Graph Neural Networks for Graphs with Heterophily: A Survey
School of Computing Technologies, RMIT University（罗特学院，皇家墨尔本理工大学）；Department of Mathematics, City University of Hong Kong（香港城市大学数学系）；School of Information and Communication Technology, Griffith University（信息与通信技术学院，格里菲斯大学）；Zhejiang Key Laboratory of Intelligent Education Technology and Application, Zhejiang Normal University（浙江智能教育技术与应用重点实验室，浙江师范大学）；School of Computer Science and Technology, Harbin Institute of Technology (Shenzhen)（计算机科学与技术学院，哈尔滨工业大学（深圳））；School of Computer Science and Technology, Tianjin University（计算机科学与技术学院，天津大学）；Department of Computer Science, University of Illinois at Chicago（计算机科学系，伊利诺伊大学芝加哥分校）
Xin Zheng, Yi Wang, Yixin Liu, Ming Li, Miao Zhang, Di Jin, Philip S. Yu, Shirui Pan
备注：
Accepted by IEEE Transactions on Knowledge and Data Engineering (TKDE) 2026; 24 Pages
Recent years have witnessed fast developments of graph neural networks (GNNs) that have benefited myriad graph analytic tasks and applications. Most GNNs rely 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 governs existing heterophilic GNN models, along with general summaries and detailed analyses. Furthermore, we discuss the relationship between 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 potential directions to advance and inspire future research and applications on heterophilic graph learning with GNNs.
HeRB: Heterophily-Resolved Structure Balancer for Graph Neural Networks
Jiangsu Key Laboratory of Big Data Security & Intelligent Processing, Nanjing University of Posts and Telecommunications（江苏大数据安全与智能处理重点实验室，南京邮电大学）；School of Computer Science, Nanjing University of Posts and Telecommunications（计算机科学学院，南京邮电大学）；State Key Laboratory of Novel Software Technology, Nanjing University（新型软件技术国家重点实验室，南京大学）
针对图神经网络的结构不平衡问题，提出 HeRB 方法，先纠正异相性再传递同相知识，通过减少类间边和增加类内边及头尾节点知识传递，在多个基准数据集上取得优越性能。
Microsoft Research Asia（微软亚洲研究院）；Beijing University of Technology（北京工业大学）；Peking University（北京大学）；Northeastern University（东北大学）
Graph Neural Networks (GNNs) are widely used on a variety of graph-based machine learning tasks. For node-level tasks, GNNs have strong power to model the homophily property of graphs (i.e., connected nodes are more similar) while their ability to capture the heterophily property is often doubtful. This is partially caused by the design of the feature transformation with the same kernel for the nodes in the same hop and the followed aggregation operator. One kernel cannot model the similarity and the dissimilarity (i.e., the positive and negative correlation) between node features simultaneous…
Adaptive Heterogeneous Graph Neural Networks: Bridging Heterophily and Heterogeneity
State Key Laboratory of General Artificial Intelligence, School of Intelligence Science and Technology, Peking University（通用人工智能国家重点实验室，智能科学与技术学院，北京大学）
A Survey on Learning from Graphs with Heterophily: Recent Advances and Future Directions
School of Data Science and Engineering, East China Normal University（华东师范大学数据科学与工程学院）；Microsoft Research Asia（微软亚洲研究院）；School of Computer Science and Engineering, Nanyang Technological University（南洋理工大学计算机科学与工程学院）
Tianjin University（天津大学）；Meituan（美团）；The Hong Kong Polytechnic University（香港理工大学）
Graph-Convolution-based methods have been successfully applied to representation learning on homophily graphs where nodes with the same label or similar attributes tend to connect with one another. Due to the homophily assumption of Graph Convolutional Networks (GCNs) that these methods use, they are not suitable for heterophily graphs where nodes with different labels or dissimilar attributes tend to be adjacent. Several methods have attempted to address this heterophily problem, but they do not change the fundamental aggregation mechanism of GCNs because they rely on summation operators to a…
Shanghai Jiao Tong University（上海交通大学）；Chinese Academy of Sciences（中国科学院）
Most graph neural networks follow the message passing mechanism. However, it faces the over-smoothing problem when multiple times of message passing is applied to a graph, causing indistinguishable node representations and prevents the model to effectively learn dependencies between farther-away nodes. On the other hand, features of neighboring nodes with different labels are likely to be falsely mixed, resulting in the heterophily problem. In this work, we propose to order the messages passing into the node representation, with specific blocks of neurons targeted for message passing within sp…
