mlsanityData to 7 Oct 2026

Breaking the Limit of Graph Neural Networks by Improving the Assortativity of Graphs with Local Mixing Patterns

arXiv 2106.06586 ↗First posted 11 Jun 2021cs.LG cs.SIcited by 95

Not on the map. Why?

Abstract (arXiv)

Graph neural networks (GNNs) have achieved tremendous success on multiple graph-based learning tasks by fusing network structure and node features. Modern GNN models are built upon iterative aggregation of neighbor's/proximity features by message passing. Its prediction performance has been shown to be strongly bounded by assortative mixing in the graph, a key property wherein nodes with similar attributes mix/connect with each other. We observe that real world networks exhibit heterogeneous or diverse mixing patterns and the conventional global measurement of assortativity, such as global assortativity coefficient, may not be a representative statistic in quantifying this mixing. We adopt a generalized concept, node-level assortativity, one that is based at the node level to better represent the diverse patterns and accurately quantify the learnability of GNNs. We find that the prediction performance of a wide range of GNN models is highly correlated with the node level assortativity. To break this limit, in this work, we focus on transforming the input graph into a computation graph which contains both proximity and structural information as distinct type of edges. The resulted multi-relational graph has an enhanced level of assortativity and, more importantly, preserves rich information from the original graph. We then propose to run GNNs on this computation graph and show that adaptively choosing between structure and proximity leads to improved performance under diverse mixing. Empirically, we show the benefits of adopting our transformation framework for semi-supervised node classification task on a variety of real world graph learning benchmarks.

Key facts. Cited by 95 papers in the map (data through 7 Oct 2026). Builds on 36 of its 54 references that are in the map. First posted on arXiv 11 Jun 2021.

Builds on

36 of 54 references.

References · 36

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  3. 2017Graph Attention Networkscited by 8,854
  4. 2017Inductive Representation Learning on Large Graphscited by 6,284
  5. 2018How Powerful are Graph Neural Networks?cited by 4,355
  6. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  7. 2018Dynamic Graph CNN for Learning on Point Cloudscited by 2,220
  8. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,085
  9. 2017Modeling Relational Data with Graph Convolutional Networkscited by 1,684
  10. 2018Graph Convolutional Neural Networks for Web-Scale Recommender Systemscited by 1,133
  11. 2018Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learningcited by 1,099
  12. 2018Predict then Propagate: Graph Neural Networks meet Personalized PageRankcited by 987
24 more
  1. 2018Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networkscited by 878
  2. 2018Representation Learning on Graphs with Jumping Knowledge Networkscited by 875
  3. 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 821
  4. 2015Convolutional Networks on Graphs for Learning Molecular Fingerprintscited by 751
  5. 2020Adaptive Universal Generalized PageRank Graph Neural Networkcited by 592
  6. 2019Multi-scale Attributed Node Embeddingcited by 543
  7. 2019MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixingcited by 442
  8. 2019Diffusion Improves Graph Learningcited by 414
  9. 2018Deep Learning on Graphs: A Surveycited by 393
  10. 2019Revisiting Graph Neural Networks: All We Have is Low-Pass Filterscited by 260
  11. 2017Learning to Represent Programs with Graphscited by 219
  12. 2017struc2vec: Learning Node Representations from Structural Identitycited by 214
  13. 2020Machine Learning on Graphs: A Model and Comprehensive Taxonomycited by 156
  14. 2020A Survey on The Expressive Power of Graph Neural Networkscited by 111
  15. 2017Learning Structural Node Embeddings Via Diffusion Waveletscited by 97
  16. 2020Non-Local Graph Neural Networkscited by 91
  17. 2020Graph signal processing for machine learning: A review and new perspectivescited by 73
  18. 2019DEMO-Net: Degree-specific Graph Neural Networks for Node and Graph Classificationcited by 59
  19. 2020Scattering GCN: Overcoming Oversmoothness in Graph Convolutional Networkscited by 57
  20. 2019Optimizing Generalized PageRank Methods for Seed-Expansion Community Detectioncited by 35
  21. 2020On Graph Neural Networks versus Graph-Augmented MLPscited by 30
  22. 2020Understanding Graph Neural Networks from Graph Signal Denoising Perspectivescited by 11
  23. 2017Multiscale mixing patterns in networkscited by 7
  24. 2018Mixing patterns and individual differences in networkscited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 22; 2023: 26; 2024: 30; 2025: 11; 2026: 5.

95 papers.

