# Feature Distribution on Graph Topology Mediates the Effect of Graph Convolution: Homophily Perspective

arXiv: https://arxiv.org/abs/2402.04621 · HTML: https://mlsanity.com/paper/2402.04621/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 53 references that are in the map.
- First posted on arXiv 7 Feb 2024.

## Builds on (most cited first, 30 of 39)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [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)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [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)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (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)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [Wiki-CS: A Wikipedia-Based Benchmark for Graph Neural Networks](https://mlsanity.com/paper/2007.02901/) (2020)
- [Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs](https://mlsanity.com/paper/2202.04579/) (2022)
- [The Surprising Power of Graph Neural Networks with Random Node Initialization](https://mlsanity.com/paper/2010.01179/) (2020)
- [Identity-aware Graph Neural Networks](https://mlsanity.com/paper/2101.10320/) (2021)
- [Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2102.06462/) (2021)
- [Is Homophily a Necessity for Graph Neural Networks?](https://mlsanity.com/paper/2106.06134/) (2021)
- [How Powerful are Spectral Graph Neural Networks](https://mlsanity.com/paper/2205.11172/) (2022)
- [Revisiting Heterophily For Graph Neural Networks](https://mlsanity.com/paper/2210.07606/) (2022)
- [Contextual Stochastic Block Models](https://mlsanity.com/paper/1807.09596/) (2018)
- [Rethinking the Expressive Power of GNNs via Graph Biconnectivity](https://mlsanity.com/paper/2301.09505/) (2023)
- [A Unified View on Graph Neural Networks as Graph Signal Denoising](https://mlsanity.com/paper/2010.01777/) (2020)
- [Graph Convolution for Semi-Supervised Classification: Improved Linear Separability and Out-of-Distribution Generalization](https://mlsanity.com/paper/2102.06966/) (2021)
- [Characterizing Graph Datasets for Node Classification: Homophily-Heterophily Dichotomy and Beyond](https://mlsanity.com/paper/2209.06177/) (2022)
- [Anti-Symmetric DGN: a stable architecture for Deep Graph Networks](https://mlsanity.com/paper/2210.09789/) (2022)
- [GraphWorld: Fake Graphs Bring Real Insights for GNNs](https://mlsanity.com/paper/2203.00112/) (2022)

## Built on by (most cited first, 9 of 9)

- [The Heterophilic Graph Learning Handbook: Benchmarks, Models, Theoretical Analysis, Applications and Challenges](https://mlsanity.com/paper/2407.09618/) (2024)
- [A Survey on Hypergraph Neural Networks: An In-Depth and Step-By-Step Guide](https://mlsanity.com/paper/2404.01039/) (2024)
- [Rethinking Reconstruction-based Graph-Level Anomaly Detection: Limitations and a Simple Remedy](https://mlsanity.com/paper/2410.20366/) (2024)
- [What Is Missing In Homophily? Disentangling Graph Homophily For Graph Neural Networks](https://mlsanity.com/paper/2406.18854/) (2024)
- [Sign is Not a Remedy: Multiset-to-Multiset Message Passing for Learning on Heterophilic Graphs](https://mlsanity.com/paper/2405.20652/) (2024)
- [Curriculum Guided Personalized Subgraph Federated Learning](https://mlsanity.com/paper/2509.00402/) (2025)
- [Gumbel-MPNN: Graph Rewiring with Gumbel-Softmax](https://mlsanity.com/paper/2508.17531/) (2025)
- [Feature-Centric Unsupervised Node Representation Learning Without Homophily Assumption](https://mlsanity.com/paper/2512.15112/) (2025)
- [Not All Nodes Are Created Equal: Homophily-Aware Stratification for Stable GNN Evaluation](https://mlsanity.com/paper/2609.19210/) (2026)

## Abstract (arXiv)

How would randomly shuffling feature vectors among nodes from the same class affect graph neural networks (GNNs)? The feature shuffle, intuitively, perturbs the dependence between graph topology and features (A-X dependence) for GNNs to learn from. Surprisingly, we observe a consistent and significant improvement in GNN performance following the feature shuffle. Having overlooked the impact of A-X dependence on GNNs, the prior literature does not provide a satisfactory understanding of the phenomenon. Thus, we raise two research questions. First, how should A-X dependence be measured, while controlling for potential confounds? Second, how does A-X dependence affect GNNs? In response, we (i) propose a principled measure for A-X dependence, (ii) design a random graph model that controls A-X dependence, (iii) establish a theory on how A-X dependence relates to graph convolution, and (iv) present empirical analysis on real-world graphs that align with the theory. We conclude that A-X dependence mediates the effect of graph convolution, such that smaller dependence improves GNN-based node classification.