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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

arXiv:2202.07082v4cs.LG

TL;DR

On spatial-temporal graphs, fixed homophilic message-passing topologies can aggregate neighbors that do not match the intended target. This survey classifies heterophilic GNNs and reports that recent specialized architectures outperform traditional baselines on high-quality benchmark datasets.

  • Problem

    For node-level regression on spatial-temporal graphs, fixed homophilic message-passing topologies can aggregate neighbors that do not match the intended target.

    Source: 1) Heterophily GNNs on Dynamic Graphs · p. 13

  • Method

    The survey categorizes heterophilic GNNs into non-local neighbor extension, architecture refinement, and hybrid approaches.

    Source: §IX · p. 16

  • Results

    Recent state-of-the-art heterophilic architectures consistently outperform traditional baselines on five high-quality benchmark datasets.

    Source: C PERFORMANCE COMPARISON · p. 21

  • Takeaways & Limitations

    The benchmark comparison supports the practical efficacy of heterophily-specific inductive biases across diverse and challenging graph structures.

    Source: C PERFORMANCE COMPARISON · p. 21

    Research predominantly focuses on social and web-page networks, while heterophilic applications in biomedicine and chemistry warrant more exploration.

    Source: §VIII · p. 16

Abstract

from arXiv · show

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.

I. INTRODUCTION

Homophily-based GNNs can perform poorly on heterophilic graphs because local neighbor aggregation misses useful non-local relationships and fails to distinguish their information from dissimilar local neighbors. The survey organizes heterophilic GNN research, connects it to broader graph domains, and identifies future directions.

Core Challenges of GNNs for Heterophily

  • Heterophily limits homophily-based GNNs: local aggregation misses same-class non-local neighbors and struggles to distinguish their information from dissimilar local neighbors.The survey identifies these as two core challenges: discovering informative non-local nodes and learning discriminative representations that capture heterophily.Source: §I · pp. 1–2

Importance and Contributions

  • The survey examines connections between heterophily and model robustness, over-smoothing, and graph anomaly detection.It argues that understanding diverse heterophilic graphs can guide model development and broaden GNN adaptability across graph research domains.Source: §I · pp. 2–3

Future Directions

  • It identifies limitations and future directions in interpretability, robustness, scalability, and heterophilic graph data exploration.The survey also frames heterophilic graph analysis and learning as promising areas with open challenges in expressive performance, robustness, and generalization.Source: §I · pp. 2–3

Distinctions from Existing Surveys

  • Unlike Zhu et al. and Gong et al. [33], the survey integrates developments through March 2025, adds a hierarchical taxonomy, and presents technical visualizations and mathematical formulations.It also extends beyond Luan et al. [34] by incorporating critical March 2025 advances after their Q2-2024 cutoff and providing a clearer hierarchical classification.Source: §I · p. 2

Contributions

  • The survey offers a comprehensive overview of heterophilic GNN data, algorithms, and applications, and classifies methods as non-local neighbor extension, architecture refinement, or hybrid approaches.It describes model types and compares their approaches to heterophily learning.Source: §I · p. 2

II. PRELIMINARY … D. Measure of Heterophily & Homophily

The preliminary sections define graph notation and standard GNN and spectral-convolution operations, then describe several measures of homophily, including measures designed to address limitations of simpler metrics.

A. Notations

  • The graph is represented by nodes, edges, features, and an adjacency matrix; its Laplacian can use symmetric or random-walk normalization and has an eigendecomposition.Source: A. Notations · p. 3

B. Graph Neural Networks

  • GNN layers update node representations by aggregating neighbor messages and combining them with each node’s own representation.The first layer takes the feature matrix as input, and the final representations are fed to a classifier for node classification.Source: B. Graph Neural Networks · p. 3

C. Spectral Graph Convolution

  • Spectral methods learn a frequency-response function that reweights eigenvalue-associated signals; low-pass filters retain more low-frequency information, while high-pass filters retain more high-frequency information.The passage gives FLP = ϵI + D−1/2AD−1/2 and FHP = ϵI − D−1/2AD−1/2 as low- and high-pass filters, respectively.Source: C. Spectral Graph Convolution · p. 3

D. Measure of Heterophily & Homophily

E. Real-World Benchmarks · F. Mainstream Heterophily Learning Task

The survey reviews benchmark datasets for heterophilic graphs and frames semi-supervised node classification as the main learning task, with cross-entropy training on labeled nodes used to predict unlabeled nodes.