Sort:

By area:

  1. 2023A critical look at the evaluation of GNNs under heterophily: Are we really making progress?cited by 332
  2. 2022Finding Global Homophily in Graph Neural Networks When Meeting Heterophilycited by 179
  3. 2022Graph Neural Networks for Graphs with Heterophily: A Surveycited by 175
  4. 2022Data Augmentation for Deep Graph Learning: A Surveycited by 132
  5. 2023Ordered GNN: Ordering Message Passing to Deal with Heterophily and Over-smoothingcited by 67
  6. 2022A Survey on Graph Representation Learning Methodscited by 66
  7. 2022Characterizing Graph Datasets for Node Classification: Homophily-Heterophily Dichotomy and Beyondcited by 60
  8. 2022Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminatingcited by 57
  9. 2021Simplifying approach to Node Classification in Graph Neural Networkscited by 56
  10. 2022GREAD: Graph Neural Reaction-Diffusion Networkscited by 54
  11. 2023Simple and Asymmetric Graph Contrastive Learning without Augmentationscited by 37
  12. 2024VCR-Graphormer: A Mini-batch Graph Transformer via Virtual Connectionscited by 34
38 more
  1. 2023PC-Conv: Unifying Homophily and Heterophily with Two-fold Filteringcited by 28
  2. 2024How Universal Polynomial Bases Enhance Spectral Graph Neural Networks: Heterophily, Over-smoothing, and Over-squashingcited by 24
  3. 2023Auto-HeG: Automated Graph Neural Network on Heterophilic Graphscited by 23
  4. 2022Understanding Non-linearity in Graph Neural Networks from the Bayesian-Inference Perspectivecited by 19
  5. 2022Improving Graph Neural Networks with Learnable Propagation Operatorscited by 19
  6. 2023Permutation Equivariant Graph Framelets for Heterophilous Graph Learningcited by 19
  7. 2022Interpreting Unfairness in Graph Neural Networks via Training Node Attributioncited by 18
  8. 2022Simplified Graph Convolution with Heterophilycited by 17
  9. 2022Node-oriented Spectral Filtering for Graph Neural Networkscited by 17
  10. 2024Node-wise Filtering in Graph Neural Networks: A Mixture of Experts Approachcited by 17
  11. 2023Feature Transportation Improves Graph Neural Networkscited by 15
  12. 2024Understanding Heterophily for Graph Neural Networkscited by 15
  13. 2023Transitivity-Preserving Graph Representation Learning for Bridging Local Connectivity and Role-based Similaritycited by 14
  14. 2022ES-GNN: Generalizing Graph Neural Networks Beyond Homophily with Edge Splittingcited by 13
  15. 2023MUSE: Multi-View Contrastive Learning for Heterophilic Graphscited by 13
  16. 2024A Survey on Learning from Graphs with Heterophily: Recent Advances and Future Directionscited by 13
  17. 2022Decoupled Self-supervised Learning for Non-Homophilous Graphscited by 10
  18. 2023SIGMA: An Efficient Heterophilous Graph Neural Network with Fast Global Aggregationcited by 10
  19. 2022Restructuring Graph for Higher Homophily via Adaptive Spectral Clusteringcited by 9
  20. 2023Graph Neural Networks with Diverse Spectral Filteringcited by 9
  21. 2024What Is Missing In Homophily? Disentangling Graph Homophily For Graph Neural Networkscited by 9
  22. 2023Neighborhood Homophily-based Graph Convolutional Networkcited by 7
  23. 2023Heterophily-Aware Graph Attention Networkcited by 7
  24. 2023Spatial Heterophily Aware Graph Neural Networkscited by 7
  25. 2023Mixture of Weak & Strong Experts on Graphscited by 7
  26. 2023PGODE: Towards High-quality System Dynamics Modelingcited by 7
  27. 2024Graph Neural Reaction Diffusion Modelscited by 6
  28. 2024The Heterophilic Snowflake Hypothesis: Training and Empowering GNNs for Heterophilic Graphscited by 6
  29. 2024When Heterophily Meets Heterogeneity: Challenges and a New Large-Scale Graph Benchmarkcited by 6
  30. 2024Leveraging Invariant Principle for Heterophilic Graph Structure Distribution Shiftscited by 6
  31. 2024Preventing Representational Rank Collapse in MPNNs by Splitting the Computational Graphcited by 6
  32. 2024Diss-l-ECT: Dissecting Graph Data with Local Euler Characteristic Transformscited by 6
  33. 2023Causal-Based Supervision of Attention in Graph Neural Network: A Better and Simpler Choice towards Powerful Attentioncited by 5
  34. 2023Clarify Confused Nodes via Separated Learningcited by 5
  35. 2023Examining the Effects of Degree Distribution and Homophily in Graph Learning Modelscited by 5
  36. 2024Revisiting the Message Passing in Heterophilous Graph Neural Networkscited by 5
  37. 2025Beyond Fixed Depth: Adaptive Graph Neural Networks for Node Classification Under Varying Homophilycited by 5
  38. 2022Incorporating Heterophily into Graph Neural Networks for Graph Classificationcited by 4

50 most cited of 95 All 95 (JSON)