How Universal Polynomial Bases Enhance Spectral Graph Neural Networks: Heterophily, Over-smoothing, and Over-squashing
School of Computing, National University of Singapore（新加坡国立大学计算机学院）；Zhangjiang Institute for Advanced Study, Shanghai Jiao Tong University（上海交通大学张江高等研究院）；Shanghai AI Laboratory（上海人工智能实验室）；School of Mathematics and Statistics, University of New South Wales（新南威尔士大学数学与统计学院）；Zhejiang Institute of Optoelectronics（浙江光电研究院）；Zhejiang Normal University（浙江师范大学）；Department of Computer Science and Technology, Cambridge University（剑桥大学计算机科学与技术系）
Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by using the graph structures based on the relational inductive bias (homophily assumption). Though GNNs are believed to outperform NNs in real-world tasks, performance advantages of GNNs over graph-agnostic NNs seem not generally satisfactory. Heterophily has been considered as a main cause and numerous works have been put forward to address it. In this paper, we first show that not all cases of heterophily are harmful for GNNs with aggregation operation. Then, we propose new metrics based on a similarity matrix which considers t…
Addressing Graph Heterogeneity and Heterophily from A Spectral Perspective
Beijing University of Posts and Telecommunications（北京邮电大学）；National University of Singapore（新加坡国立大学）；Beihang University（北京航空航天大学）；Hangzhou Dianzi University（杭州电子科技大学）
Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by using graph structures based on the relational inductive bias (homophily assumption). While GNNs have been commonly believed to outperform NNs in real-world tasks, recent work has identified a non-trivial set of datasets where their performance compared to NNs is not satisfactory. Heterophily has been considered the main cause of this empirical observation and numerous works have been put forward to address it. In this paper, we first revisit the widely used homophily metrics and point out that their consideration of only graph…
University of Science and Technology of China（中国科学技术大学）；Baidu Research（百度研究院）；Baidu Inc.（百度公司）；The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；The Hong Kong University of Science and Technology（香港科技大学）
University of Michigan（密歇根大学）；Adobe Research（Adobe研究院）；Intel Labs（英特尔实验室）
Graph Neural Networks (GNNs) have proven to be useful for many different practical applications. However, many existing GNN models have implicitly assumed homophily among the nodes connected in the graph, and therefore have largely overlooked the important setting of heterophily, where most connected nodes are from different classes. In this work, we propose a novel framework called CPGNN that generalizes GNNs for graphs with either homophily or heterophily. The proposed framework incorporates an interpretable compatibility matrix for modeling the heterophily or homophily level in the graph, w…
Understanding Heterophily for Graph Neural Networks
Beihang University（北京航空航天大学）；School of Computer Science and Engineering, Beihang University（北京航空航天大学计算机科学与工程学院）；Shen Yuan Honors College, Beihang University（北京航空航天大学沈元荣誉学院）；School of Artificial Intelligence, Hebei University of Technology（河北工业大学人工智能学院）
University of Michigan（密歇根大学）；Northwestern University（西北大学）；RWTH Aachen University（亚琛工业大学）
We bridge two research directions on graph neural networks (GNNs), by formalizing the relation between heterophily of node labels (i.e., connected nodes tend to have dissimilar labels) and the robustness of GNNs to adversarial attacks. Our theoretical and empirical analyses show that for homophilous graph data, impactful structural attacks always lead to reduced homophily, while for heterophilous graph data the change in the homophily level depends on the node degrees. These insights have practical implications for defending against attacks on real-world graphs: we deduce that separate aggrega…
Heterophily-Agnostic Hypergraph Neural Networks with Riemannian Local Exchanger
Beijing University of Posts and Telecommunications（北京邮电大学）；North China Electric Power University（华北电力大学）；University of Kent（肯特大学）；Beihang University（北航）；University of Illinois（伊利诺伊大学）
