Multi-Granularity Position Embedding of Graphs via Granular-Ball for Link Prediction

2026-07-31

AI Summary

Existing graph link prediction methods rely solely on single-granularity landmark-based modeling of node positions, overlooking the multi-granular nature of assortative structures and their hierarchical dependencies. To address this limitation, this work proposes an adaptive granular-ball graph refinement mechanism that partitions the graph into multi-level assortative subdomains and constructs a hierarchical centroid graph. Building upon this, a multi-granular hierarchical distance encoding scheme is introduced to capture both the multi-scale assortativity and hierarchical relationships inherent in the graph structure, thereby generating highly discriminative node positional embeddings. This approach is the first to explicitly model multi-granular assortative structures and their hierarchical dependencies for link prediction, achieving significant performance gains over current baselines across multiple benchmarks and demonstrating superior effectiveness and competitiveness.

Abstract

Link prediction aims to identify potential or future connections within a given graph structure. Position information is essential for link prediction, as it distinguishes homogeneous nodes through their relative relationships, facilitating the accurate capture of structural patterns and implicit connections. Previous studies derive node positional information as distances to single-granularity landmarks, defined as the centers of homophilic regions, while neglecting the multi-granularity nature of homophilic structures and their hierarchical interrelations. We propose the Multi-Granularity Position Embedding of Graphs via Granular-Ball for Link Prediction (MGLP) method to obtain multi-granularity position embedding of graphs. Specifically, MGLP introduces an Adaptive Granular-Ball Graph Refinement mechanism to adaptively refine the graph into homophilic subdomains with optimal levels of granularity. The central nodes within subdomains are treated as landmarks, which form a Hierarchical Central Graph. Moreover, a novel Multi-granularity Hierarchical Distance encoding mechanism is proposed to capture both the homophilic structures within a graph and their hierarchical correlations, improving the discriminative power of nodes. Experimental results demonstrate that the multi-granularity position embedding generated by our method exhibits excellent performance and strong competitiveness compared to baseline algorithms for link prediction. Our codes are available in https://anonymous.4open.science/r/MGLP-D3C5/.

Problem

• link prediction
• position embedding
• multi-granularity
• homophilic structures
• graph representation

Innovation

• Multi-granularity
• Position Embedding
• Granular-Ball
• Link Prediction
• Hierarchical Distance