mlsanityData to 14 Oct 2026

PC-Conv: Unifying Homophily and Heterophily with Two-fold Filtering

arXiv 2312.14438 ↗First posted 22 Dec 2023cs.LG cs.AI cs.SIcited by 28

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Abstract (arXiv)

Recently, many carefully crafted graph representation learning methods have achieved impressive performance on either strong heterophilic or homophilic graphs, but not both. Therefore, they are incapable of generalizing well across real-world graphs with different levels of homophily. This is attributed to their neglect of homophily in heterophilic graphs, and vice versa. In this paper, we propose a two-fold filtering mechanism to extract homophily in heterophilic graphs and vice versa. In particular, we extend the graph heat equation to perform heterophilic aggregation of global information from a long distance. The resultant filter can be exactly approximated by the Possion-Charlier (PC) polynomials. To further exploit information at multiple orders, we introduce a powerful graph convolution PC-Conv and its instantiation PCNet for the node classification task. Compared with state-of-the-art GNNs, PCNet shows competitive performance on well-known homophilic and heterophilic graphs. Our implementation is available at https://github.com/uestclbh/PC-Conv.

Key facts. Cited by 28 papers in the map (data through 14 Oct 2026). Builds on 29 of its 42 references that are in the map. First posted on arXiv 22 Dec 2023.

Builds on

29 of 42 references.

References · 29

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  2. 2017Graph Attention Networkscited by 8,923
  3. 2017Inductive Representation Learning on Large Graphscited by 6,320
  4. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,089
  5. 2019Simplifying Graph Convolutional Networkscited by 1,477
  6. 2016Revisiting Semi-Supervised Learning with Graph Embeddingscited by 976
  7. 2020Simple and Deep Graph Convolutional Networkscited by 860
  8. 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 826
  9. 2020Adaptive Universal Generalized PageRank Graph Neural Networkcited by 595
  10. 2019Diffusion Improves Graph Learningcited by 414
  11. 2021Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methodscited by 311
  12. 2021BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximationcited by 195
17 more
  1. 2019Graph Neural Networks with convolutional ARMA filterscited by 185
  2. 2022Finding Global Homophily in Graph Neural Networks When Meeting Heterophilycited by 179
  3. 2021Interpreting and Unifying Graph Neural Networks with An Optimization Frameworkcited by 131
  4. 2021PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equationscited by 106
  5. 2021Dirichlet Energy Constrained Learning for Deep Graph Neural Networkscited by 97
  6. 2021Breaking the Limit of Graph Neural Networks by Improving the Assortativity of Graphs with Local Mixing Patternscited by 95
  7. 2021Is Heterophily A Real Nightmare For Graph Neural Networks To Do Node Classification?cited by 82
  8. 2021Multi-view Contrastive Graph Clusteringcited by 76
  9. 2019Break the Ceiling: Stronger Multi-scale Deep Graph Convolutional Networkscited by 62
  10. 2021Graph Neural Networks Inspired by Classical Iterative Algorithmscited by 60
  11. 2021Dissecting the Diffusion Process in Linear Graph Convolutional Networkscited by 58
  12. 2020Graph Convolutional Networks using Heat Kernel for Semi-supervised Learningcited by 51
  13. 2021Node Dependent Local Smoothing for Scalable Graph Learningcited by 45
  14. 2023Beyond Homophily: Reconstructing Structure for Graph-agnostic Clusteringcited by 29
  15. 2023Finding the Missing-half: Graph Complementary Learning for Homophily-prone and Heterophily-prone Graphscited by 25
  16. 2022Feature Overcorrelation in Deep Graph Neural Networks: A New Perspectivecited by 19
  17. 2021Self-supervised Consensus Representation Learning for Attributed Graphcited by 15

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 8; 2025: 15; 2026: 5.

28 papers.

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  1. 2025Multi-Domain Graph Foundation Models: Robust Knowledge Transfer via Topology Alignmentcited by 42
  2. 2025On the Benefits of Attribute-Driven Graph Domain Adaptationcited by 19
  3. 2024Node-wise Filtering in Graph Neural Networks: A Mixture of Experts Approachcited by 17
  4. 2024Beyond Redundancy: Information-aware Unsupervised Multiplex Graph Structure Learningcited by 12
  5. 2025Homophily Enhanced Graph Domain Adaptationcited by 9
  6. 2025Cooperation of Experts: Fusing Heterogeneous Information with Large Margincited by 6
  7. 2024Provable Filter for Real-world Graph Clusteringcited by 5
  8. 2024ERGNN: Spectral Graph Neural Network With Explicitly-Optimized Rational Graph Filterscited by 5
  9. 2026Structure-Centric Graph Foundation Model via Geometric Basescited by 5
  10. 2024Enhancing the Influence of Labels on Unlabeled Nodes in Graph Convolutional Networkscited by 4
  11. 2024Simplified PCNet with Robustnesscited by 3
  12. 2025Unveiling Mode Connectivity in Graph Neural Networkscited by 3
16 more
  1. 2026The Post-GCN Decade Revisited: Curvature-Stratified Evaluation of Relational Learningcited by 3
  2. 2025ScaleGNN: Towards Scalable Graph Neural Networks via Adaptive High-order Neighboring Feature Fusioncited by 2
  3. 2025Partition-wise Graph Filtering: A Unified Perspective Through the Lens of Graph Coarseningcited by 2
  4. 2024Polynomial Selection in Spectral Graph Neural Networks: An Error-Sum of Function Slices Approachcited by 1
  5. 2025Hierarchical Uncertainty-Aware Graph Neural Networkcited by 1
  6. 2025A Re-node Self-training Approach for Deep Graph-based Semi-supervised Classification on Multi-view Image Datacited by 1
  7. 2025Gauge-Equivariant Graph Networks via Self-Interference Cancellationcited by 1
  8. 2024Dual-Frequency Filtering Self-aware Graph Neural Networks for Homophilic and Heterophilic Graphscited by 0
  9. 2025H3GNNs: Harmonizing Heterophily and Homophily in GNNs via Joint Structural Node Encoding and Self-Supervised Learningcited by 0
  10. 2025Aggregation-aware MLP: An Unsupervised Approach for Graph Message-passingcited by 0
  11. 2025GraphTorque: Torque-Driven Rewiring Graph Neural Networkcited by 0
  12. 2025Bridging Computational Social Science and Deep Learning: Cultural Dissemination-Inspired Graph Neural Networkscited by 0
  13. 2025Pure Node Selection for Imbalanced Graph Node Classificationcited by 0
  14. 2026Persistent Tri-State Message Passingcited by 0
  15. 2026Continuous-Time Quantum Walks based Graph Neural Networkcited by 0
  16. 2026Spectral Reversal: Counteracting Singular Value Bias for Graph Promptingcited by 0