry
Paper
New BTC Graph
Elliptic
GCN
GraphSAGE
GAT
HyperGNN
Precision
Recall
F1
Euclidean
Hyperbolic
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TABLE I: Comparison of prior work by dataset, models, metrics, and embedding geometry.
Fig. 1: Workflow for Bitcoin Address Classification.
Fig. 2: HyperbolicSAGE architecture showing the computational flow across layers.
Layers
Metric
GCN
HGCN
GraphSAGE
HGraphSAGE
GAT
HGAT
2-layer
Precision
0.68
0.67
0.81
0.82
0.79
0.82
Recall
0.49
0.55
0.67
0.71
0.65
0.71
Macro-F1
0.55
0.59
0.72
0.76
0.71
0.75
3-layer
Precision
0.67
0.75
0.82
0.87
0.79
0.86
Recall
0.54
0.57
0.67
0.75
0.69
0.72
Macro-F1
0.59
0.64
0.73
0.80
0.73
0.78
TABLE II: Node classification performance on depth-two subgraphs (macro-averaged). Columns correspond to different GNN architectures; rows indicate model depth and evaluation metric. The highest value in each row is highlighted in bold.
Layers
Metric
GCN
HGCN
GraphSAGE
HGraphSAGE
GAT
HGAT
2-layer
Precision
0.68
0.74
0.84
0.83
0.77
0.85
Recall
0.52
0.58
0.72
0.71
0.70
0.71
Macro-F1
0.58
0.64
0.77
0.76
0.73
0.77
3-layer
Precision
0.71
0.74
0.84
0.88
0.85
0.86
Recall
0.60
0.63
0.73
0.76
0.73
0.77
Macro-F1
0.64
0.68
0.78
0.81
0.78
0.81
TABLE III: Node classification performance on depth-three subgraphs (macro-averaged). Columns correspond to different GNN architectures; rows indicate model depth and evaluation metric. The highest value in each row is highlighted in bold.
Class
Metric
GCN
HGCN
GraphSAGE
HGraphSAGE
GAT
HGAT
BET
Precision
0.96
0.96
0.97
0.98
0.97
0.98
Recall
0.95
0.96
0.99
0.99
0.99
0.99
F1
0.95
0.96
0.98
0.99
0.98
0.99
EXCHANGE
Precision
0.73
0.67
0.83
0.85
0.84
0.82
Recall
0.40
0.53
0.62
0.67
0.63
0.70
F1
0.51
0.59
0.71
0.75
0.72
0.76
TABLE IV: Per-class node classification performance (macro-averaged metrics) for selected Euclidean and hyperbolic GNNs. Bold indicates the best value per class; ties are all bolded.
Fig. 3: Macro-F1 versus learning rate for different curvature ( c ) in tangent-space Hyperbolic GraphSAGE. Low curvature values at low to moderate learning rates produce large regions of convergent but uninformative solutions. Moderate to high curvature values achieve effective performance across a wider learning-rate range, highlighting the importance of joint learning-rate and curvature selection.
Facultad de Ingenier´ıa, Universidad de la Rep´ublica, Uruguay · Centro Interdisciplinario en Ciencia de Datos y Aprendizaje Autom´atico (CICADA), Universidad de la Rep´ublica, Uruguay