# RAW-GNN: RAndom Walk Aggregation based Graph Neural Network

arXiv: https://arxiv.org/abs/2206.13953 · HTML: https://mlsanity.com/paper/2206.13953/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 27 references that are in the map.
- First posted on arXiv 28 Jun 2022.

## Builds on (most cited first, 13 of 13)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [MAGNN: Metapath Aggregated Graph Neural Network for Heterogeneous Graph Embedding](https://mlsanity.com/paper/2002.01680/) (2020)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2102.06462/) (2021)
- [Interpreting and Unifying Graph Neural Networks with An Optimization Framework](https://mlsanity.com/paper/2101.11859/) (2021)
- [Block Modeling-Guided Graph Convolutional Neural Networks](https://mlsanity.com/paper/2112.13507/) (2021)
- [Powerful Graph Convolutioal Networks with Adaptive Propagation Mechanism for Homophily and Heterophily](https://mlsanity.com/paper/2112.13562/) (2021)

## Built on by (most cited first, 25 of 25)

- [Path Neural Networks: Expressive and Accurate Graph Neural Networks](https://mlsanity.com/paper/2306.05955/) (2023)
- [Beyond Message Passing: Neural Graph Pattern Machine](https://mlsanity.com/paper/2501.18739/) (2025)
- [Generative Graph Pattern Machine](https://mlsanity.com/paper/2505.16130/) (2025)
- [What Is Missing In Homophily? Disentangling Graph Homophily For Graph Neural Networks](https://mlsanity.com/paper/2406.18854/) (2024)
- [PathMLP: Smooth Path Towards High-order Homophily](https://mlsanity.com/paper/2306.13532/) (2023)
- [When Do Graph Neural Networks Help with Node Classification? Investigating the Impact of Homophily Principle on Node Distinguishability](https://mlsanity.com/paper/2304.14274/) (2023)
- [Graph Spectral Filtering with Chebyshev Interpolation for Recommendation](https://mlsanity.com/paper/2505.00552/) (2025)
- [Semantic Refinement with LLMs for Graph Representations](https://mlsanity.com/paper/2512.21106/) (2025)
- [Revealing the Pitfalls and Re-Evaluating the Advancement of Heterophilic Graph Learning](https://mlsanity.com/paper/2409.05755/) (2024)
- [Referral Augmentation for Zero-Shot Information Retrieval](https://mlsanity.com/paper/2305.15098/) (2023)
- [DiRW: Path-Aware Digraph Learning for Heterophily](https://mlsanity.com/paper/2410.10320/) (2024)
- [On provable privacy vulnerabilities of graph representations](https://mlsanity.com/paper/2402.04033/) (2024)
- [PROXI: Challenging the GNNs for Link Prediction](https://mlsanity.com/paper/2410.01802/) (2024)
- [Toward General Digraph Contrastive Learning: A Dual Spatial Perspective](https://mlsanity.com/paper/2510.16311/) (2025)
- [Graph homophily booster: Reimagining the role of discrete features in heterophilic graph learning](https://mlsanity.com/paper/2602.07256/) (2026)
- [Robust Node Affinities via Jaccard-Biased Random Walks and Rank Aggregation](https://mlsanity.com/paper/2603.05375/) (2026)
- [GLINKX: A Scalable Unified Framework For Homophilous and Heterophilous Graphs](https://mlsanity.com/paper/2211.00550/) (2022)
- [Learning From Simplicial Data Based on Random Walks and 1D Convolutions](https://mlsanity.com/paper/2404.03434/) (2024)
- [Rethinking the Graph Polynomial Filter via Positive and Negative Coupling Analysis](https://mlsanity.com/paper/2404.10353/) (2024)
- [RW-NSGCN: A Robust Approach to Structural Attacks via Negative Sampling](https://mlsanity.com/paper/2408.06665/) (2024)
- [SCNode: Spatial and Contextual Coordinates for Graph Representation Learning](https://mlsanity.com/paper/2410.02158/) (2024)
- [Are Graph Attention Networks Able to Model Structural Information?](https://mlsanity.com/paper/2505.21288/) (2025)
- [Aggregation-aware MLP: An Unsupervised Approach for Graph Message-passing](https://mlsanity.com/paper/2507.20127/) (2025)
- [Adaptive Node Feature Selection For Graph Neural Networks](https://mlsanity.com/paper/2510.03096/) (2025)
- [GCN-MPPR: Enhancing the Propagation of Message Passing Neural Networks via Motif-Based Personalized PageRank](https://mlsanity.com/paper/2602.07903/) (2026)

## Abstract (arXiv)

Graph-Convolution-based methods have been successfully applied to representation learning on homophily graphs where nodes with the same label or similar attributes tend to connect with one another. Due to the homophily assumption of Graph Convolutional Networks (GCNs) that these methods use, they are not suitable for heterophily graphs where nodes with different labels or dissimilar attributes tend to be adjacent. Several methods have attempted to address this heterophily problem, but they do not change the fundamental aggregation mechanism of GCNs because they rely on summation operators to aggregate information from neighboring nodes, which is implicitly subject to the homophily assumption. Here, we introduce a novel aggregation mechanism and develop a RAndom Walk Aggregation-based Graph Neural Network (called RAW-GNN) method. The proposed approach integrates the random walk strategy with graph neural networks. The new method utilizes breadth-first random walk search to capture homophily information and depth-first search to collect heterophily information. It replaces the conventional neighborhoods with path-based neighborhoods and introduces a new path-based aggregator based on Recurrent Neural Networks. These designs make RAW-GNN suitable for both homophily and heterophily graphs. Extensive experimental results showed that the new method achieved state-of-the-art performance on a variety of homophily and heterophily graphs.