E. Real-World Benchmarks

  • Pei et al. introduced six small-scale heterophilic graph benchmarks that remain the most widely adopted: Cornell, Texas, Wisconsin, Chameleon, Squirrel, and Actor.Source: E. Real-World Benchmarks · p. 4
  • Lim et al., expanded the benchmark landscape with large-scale datasets including ArXiv-Year, Snap-Patents, Penn94, Pokec, Genius, Deezer-Europe, Twitch-Gamers, and YelpChi.Source: E. Real-World Benchmarks · p. 4
  • Work in identified small scale, class imbalance, and class leakage in earlier datasets, then introduced Roman-Empire, Amazon-Ratings, Minesweeper, Tolokers, and Questions.Source: E. Real-World Benchmarks · p. 4

F. Mainstream Heterophily Learning Task

III. GNNS WITH HETEROPHILY: FRAMEWORK AND TAXONOMY … A. High-order Neighbor Mixing

The paper frames heterophilic GNN design around tailored neighborhood aggregation and feature updates, then organizes methods by how they capture non-local information and distinguish or fuse messages. High-order neighbor mixing combines information from multiple graph distances to incorporate richer, potentially homophilic signals.

A. Framework of heterophilic GNNs

  • Heterophilic GNNs tailor aggregation and feature updates around non-local neighbors, class distinguishability, and fusion of information across layers.These three principles guide the paper’s framework and taxonomy.Source: A. Framework of heterophilic GNNs · p. 4, §III · p. 4

B. Taxonomy of GNNs with Heterophily

  • The taxonomy groups methods into non-local neighbor extension, architecture refinement, and hybrid approaches combining both.Non-local extension reconstructs neighbor sets using multi-hop nodes; the set Np(v) includes nodes within distance threshold p and reduces to one-hop neighbors when p = 1 under shortest-path distance.Source: B. Taxonomy of GNNs with Heterophily · pp. 4–5
  • Extension methods can be memory-intensive on large graphs, refinement methods depend on limited observable relationships, and hybrids combine their advantages.Refinement methods use identifiable aggregation or inter-layer combinations; identifiable aggregation may weight edges, features, or both.Source: B. Taxonomy of GNNs with Heterophily · p. 5

IV. HETEROPHILIC GNNS WITH NON-LOCAL NEIGHBOR EXTENSION

  • Heterophilic GNNs extend one-hop neighborhoods through high-order mixing or potential-neighbor discovery to capture informative features from distant nodes.Nodes of the same class may be structurally similar yet farther apart, making a strictly local neighborhood inadequate.Source: §IV · p. 5

A. High-order Neighbor Mixing

  • High-order mixing lets each node receive representations from one-hop and further k-hop neighbors, combining information from neighborhoods at different distances.Its goal is to mitigate local heterophily by incorporating richer homophilic information from higher-order neighborhoods.Source: A. High-order Neighbor Mixing · pp. 5–6
  • MixHop transforms and concatenates messages from one- and two-hop neighbors, while TDGNN uses tree decomposition to fuse neighborhood information across layers.MixHop fuses hop-level information after aggregation and updating; TDGNN instead merges cross-hop neighbors before aggregation.Source: A. High-order Neighbor Mixing · pp. 5–6
  • Ordered GNN assigns hop-specific messages to neuron blocks, whereas EvenNet retains only even-order messages using a balance-theory-inspired graph filter.EvenNet’s filter generalizes to graphs with different homophily.Source: A. High-order Neighbor Mixing · p. 6

B. Potential Neighbor Discovery … 3) Hybrid Distance:

Potential neighbor discovery redefines neighborhood structure in heterophilic graphs by exploring the topology to add nodes beyond the original neighbors. Methods use structural, feature-based, or hybrid distance measures to identify potential neighbors.

