# Beyond Fixed Depth: Adaptive Graph Neural Networks for Node Classification Under Varying Homophily

arXiv: https://arxiv.org/abs/2511.06608 · HTML: https://mlsanity.com/paper/2511.06608/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 57 references that are in the map.
- First posted on arXiv 10 Nov 2025.

## Builds on (most cited first, 30 of 31)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [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)
- [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)
- [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)
- [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)
- [Finding Global Homophily in Graph Neural Networks When Meeting Heterophily](https://mlsanity.com/paper/2205.07308/) (2022)
- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [Contextual Stochastic Block Models](https://mlsanity.com/paper/1807.09596/) (2018)
- [Breaking the Limit of Graph Neural Networks by Improving the Assortativity of Graphs with Local Mixing Patterns](https://mlsanity.com/paper/2106.06586/) (2021)
- [Edge Directionality Improves Learning on Heterophilic Graphs](https://mlsanity.com/paper/2305.10498/) (2023)
- [Is Heterophily A Real Nightmare For Graph Neural Networks To Do Node Classification?](https://mlsanity.com/paper/2109.05641/) (2021)
- [Ordered GNN: Ordering Message Passing to Deal with Heterophily and Over-smoothing](https://mlsanity.com/paper/2302.01524/) (2023)
- [A Survey on Graph Representation Learning Methods](https://mlsanity.com/paper/2204.01855/) (2022)
- [Finding the Missing-half: Graph Complementary Learning for Homophily-prone and Heterophily-prone Graphs](https://mlsanity.com/paper/2306.07608/) (2023)
- [Auto-HeG: Automated Graph Neural Network on Heterophilic Graphs](https://mlsanity.com/paper/2302.12357/) (2023)
- [Breaking the Entanglement of Homophily and Heterophily in Semi-supervised Node Classification](https://mlsanity.com/paper/2312.04111/) (2023)
- [ES-GNN: Generalizing Graph Neural Networks Beyond Homophily with Edge Splitting](https://mlsanity.com/paper/2205.13700/) (2022)
- [Restructuring Graph for Higher Homophily via Adaptive Spectral Clustering](https://mlsanity.com/paper/2206.02386/) (2022)
- [Depth-Adaptive Graph Neural Networks via Learnable Bakry-'Emery Curvature](https://mlsanity.com/paper/2503.01079/) (2025)
- [The Heterophilic Snowflake Hypothesis: Training and Empowering GNNs for Heterophilic Graphs](https://mlsanity.com/paper/2406.12539/) (2024)

## Built on by (most cited first, 5 of 5)

- [QoSDiff: An Implicit Topological Embedding Learning Framework Leveraging Denoising Diffusion and Adversarial Attention for Robust QoS Prediction](https://mlsanity.com/paper/2512.04596/) (2025)
- [MLGIB: Multi-Label Graph Information Bottleneck for Expressive and Robust Message Passing](https://mlsanity.com/paper/2605.13126/) (2026)
- [Graph Navier Stokes Networks](https://mlsanity.com/paper/2605.21247/) (2026)
- [When Design Rules Break: Benchmark Composition Determines Whether Label Informativeness Predicts GNN Aggregator Choice](https://mlsanity.com/paper/2606.10249/) (2026)
- [Not Just Oversmoothing: Detecting the Echo Chamber Effect in Graph Neural Networks](https://mlsanity.com/paper/2609.06521/) (2026)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have achieved significant success in addressing node classification tasks. However, the effectiveness of traditional GNNs degrades on heterophilic graphs, where connected nodes often belong to different labels or properties. While recent work has introduced mechanisms to improve GNN performance under heterophily, certain key limitations still exist. Most existing models apply a fixed aggregation depth across all nodes, overlooking the fact that nodes may require different propagation depths based on their local homophily levels and neighborhood structures. Moreover, many methods are tailored to either homophilic or heterophilic settings, lacking the flexibility to generalize across both regimes. To address these challenges, we develop a theoretical framework that links local structural and label characteristics to information propagation dynamics at the node level. Our analysis shows that optimal aggregation depth varies across nodes and is critical for preserving class-discriminative information. Guided by this insight, we propose a novel adaptive-depth GNN architecture that dynamically selects node-specific aggregation depths using theoretically grounded metrics. Our method seamlessly adapts to both homophilic and heterophilic patterns within a unified model. Extensive experiments demonstrate that our approach consistently enhances the performance of standard GNN backbones across diverse benchmarks.