# EvenNet: Ignoring Odd-Hop Neighbors Improves Robustness of Graph Neural Networks

arXiv: https://arxiv.org/abs/2205.13892 · HTML: https://mlsanity.com/paper/2205.13892/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 46 references that are in the map.
- First posted on arXiv 27 May 2022.

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

- [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)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [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)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [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)
- [Heterogeneous Graph Attention Network](https://mlsanity.com/paper/1903.07293/) (2019)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [Adversarial Attacks on Graph Neural Networks via Meta Learning](https://mlsanity.com/paper/1902.08412/) (2019)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [Topology Attack and Defense for Graph Neural Networks: An Optimization Perspective](https://mlsanity.com/paper/1906.04214/) (2019)
- [GNNGuard: Defending Graph Neural Networks against Adversarial Attacks](https://mlsanity.com/paper/2006.08149/) (2020)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Graph Neural Networks with convolutional ARMA filters](https://mlsanity.com/paper/1901.01343/) (2019)
- [Contextual Stochastic Block Models](https://mlsanity.com/paper/1807.09596/) (2018)
- [Stability Properties of Graph Neural Networks](https://mlsanity.com/paper/1905.04497/) (2019)
- [DeepRobust: A PyTorch Library for Adversarial Attacks and Defenses](https://mlsanity.com/paper/2005.06149/) (2020)
- [Hiding Individuals and Communities in a Social Network](https://mlsanity.com/paper/1608.00375/) (2016)
- [Understanding and Improving Graph Injection Attack by Promoting Unnoticeability](https://mlsanity.com/paper/2202.08057/) (2022)
- [Graph Neural Networks Inspired by Classical Iterative Algorithms](https://mlsanity.com/paper/2103.06064/) (2021)

## Built on by (most cited first, 26 of 26)

- [A Survey on Spectral Graph Neural Networks](https://mlsanity.com/paper/2302.05631/) (2023)
- [AdaFGL: A New Paradigm for Federated Node Classification with Topology Heterogeneity](https://mlsanity.com/paper/2401.11750/) (2024)
- [How Universal Polynomial Bases Enhance Spectral Graph Neural Networks: Heterophily, Over-smoothing, and Over-squashing](https://mlsanity.com/paper/2405.12474/) (2024)
- [Robust Mid-Pass Filtering Graph Convolutional Networks](https://mlsanity.com/paper/2302.08048/) (2023)
- [Optimal Inference in Contextual Stochastic Block Models](https://mlsanity.com/paper/2306.07948/) (2023)
- [Bounding the Expected Robustness of Graph Neural Networks Subject to Node Feature Attacks](https://mlsanity.com/paper/2404.17947/) (2024)
- [Robust Graph Neural Networks via Unbiased Aggregation](https://mlsanity.com/paper/2311.14934/) (2023)
- [Provable Filter for Real-world Graph Clustering](https://mlsanity.com/paper/2403.03666/) (2024)
- [LON-GNN: Spectral GNNs with Learnable Orthonormal Basis](https://mlsanity.com/paper/2303.13750/) (2023)
- [Heterophilic Graph Neural Networks Optimization with Causal Message-passing](https://mlsanity.com/paper/2411.13821/) (2024)
- [Asymptotic generalization error of a single-layer graph convolutional network](https://mlsanity.com/paper/2402.03818/) (2024)
- [Simplified PCNet with Robustness](https://mlsanity.com/paper/2403.03676/) (2024)
- [Statistical physics analysis of graph neural networks: Approaching optimality in the contextual stochastic block model](https://mlsanity.com/paper/2503.01361/) (2025)
- [Hyperbolic-PDE GNN: Spectral Graph Neural Networks in the Perspective of A System of Hyperbolic Partial Differential Equations](https://mlsanity.com/paper/2505.23014/) (2025)
- [Robustness in Text-Attributed Graph Learning: Insights, Trade-offs, and New Defenses](https://mlsanity.com/paper/2510.17185/) (2025)
- [GLINKX: A Scalable Unified Framework For Homophilous and Heterophilous Graphs](https://mlsanity.com/paper/2211.00550/) (2022)
- [Invariant Layers for Graphs with Nodes of Different Types](https://mlsanity.com/paper/2302.13551/) (2023)
- [An Effective Universal Polynomial Basis for Spectral Graph Neural Networks](https://mlsanity.com/paper/2311.18177/) (2023)
- [Graph Adversarial Diffusion Convolution](https://mlsanity.com/paper/2406.02059/) (2024)
- [Training Robust Graph Neural Networks by Modeling Noise Dependencies](https://mlsanity.com/paper/2502.19670/) (2025)
- [Towards Anomaly-Aware Pre-Training and Fine-Tuning for Graph Anomaly Detection](https://mlsanity.com/paper/2504.14250/) (2025)
- [Aggregation-aware MLP: An Unsupervised Approach for Graph Message-passing](https://mlsanity.com/paper/2507.20127/) (2025)
- [Aligning the Spectrum: Hybrid Graph Pre-training and Prompt Tuning across Homophily and Heterophily](https://mlsanity.com/paper/2508.11328/) (2025)
- [Fixed-point graph convolutional networks against adversarial attacks](https://mlsanity.com/paper/2511.00083/) (2025)
- [Hierarchical Multi-Scale Graph Neural Networks: Scalable Heterophilous Learning with Oversmoothing and Oversquashing Mitigation](https://mlsanity.com/paper/2605.10975/) (2026)
- [Convex--Concave Quadratic Spectral Filtering for Graph Neural Networks](https://mlsanity.com/paper/2606.24956/) (2026)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have received extensive research attention for their promising performance in graph machine learning. Despite their extraordinary predictive accuracy, existing approaches, such as GCN and GPRGNN, are not robust in the face of homophily changes on test graphs, rendering these models vulnerable to graph structural attacks and with limited capacity in generalizing to graphs of varied homophily levels. Although many methods have been proposed to improve the robustness of GNN models, most of these techniques are restricted to the spatial domain and employ complicated defense mechanisms, such as learning new graph structures or calculating edge attentions. In this paper, we study the problem of designing simple and robust GNN models in the spectral domain. We propose EvenNet, a spectral GNN corresponding to an even-polynomial graph filter. Based on our theoretical analysis in both spatial and spectral domains, we demonstrate that EvenNet outperforms full-order models in generalizing across homophilic and heterophilic graphs, implying that ignoring odd-hop neighbors improves the robustness of GNNs. We conduct experiments on both synthetic and real-world datasets to demonstrate the effectiveness of EvenNet. Notably, EvenNet outperforms existing defense models against structural attacks without introducing additional computational costs and maintains competitiveness in traditional node classification tasks on homophilic and heterophilic graphs.