B. Potential Neighbor Discovery

  • These methods extend original neighbor sets with potential neighbors discovered through topology exploration, using structural, feature, or hybrid distance measures.The distance function measures node separation in a defined latent space, while a threshold can limit the number of neighbors.Source: B. Potential Neighbor Discovery · p. 6

1) Structure-based Distance:

  • Geom-GCN maps the input graph into a continuous latent space and adds nodes with qualifying geometric relationships to GCN message aggregation.Its structural neighborhood combines original adjacent nodes with potential neighbors whose latent-space distance is below a threshold.Source: 1) Structure-based Distance · p. 6

2) Feature-based Distance:

  • U-GCN and SimP-GCN select each ego node’s top k feature-similar nodes by cosine similarity, while HES-GSL adds homophily-enhanced self-supervision for similarity learning.The number of nearest neighbors is manually set; HES-GSL also uses cosine similarity to determine node-pair relationships.Source: 2) Feature-based Distance · p. 6

3) Hybrid Distance:

  • HOG-GCN uses class-aware propagation to estimate same-class relationships across the graph, giving greater aggregation weight to intra-class nodes with lower homophily degree.GloGNN measures global node correlations using both attribute and topology similarity, regularizing representations with multi-hop reachability.Source: 3) Hybrid Distance · pp. 6–7
  • SE-GSL uses structural entropy and sampling to restore graph structure, increasing connectivity among nodes with greater uncertainty in lower-level communities.Its structural-diversity measure incorporates both kNN and original topology structures.Source: 3) Hybrid Distance · p. 7
  • GraphTU probabilistically creates potential neighbor sets through a non-parametric method using statistical-variance features and local-neighborhood topology, especially to address heterophily involving minor-class nodes.Source: 3) Hybrid Distance · p. 7
  • GOAL completes the graph with homophilic and heterophilic connections, distinguishing them through Connected Structure Difference between connected and randomly selected node pairs.The distinction guides optimization of the complemented graph.Source: 3) Hybrid Distance · p. 7
  • Overall, potential neighbor discovery seeks homophilic high-order neighbors to add to local sets, enabling homophilic message passing through similarity-based identification.Source: 3) Hybrid Distance · p. 7

V. HETEROPHILIC GNN ARCHITECTURE REFINEMENT · A. Identifiable Message Aggregation · 1) Edge-Related Weight:

Architecture refinements seek to exploit local and non-local neighbors by revising aggregation and update functions, with identifiable message aggregation distinguishing similar from dissimilar neighbors. Edge-related weights use spectral filters or spatial graph information to adapt neighbor messages on heterophilic graphs.

V. HETEROPHILIC GNN ARCHITECTURE REFINEMENT

  • Architecture refinements revise aggregation and update functions to exploit local and non-local neighbors and produce more distinguishable node representations.The two refinement aspects are identifiable message aggregation and inter-layer combination, which emphasize different propagation ranges.Source: §V · pp. 7–8

A. Identifiable Message Aggregation

1) Edge-Related Weight:

  • Spectral methods combine low-pass filters that retain commonality with high-pass filters that capture differences between node features.FAGCN uses self-gating attention to adapt the proportions of low- and high-frequency signals, while RFA-GNN uses higher-order relation context for edge-aware weights.Source: 1) Edge-Related Weight · pp. 8–9
  • ACM, AutoGCN, and Mid-GCN adaptively use different filter channels, while identity or mid-pass filters help limit input-signal information loss.Mid-GCN's mid-pass signal robustness is theoretically guaranteed by its analyses.Source: 1) Edge-Related Weight · p. 9
  • Spatial methods assign edge weights using graph topology and node labels; DMP uses node attributes as weak labels for diverse message passing.DMP extends scalar node-level weights to vectors across attributes, calculated by relaxing GAT weights to real values or averaging neighbor weights element-wise.Source: 1) Edge-Related Weight · p. 9
  • GDAMNs use variational inference and hard label-similarity and soft feature-dissimilarity attention to learn edge weights and reduce inter-class edges.Soft attention then weights messages using features over the refined graph to enhance information gains.Source: 1) Edge-Related Weight · p. 9
  • For large-scale graphs, CGP prunes graphs during training to discover sparse GNNs, while GOAT samples k-hop candidate neighbors and learns global attention scores.GOAT uses the attention scores to distinguish potential neighbors from source nodes by topology information during propagation.Source: 1) Edge-Related Weight · p. 9

2) Feature-Related Weight:

Feature-related weighting improves heterophilic GNNs by revising neighbor representations and learning node-level weights that use heterophily-relevant properties to guide aggregation. The survey groups these approaches into prior-based and attention-based schemes.