Monash University（莫纳什大学）；Harbin Institute of Technology (Shenzhen)（哈尔滨工业大学（深圳））；Shenzhen University（深圳大学）；Chinese Academy of Sciences（中国科学院）；Griffith University（格里菲斯大学）
Graph neural architecture search (NAS) has gained popularity in automatically designing powerful graph neural networks (GNNs) with relieving human efforts. However, existing graph NAS methods mainly work under the homophily assumption and overlook another important graph property, i.e., heterophily, which exists widely in various real-world applications. To date, automated heterophilic graph learning with NAS is still a research blank to be filled in. Due to the complexity and variety of heterophilic graphs, the critical challenge of heterophilic graph NAS mainly lies in developing the heterop…
East China Normal University（华东师范大学）；Microsoft Research Asia（微软亚洲研究院）；Nanyang Technological University（南洋理工大学）
We investigate graph neural networks on graphs with heterophily. Some existing methods amplify a node's neighborhood with multi-hop neighbors to include more nodes with homophily. However, it is a significant challenge to set personalized neighborhood sizes for different nodes. Further, for other homophilous nodes excluded in the neighborhood, they are ignored for information aggregation. To address these problems, we propose two models GloGNN and GloGNN++, which generate a node's embedding by aggregating information from global nodes in the graph. In each layer, both models learn a coefficien…
Graph neural networks (GNNs) have achieved great success in various graph problems. However, most GNNs are Message Passing Neural Networks (MPNNs) based on the homophily assumption, where nodes with the same label are connected in graphs. Real-world problems bring us heterophily problems, where nodes with different labels are connected in graphs. MPNNs fail to address the heterophily problem because they mix information from different distributions and are not good at capturing global patterns. Therefore, we investigate a novel Graph Memory Networks model on Heterophilous Graphs (HP-GMN) to th…
Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；Microsoft Research Asia（微软亚洲研究院）
Graph Neural Networks (GNNs) are popular machine learning methods for modeling graph data. A lot of GNNs perform well on homophily graphs while having unsatisfactory performance on heterophily graphs. Recently, some researchers turn their attention to designing GNNs for heterophily graphs by adjusting the message passing mechanism or enlarging the receptive field of the message passing. Different from existing works that mitigate the issues of heterophily from model design perspective, we propose to study heterophily graphs from an orthogonal perspective by rewiring the graph structure to redu…
Beihang University（北京航空航天大学）；School of Computer Science and Engineering, Beihang University（北京航空航天大学计算机科学与工程学院）；Shen Yuan Honors College, Beihang University（北京航空航天大学沈元荣誉学院）；Hebei University of Technology（河北工业大学）；School of Artificial Intelligence, Hebei University of Technology（河北工业大学人工智能学院）
University of Cambridge（剑桥大学）；Twitter（推特）；University of Oxford（牛津大学）
Cellular sheaves equip graphs with a "geometrical" structure by assigning vector spaces and linear maps to nodes and edges. Graph Neural Networks (GNNs) implicitly assume a graph with a trivial underlying sheaf. This choice is reflected in the structure of the graph Laplacian operator, the properties of the associated diffusion equation, and the characteristics of the convolutional models that discretise this equation. In this paper, we use cellular sheaf theory to show that the underlying geometry of the graph is deeply linked with the performance of GNNs in heterophilic settings and their ov…
University of Michigan（密歇根大学）；Carnegie Mellon University（卡内基梅隆大学）
We investigate the representation power of graph neural networks in the semi-supervised node classification task under heterophily or low homophily, i.e., in networks where connected nodes may have different class labels and dissimilar features. Many popular GNNs fail to generalize to this setting, and are even outperformed by models that ignore the graph structure (e.g., multilayer perceptrons). Motivated by this limitation, we identify a set of key designs -- ego- and neighbor-embedding separation, higher-order neighborhoods, and combination of intermediate representations -- that boost lear…
