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Graph Neural Networks for Graphs with Heterophily: A Survey

Xin Zheng, Yi Wang, Yixin Liu, Ming Li, Miao Zhang, Di Jin, Philip S. Yu, Shirui Pan

TL;DR

This survey addresses the gap of graph neural networks (GNNs) on heterophilic graphs, where connected nodes may have different labels. It introduces a unified framework and taxonomy that categorize heterophilic GNNs into non-local neighbor extension, architecture refinement, and hybrid methods, detailing techniques that extend neighborhoods, refine message passing, and blend approaches. By connecting heterophily to robustness, over-smoothing, anomaly detection, and uncertainty modeling, the paper highlights practical implications and cross-domain relevance while outlining open challenges in scalability, theory, and diverse graph types. Overall, the work provides a systematic blueprint for designing, analyzing, and applying heterophilic GNNs across real-world, complex graph-structured data.

Abstract

Recent years have witnessed fast developments of graph neural networks (GNNs) that have benefited myriads of graph analytic tasks and applications. In general, most GNNs depend on the homophily assumption that nodes belonging to the same class are more likely to be connected. However, as a ubiquitous graph property in numerous real-world scenarios, heterophily, i.e., nodes with different labels tend to be linked, significantly limits the performance of tailor-made homophilic GNNs. Hence, GNNs for heterophilic graphs are gaining increasing research attention to enhance graph learning with heterophily. In this paper, we provide a comprehensive review of GNNs for heterophilic graphs. Specifically, we propose a systematic taxonomy that essentially governs existing heterophilic GNN models, along with a general summary and detailed analysis. Furthermore, we discuss the correlation between graph heterophily and various graph research domains, aiming to facilitate the development of more effective GNNs across a spectrum of practical applications and learning tasks in the graph research community. In the end, we point out the potential directions to advance and stimulate more future research and applications on heterophilic graph learning with GNNs.

Graph Neural Networks for Graphs with Heterophily: A Survey

TL;DR

This survey addresses the gap of graph neural networks (GNNs) on heterophilic graphs, where connected nodes may have different labels. It introduces a unified framework and taxonomy that categorize heterophilic GNNs into non-local neighbor extension, architecture refinement, and hybrid methods, detailing techniques that extend neighborhoods, refine message passing, and blend approaches. By connecting heterophily to robustness, over-smoothing, anomaly detection, and uncertainty modeling, the paper highlights practical implications and cross-domain relevance while outlining open challenges in scalability, theory, and diverse graph types. Overall, the work provides a systematic blueprint for designing, analyzing, and applying heterophilic GNNs across real-world, complex graph-structured data.

Abstract

Recent years have witnessed fast developments of graph neural networks (GNNs) that have benefited myriads of graph analytic tasks and applications. In general, most GNNs depend on the homophily assumption that nodes belonging to the same class are more likely to be connected. However, as a ubiquitous graph property in numerous real-world scenarios, heterophily, i.e., nodes with different labels tend to be linked, significantly limits the performance of tailor-made homophilic GNNs. Hence, GNNs for heterophilic graphs are gaining increasing research attention to enhance graph learning with heterophily. In this paper, we provide a comprehensive review of GNNs for heterophilic graphs. Specifically, we propose a systematic taxonomy that essentially governs existing heterophilic GNN models, along with a general summary and detailed analysis. Furthermore, we discuss the correlation between graph heterophily and various graph research domains, aiming to facilitate the development of more effective GNNs across a spectrum of practical applications and learning tasks in the graph research community. In the end, we point out the potential directions to advance and stimulate more future research and applications on heterophilic graph learning with GNNs.
Paper Structure (40 sections, 24 equations, 12 figures, 8 tables)

This paper contains 40 sections, 24 equations, 12 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Notations
  4. Graph Neural Networks
  5. Spectral Graph Convolution
  6. Measure of Heterophily & Homophily
  7. Mainstream Heterophily Learning Task
  8. GNNs with Heterophily: Framework and Taxonomy
  9. Framework of heterophilic GNNs
  10. Taxonomy of GNNs with Heterophily
  11. Heterophilic GNNs With Non-Local Neighbor Extension
  12. High-order Neighbor Mixing
  13. Potential Neighbor Discovery
  14. Structure-based Distance
  15. Feature-based Distance
  16. ...and 25 more sections

Figures (12)

  • Figure 1: Examples of homophilic and heterophilic graphs (Left: (a) a citation network; Right: (b) an online transaction network).
  • Figure 2: Categorization of Heterophily GNNs.
  • Figure 3: Schematic diagram of high-order neighbor mixing method and potential neighbor discovery method.
  • Figure 4: Illustration of identifiable message passing with edge-related weight and feature-related weight assignment schemes in GNN architecture refinement methods.
  • Figure 5: Illustration of typical inter-layer combination methods: (1) GPR-GNN chien2020adaptive; (2) JK-Net xu2018representation; and (3) GCNII chen2020simple.
  • ...and 7 more figures