# PathMLP: Smooth Path Towards High-order Homophily

arXiv: https://arxiv.org/abs/2306.13532 · HTML: https://mlsanity.com/paper/2306.13532/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 43 references that are in the map.
- First posted on arXiv 23 Jun 2023.

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

- [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)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Graph Neural Networks in Recommender Systems: A Survey](https://mlsanity.com/paper/2011.02260/) (2020)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [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)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2102.06462/) (2021)
- [Finding Global Homophily in Graph Neural Networks When Meeting Heterophily](https://mlsanity.com/paper/2205.07308/) (2022)
- [Revisiting Heterophily For Graph Neural Networks](https://mlsanity.com/paper/2210.07606/) (2022)
- [Say No to the Discrimination: Learning Fair Graph Neural Networks with Limited Sensitive Attribute Information](https://mlsanity.com/paper/2009.01454/) (2020)
- [Attention-based Graph Neural Network for Semi-supervised Learning](https://mlsanity.com/paper/1803.03735/) (2018)
- [Inferring Networks of Substitutable and Complementary Products](https://mlsanity.com/paper/1506.08839/) (2015)
- [GeniePath: Graph Neural Networks with Adaptive Receptive Paths](https://mlsanity.com/paper/1802.00910/) (2018)
- [Simplifying approach to Node Classification in Graph Neural Networks](https://mlsanity.com/paper/2111.06748/) (2021)
- [SPAGAN: Shortest Path Graph Attention Network](https://mlsanity.com/paper/2101.03464/) (2021)
- [RAW-GNN: RAndom Walk Aggregation based Graph Neural Network](https://mlsanity.com/paper/2206.13953/) (2022)
- [Behavior-aware Account De-anonymization on Ethereum Interaction Graph](https://mlsanity.com/paper/2203.09360/) (2022)

## Built on by (most cited first, 8 of 8)

- [The Heterophilic Graph Learning Handbook: Benchmarks, Models, Theoretical Analysis, Applications and Challenges](https://mlsanity.com/paper/2407.09618/) (2024)
- [A Survey on Learning from Graphs with Heterophily: Recent Advances and Future Directions](https://mlsanity.com/paper/2401.09769/) (2024)
- [Rethinking Graph Contrastive Learning through Relative Similarity Preservation](https://mlsanity.com/paper/2505.05533/) (2025)
- [Mixture of Experts Meets Decoupled Message Passing: Towards General and Adaptive Node Classification](https://mlsanity.com/paper/2412.08193/) (2024)
- [CAT: A Causally Graph Attention Network for Trimming Heterophilic Graph](https://mlsanity.com/paper/2312.08672/) (2023)
- [Rethinking Graph Transformer Architecture Design for Node Classification](https://mlsanity.com/paper/2410.11189/) (2024)
- [Mixture of Scope Experts at Test: Generalizing Deeper Graph Neural Networks with Shallow Variants](https://mlsanity.com/paper/2409.06998/) (2024)
- [A Federated Parameter Aggregation Method for Node Classification Tasks with Different Graph Network Structures](https://mlsanity.com/paper/2403.16004/) (2024)

## Abstract (arXiv)

Real-world graphs exhibit increasing heterophily, where nodes no longer tend to be connected to nodes with the same label, challenging the homophily assumption of classical graph neural networks (GNNs) and impeding their performance. Intriguingly, from the observation of heterophilous data, we notice that certain high-order information exhibits higher homophily, which motivates us to involve high-order information in node representation learning. However, common practices in GNNs to acquire high-order information mainly through increasing model depth and altering message-passing mechanisms, which, albeit effective to a certain extent, suffer from three shortcomings: 1) over-smoothing due to excessive model depth and propagation times; 2) high-order information is not fully utilized; 3) low computational efficiency. In this regard, we design a similarity-based path sampling strategy to capture smooth paths containing high-order homophily. Then we propose a lightweight model based on multi-layer perceptrons (MLP), named PathMLP, which can encode messages carried by paths via simple transformation and concatenation operations, and effectively learn node representations in heterophilous graphs through adaptive path aggregation. Extensive experiments demonstrate that our method outperforms baselines on 16 out of 20 datasets, underlining its effectiveness and superiority in alleviating the heterophily problem. In addition, our method is immune to over-smoothing and has high computational efficiency. The source code will be available in https://github.com/Graph4Sec-Team/PathMLP.