# Leveraging Personalized PageRank and Higher-Order Topological Structures for Heterophily Mitigation in Graph Neural Networks

arXiv: https://arxiv.org/abs/2507.16347 · HTML: https://mlsanity.com/paper/2507.16347/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 45 references that are in the map.
- First posted on arXiv 22 Jul 2025.

## Builds on (most cited first, 29 of 29)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Graph Neural Networks with convolutional ARMA filters](https://mlsanity.com/paper/1901.01343/) (2019)
- [How Powerful are Spectral Graph Neural Networks](https://mlsanity.com/paper/2205.11172/) (2022)
- [Networks beyond pairwise interactions: structure and dynamics](https://mlsanity.com/paper/2006.01764/) (2020)
- [Higher-order organization of complex networks](https://mlsanity.com/paper/1612.08447/) (2016)
- [Simplicial Neural Networks](https://mlsanity.com/paper/2010.03633/) (2020)
- [Random Walks on Simplicial Complexes and the normalized Hodge 1-Laplacian](https://mlsanity.com/paper/1807.05044/) (2018)
- [Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond](https://mlsanity.com/paper/2101.05510/) (2021)
- [Principled Simplicial Neural Networks for Trajectory Prediction](https://mlsanity.com/paper/2102.10058/) (2021)
- [Simplicial Convolutional Neural Networks](https://mlsanity.com/paper/2110.02585/) (2021)
- [BScNets: Block Simplicial Complex Neural Networks](https://mlsanity.com/paper/2112.06826/) (2021)
- [Efficient Algorithms for Personalized PageRank Computation: A Survey](https://mlsanity.com/paper/2403.05198/) (2024)
- [Simplicial Complex Representation Learning](https://mlsanity.com/paper/2103.04046/) (2021)
- [SGAT: Simplicial Graph Attention Network](https://mlsanity.com/paper/2207.11761/) (2022)
- [Higher-order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexes](https://mlsanity.com/paper/2309.12971/) (2023)
- [Facilitating Graph Neural Networks with Random Walk on Simplicial Complexes](https://mlsanity.com/paper/2310.19285/) (2023)
- [Simplex2Vec embeddings for community detection in simplicial complexes](https://mlsanity.com/paper/1906.09068/) (2019)
- [Dynamics on higher-order networks: A review](https://mlsanity.com/paper/2203.06601/) (2022)
- [Accelerating Personalized PageRank Vector Computation](https://mlsanity.com/paper/2306.02102/) (2023)
- [Refining Latent Homophilic Structures over Heterophilic Graphs for Robust Graph Convolution Networks](https://mlsanity.com/paper/2312.16418/) (2023)

## Abstract (arXiv)

Graph Neural Networks (GNNs) excel in node classification tasks but often assume homophily, where connected nodes share similar labels. This assumption does not hold in many real-world heterophilic graphs. Existing models for heterophilic graphs primarily rely on pairwise relationships, overlooking multi-scale information from higher-order structures. This leads to suboptimal performance, particularly under noise from conflicting class information across nodes. To address these challenges, we propose HPGNN, a novel model integrating Higher-order Personalized PageRank with Graph Neural Networks. HPGNN introduces an efficient high-order approximation of Personalized PageRank (PPR) to capture long-range and multi-scale node interactions. This approach reduces computational complexity and mitigates noise from surrounding information. By embedding higher-order structural information into convolutional networks, HPGNN effectively models key interactions across diverse graph dimensions. Extensive experiments on benchmark datasets demonstrate HPGNN's effectiveness. The model achieves better performance than five out of seven state-of-the-art methods on heterophilic graphs in downstream tasks while maintaining competitive performance on homophilic graphs. HPGNN's ability to balance multi-scale information and robustness to noise makes it a versatile solution for real-world graph learning challenges. Codes are available at https://github.com/streetcorner/HPGNN.