# DiRW: Path-Aware Digraph Learning for Heterophily

arXiv: https://arxiv.org/abs/2410.10320 · HTML: https://mlsanity.com/paper/2410.10320/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 58 references that are in the map.
- First posted on arXiv 14 Oct 2024.

## Builds on (most cited first, 30 of 35)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [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)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [SIGN: Scalable Inception Graph Neural Networks](https://mlsanity.com/paper/2004.11198/) (2020)
- [Learning Word Vectors for 157 Languages](https://mlsanity.com/paper/1802.06893/) (2018)
- [Wiki-CS: A Wikipedia-Based Benchmark for Graph Neural Networks](https://mlsanity.com/paper/2007.02901/) (2020)
- [Combining Label Propagation and Simple Models Out-performs Graph Neural Networks](https://mlsanity.com/paper/2010.13993/) (2020)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Is Homophily a Necessity for Graph Neural Networks?](https://mlsanity.com/paper/2106.06134/) (2021)
- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [MagNet: A Neural Network for Directed Graphs](https://mlsanity.com/paper/2102.11391/) (2021)
- [Unifying Graph Convolutional Neural Networks and Label Propagation](https://mlsanity.com/paper/2002.06755/) (2020)
- [LightGCL: Simple Yet Effective Graph Contrastive Learning for Recommendation](https://mlsanity.com/paper/2302.08191/) (2023)
- [Directed Acyclic Graph Neural Networks](https://mlsanity.com/paper/2101.07965/) (2021)
- [GeniePath: Graph Neural Networks with Adaptive Receptive Paths](https://mlsanity.com/paper/1802.00910/) (2018)
- [GATE: Graph Attention Transformer Encoder for Cross-lingual Relation and Event Extraction](https://mlsanity.com/paper/2010.03009/) (2020)
- [DGRec: Graph Neural Network for Recommendation with Diversified Embedding Generation](https://mlsanity.com/paper/2211.10486/) (2022)
- [SPAGAN: Shortest Path Graph Attention Network](https://mlsanity.com/paper/2101.03464/) (2021)
- [Bring Your Own View: Graph Neural Networks for Link Prediction with Personalized Subgraph Selection](https://mlsanity.com/paper/2212.12488/) (2022)
- [RAW-GNN: RAndom Walk Aggregation based Graph Neural Network](https://mlsanity.com/paper/2206.13953/) (2022)
- [Directed Graph Auto-Encoders](https://mlsanity.com/paper/2202.12449/) (2022)
- [Breaking the Entanglement of Homophily and Heterophily in Semi-supervised Node Classification](https://mlsanity.com/paper/2312.04111/) (2023)

## Built on by (most cited first, 3 of 3)

- [Towards Data-centric Machine Learning on Directed Graphs: a Survey](https://mlsanity.com/paper/2412.01849/) (2024)
- [Toward General Digraph Contrastive Learning: A Dual Spatial Perspective](https://mlsanity.com/paper/2510.16311/) (2025)
- [HOPE: Heterophily-Aware Open-Set Node Classification with Pseudo-Extrapolation](https://mlsanity.com/paper/2609.08685/) (2026)

## Abstract (arXiv)

Recently, graph neural network (GNN) has emerged as a powerful representation learning tool for graph-structured data. However, most approaches are tailored for undirected graphs, neglecting the abundant information in the edges of directed graphs (digraphs). In fact, digraphs are widely applied in the real world and confirmed to address heterophily challenges. Despite recent advancements, existing spatial- and spectral-based DiGNNs have limitations due to their complex learning mechanisms and reliance on high-quality topology, resulting in low efficiency and unstable performance. To address these issues, we propose Directed Random Walk (DiRW), a plug-and-play strategy for most spatial-based DiGNNs and also an innovative model which offers a new digraph learning paradigm. Specifically, it utilizes a direction-aware path sampler optimized from the perspectives of walk probability, length, and number in a weight-free manner by considering node profiles and topologies. Building upon this, DiRW incorporates a node-wise learnable path aggregator for generalized node representations. Extensive experiments on 9 datasets demonstrate that DiRW: (1) enhances most spatial-based methods as a plug-and-play strategy; (2) achieves SOTA performance as a new digraph learning paradigm. The source code and data are available at https://github.com/dhsiuu/DiRW.