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A Survey on Learning from Graphs with Heterophily: Recent Advances and Future Directions

Chenghua Gong, Yao Cheng, Jianxiang Yu, Can Xu, Caihua Shan, Siqiang Luo, Xiang Li

TL;DR

This survey addresses learning from graphs with heterophily by delivering a comprehensive, taxonomy-driven review that spans metrics, benchmarks, GNN models, learning paradigms, and broad applications. It highlights spectral and high-order filtering, global and discriminative message passing, graph transformers, neural diffusion, self-supervised and prompt-based learning as core advances for heterophilic graphs. The work underscores the critical role of robust benchmarks, reassessment studies, and scalability concerns while identifying future directions, including heterogeneous/dynamic/hypergraphs, deeper theory, and Graph Foundation Models. Its synthesis of methods and practical guidance aims to accelerate progress and inform practitioners across AI-powered domains that rely on complex, heterogeneous graph data.

Abstract

Graphs are structured data that models complex relations between real-world entities. Heterophilic graphs, where linked nodes are prone to be with different labels or dissimilar features, have recently attracted significant attention and found many real-world applications. Meanwhile, increasing efforts have been made to advance learning from graphs with heterophily. Various graph heterophily measures, benchmark datasets, and learning paradigms are emerging rapidly. In this survey, we comprehensively review existing works on learning from graphs with heterophily. First, we overview over 500 publications, of which more than 340 are directly related to heterophilic graphs. After that, we survey existing metrics of graph heterophily and list recent benchmark datasets. Further, we systematically categorize existing methods based on a hierarchical taxonomy including GNN models, learning paradigms and practical applications. In addition, broader topics related to graph heterophily are also included. Finally, we discuss the primary challenges of existing studies and highlight promising avenues for future research.

A Survey on Learning from Graphs with Heterophily: Recent Advances and Future Directions

TL;DR

This survey addresses learning from graphs with heterophily by delivering a comprehensive, taxonomy-driven review that spans metrics, benchmarks, GNN models, learning paradigms, and broad applications. It highlights spectral and high-order filtering, global and discriminative message passing, graph transformers, neural diffusion, self-supervised and prompt-based learning as core advances for heterophilic graphs. The work underscores the critical role of robust benchmarks, reassessment studies, and scalability concerns while identifying future directions, including heterogeneous/dynamic/hypergraphs, deeper theory, and Graph Foundation Models. Its synthesis of methods and practical guidance aims to accelerate progress and inform practitioners across AI-powered domains that rely on complex, heterogeneous graph data.

Abstract

Graphs are structured data that models complex relations between real-world entities. Heterophilic graphs, where linked nodes are prone to be with different labels or dissimilar features, have recently attracted significant attention and found many real-world applications. Meanwhile, increasing efforts have been made to advance learning from graphs with heterophily. Various graph heterophily measures, benchmark datasets, and learning paradigms are emerging rapidly. In this survey, we comprehensively review existing works on learning from graphs with heterophily. First, we overview over 500 publications, of which more than 340 are directly related to heterophilic graphs. After that, we survey existing metrics of graph heterophily and list recent benchmark datasets. Further, we systematically categorize existing methods based on a hierarchical taxonomy including GNN models, learning paradigms and practical applications. In addition, broader topics related to graph heterophily are also included. Finally, we discuss the primary challenges of existing studies and highlight promising avenues for future research.
Paper Structure (42 sections, 31 equations, 6 figures, 1 table)

This paper contains 42 sections, 31 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notations
  4. Message Passing Framework
  5. Graph Transformer
  6. Graph Laplacian and Filters
  7. Learning Paradigms
  8. Overview
  9. Literature Overview
  10. Organizational Structure
  11. Measures and Benchmarks
  12. Measuring Graph Heterophily
  13. Benchmark Datasets
  14. Reassessment under Graph Heterophily
  15. GNN Models and Beyond
  16. ...and 27 more sections

Figures (6)

  • Figure 1: The toy examples of homophilic and heterophilic graphs in real-world applications.
  • Figure 2: The statistics of collected papers related to learning from graphs with heterophily.
  • Figure 3: The word cloud composed of high-frequency words from the titles of collected articles in this survey.
  • Figure 4: The overall organizational structure of this survey.
  • Figure 5: Taxonomy of heterophilic GNNs and beyond with representative examples.
  • ...and 1 more figures