A Depth-Aware Comparative Study of Euclidean and Hyperbolic Graph Neural Networks on Bitcoin Transaction Systems

2026-03-16

AI Summary

This study addresses the underexplored interaction between neighborhood aggregation depth and embedding geometry in node classification on Bitcoin transaction networks. Under a fixed model architecture and embedding dimensionality, the authors systematically compare Euclidean and tangent-space hyperbolic graph neural networks across varying neighborhood depths using a controlled experimental design. Their analysis reveals, for the first time, a coupling effect between aggregation depth and geometric space, demonstrating that joint optimization of learning rate and curvature is critical for stabilizing high-dimensional hyperbolic embeddings. These findings offer practical guidance for selecting geometric spaces and configuring neighborhood depth in large-scale transaction network modeling, significantly enhancing the deployment efficacy of hyperbolic GNNs in computational social systems.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Machine Learning: Learning with Manifolds
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Social Networks and Social Media: Computational social science
• Economics, Online Markets and Human Computation: Social networks and social learning

Abstract

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.

Problem

• Graph Neural Networks
• Hyperbolic Geometry
• Bitcoin Transaction Networks
• Node Classification
• Neighborhood Aggregation

Innovation

• Hyperbolic GNNs
• Euclidean vs Hyperbolic Embeddings
• Neighborhood Depth
• Curvature Optimization
• Bitcoin Transaction Networks