Random Walk Guided Hyperbolic Graph Distillation

TL;DR

HyDRO introduces a hyperbolic graph distillation method guided by random walks, effectively capturing complex geometric and dynamic properties of graphs, leading to improved task performance and robustness in graph learning tasks.

Contribution

The paper proposes HyDRO, a novel hyperbolic graph distillation approach that captures geometric and dynamic graph properties, outperforming existing Euclidean-based methods.

Findings

HyDRO outperforms state-of-the-art methods in node classification and link prediction.

HyDRO preserves graph random walk properties for better continual learning.

HyDRO achieves competitive results on graph distillation benchmarks with strong privacy-utility balance.

Abstract

Graph distillation (GD) is an effective approach to extract useful information from large-scale network structures. However, existing methods, which operate in Euclidean space to generate condensed graphs, struggle to capture the inherent tree-like geometry of real-world networks, resulting in distilled graphs with limited task-specific information for downstream tasks. Furthermore, these methods often fail to extract dynamic properties from graphs, which are crucial for understanding information flow and facilitating graph continual learning. This paper presents the Hyperbolic Graph Distillation with Random Walks Optimization (HyDRO), a novel graph distillation approach that leverages hyperbolic embeddings to capture complex geometric patterns and optimize the spectral gap in hyperbolic space. Experiments show that HyDRO demonstrates strong task generalization, consistently outperforming state-of-the-art methods in both node classification and link prediction tasks. HyDRO also effectively preserves graph random walk properties, producing condensed graphs that achieve enhanced performance in continual graph learning. Additionally, HyDRO achieves competitive results on mainstream graph distillation benchmarks, while maintaining a strong balance between privacy and utility, and exhibiting robust resistance to noises.