通过分球机制捕捉图结构多粒度位置信息，提升链接预测性能

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/.