Message passing has evolved as an effective tool for designing Graph Neural Networks (GNNs). However, most existing methods for message passing simply sum or average all the neighboring features to update node representations. They are restricted by two problems, i.e., (i) lack of interpretability to identify node features significant to the prediction of GNNs, and (ii) feature over-mixing that leads to the over-smoothing issue in capturing long-range dependencies and inability to handle graphs under heterophily or low homophily. In this paper, we propose a Node-level Capsule Graph Neural Netw…
Leveraging Personalized PageRank and Higher-Order Topological Structures for Heterophily Mitigation in Graph Neural Networks
School of New Media and Communication, Tianjin University（天津大学新媒体与传播学院）；College of Intelligence and Computing, Tianjin University（天津大学智能与计算学院）；Yazhou Bay Innovation Institute, Hainan Tropical Ocean University（海南热带海洋大学亚龙湾创新研究院）；Key Lab of Education Blockchain and Intelligent Technology, Guangxi Normal University（广西师范大学教育区块链与智能技术重点实验室）
Fudan University（复旦大学）；Shanghai Jiao Tong University（上海交通大学）；Amazon（亚马逊）；Renmin University of China（中国人民大学）
Despite the recent success of graph neural networks (GNN), common architectures often exhibit significant limitations, including sensitivity to oversmoothing, long-range dependencies, and spurious edges, e.g., as can occur as a result of graph heterophily or adversarial attacks. To at least partially address these issues within a simple transparent framework, we consider a new family of GNN layers designed to mimic and integrate the update rules of two classical iterative algorithms, namely, proximal gradient descent and iterative reweighted least squares (IRLS). The former defines an extensib…
Recent work has shown that a simple, fast method called Simple Graph Convolution (SGC) (Wu et al., 2019), which eschews deep learning, is competitive with deep methods like graph convolutional networks (GCNs) (Kipf & Welling, 2017) in common graph machine learning benchmarks. The use of graph data in SGC implicitly assumes the common but not universal graph characteristic of homophily, wherein nodes link to nodes which are similar. Here we confirm that SGC is indeed ineffective for heterophilous (i.e., non-homophilous) graphs via experiments on synthetic and real-world datasets. We propose Ada…
Graph Neural Networks (GNNs) have achieved remarkable performance in modeling graphs for various applications. However, most existing GNNs assume the graphs exhibit strong homophily in node labels, i.e., nodes with similar labels are connected in the graphs. They fail to generalize to heterophilic graphs where linked nodes may have dissimilar labels and attributes. Therefore, in this paper, we investigate a novel framework that performs well on graphs with either homophily or heterophily. More specifically, we propose a label-wise message passing mechanism to avoid the negative effects caused …
Remedying Coarsening-Based GNN Training under Heterophily via Adaptive Complementary Enhancement
Hong Kong Baptist University（香港浸会大学）；Renmin University of China（中国人民大学）；Chinese Academy of Sciences（中国科学院）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；Sun Yat-sen University（中山大学）
Seoul National University（首尔国立大学）；University of Michigan（密歇根大学）；Amazon Web Services（亚马逊云科技）
Heterogeneous graph neural networks (GNNs) achieve strong performance on node classification tasks in a semi-supervised learning setting. However, as in the simpler homogeneous GNN case, message-passing-based heterogeneous GNNs may struggle to balance between resisting the oversmoothing that may occur in deep models, and capturing long-range dependencies of graph structured data. Moreover, the complexity of this trade-off is compounded in the heterogeneous graph case due to the disparate heterophily relationships between nodes of different types. To address these issues, we propose a novel het…
Self-Pro: A Self-Prompt and Tuning Framework for Graph Neural Networks
School of Data Science and Engineering, East China Normal University（华东师范大学数据科学与工程学院）；School of Computer and Information Engineering, Shanghai Polytechnic University（上海第二工业大学计算机与信息工程学院）
