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

arXiv: https://arxiv.org/abs/2607.29115 · HTML: https://mlsanity.com/paper/2607.29115/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 36 references that are in the map.
- First posted on arXiv 31 Jul 2026.

## Builds on (most cited first, 21 of 21)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [Rethinking Graph Transformers with Spectral Attention](https://mlsanity.com/paper/2106.03893/) (2021)
- [Neural Bellman-Ford Networks: A General Graph Neural Network Framework for Link Prediction](https://mlsanity.com/paper/2106.06935/) (2021)
- [A Review of Relational Machine Learning for Knowledge Graphs](https://mlsanity.com/paper/1503.00759/) (2015)
- [Position-aware Graph Neural Networks](https://mlsanity.com/paper/1906.04817/) (2019)
- [End-to-end Structure-Aware Convolutional Networks for Knowledge Base Completion](https://mlsanity.com/paper/1811.04441/) (2018)
- [Knowledge-aware Graph Neural Networks with Label Smoothness Regularization for Recommender Systems](https://mlsanity.com/paper/1905.04413/) (2019)
- [Adversarially Regularized Graph Autoencoder for Graph Embedding](https://mlsanity.com/paper/1802.04407/) (2018)
- [Hierarchical Temporal Convolutional Networks for Dynamic Recommender Systems](https://mlsanity.com/paper/1904.04381/) (2019)
- [Hierarchical Position Embedding of Graphs with Landmarks and Clustering for Link Prediction](https://mlsanity.com/paper/2402.08174/) (2024)

## Abstract (arXiv)

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/.