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

TL;DR

This study compares Euclidean and hyperbolic graph neural networks in analyzing large Bitcoin transaction networks, revealing how embedding geometry and neighborhood size affect model performance and stability.

Contribution

It provides a controlled comparison of Euclidean and hyperbolic GNNs, highlighting the impact of neighborhood sampling and embedding geometry on large-scale transaction network analysis.

Findings

Hyperbolic GNNs require careful tuning of learning rate and curvature.

Embedding geometry influences the effectiveness of neighborhood aggregation.

Hyperbolic embeddings can stabilize high-dimensional representations with proper optimization.

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.