2) Feature-Related Weight:

  • Node-level weights β(l) use heterophily-relevant properties to select useful neighbor information and make aggregation more distinguishable.The weight β(l)_v is shared across each neighbor u of node v.Source: 2) Feature-Related Weight · pp. 9–10

Prior-Based

  • CPGNN propagates prior belief estimates based on a compatibility matrix to model connection likelihoods between classes, capturing homophily and heterophily; Sinkhorn-Knopp ensures β(l) is doubly stochastic.NLGNN and GPNN rank neighbors by class similarity for sequential aggregation; GIND learns nonlinear pairwise flux features before aggregation to aggregate more information from similar neighbors and less from dissimilar ones.Source: 2) Feature-Related Weight · p. 10

Attention-Based

  • CGCN [28] uses cosine similarity and relative-degree constraints to send signed neighbor features, while GBK-GNN gates between kernels capturing homophily and heterophily.Signed messages can negate features from opposing-class neighbors and preserve positive messages from same-class neighbors.Source: 2) Feature-Related Weight · p. 10
  • MMP separates propagation memory from discriminative self-embeddings and uses a learnable control mechanism to update both from their recent states.CAGNNs use von Neumann entropy to identify inter-class edges from the perspective of the entire identifiable neighborhood, then mix discriminant features with neighbor information.Source: 2) Feature-Related Weight · p. 10
  • NCGNN dynamically routes node-level capsules from filtered subgraphs, aggregating advantageous capsules while constraining irrelevant messages to reduce excessive feature mixing and oversmoothing.The approach is designed to learn effective representations in graphs with either homophily or heterophily.Source: 2) Feature-Related Weight · p. 10

3) Hybrid Weight:

Hybrid methods use node features and edge information together to guide edge weights, while ego-neighbor separation methods preserve distinct representations for a node and its neighbors on heterophilic graphs.

Hybrid Weight

  • MWGNN models node-local distributions from features, topology, and positional identity to derive meta-weight-guided, node-specific adaptive graph convolution.Its weighted aggregation is intended to boost node representation learning.Source: 3) Hybrid Weight · p. 10
  • Ego-neighbor separation detaches self-loops during aggregation and uses non-mixing updates, helping expressive node representations survive multiple propagation rounds.H2GCN first proposes excluding self-loops and highlights non-mixing updates such as concatenation rather than averaging.Source: 3) Hybrid Weight · p. 10
  • WRGNN, GGCN [28], and ACM separately model ego and neighbor information using distinct mappings, learnable scalar parameters, and identity-filter channel-level combination, respectively.These designs separate the ego embedding from aggregated neighbor messages before combining their information.Source: 3) Hybrid Weight · p. 11

B. Inter-Layer Combination

Inter-layer combination methods merge representations from different GNN depths to use both local and global structural information, since similar-label neighbors may occur in either range. This approach supports more expressive node representations for heterophilic graphs.

B. Inter-Layer Combination

  • Combining layer-wise representations spans local and global neighbor ranges, where similar-label nodes may occur, and boosts heterophilic GNN representation power.Shallow layers collect local information, while deeper layers implicitly capture global information through repeated neighbor propagation.Source: B. Inter-Layer Combination · p. 11
  • JK-Net combines features from different layers to capture structure-aware representations across neighborhood ranges, using aggregation such as concatenation, max pooling, or LSTM attention.The layer aggregation operation can use column-wise combination, max pooling, or attention with LSTM.Source: B. Inter-Layer Combination · p. 11
  • GCNII integrates the first-layer node embedding at each layer with an initial residual connection, balancing it against the current-layer representation with hyperparameter α.This differs from methods that use all previous intermediate representations.Source: B. Inter-Layer Combination · p. 11
  • GPRGNN adaptively combines layer representations with learnable Generalized PageRank weights, while PowerEmbed uses an inception network to interpolate local message-passing features and global spectral information.These methods explore topological features and leverage multi-round propagation to make heterophilic-graph node features more distinguishable.Source: B. Inter-Layer Combination · p. 11

VI. HYBRID METHODS … 2) Heterophily GNNs on Hypergraphs:

The survey groups hybrid methods by how they extend heterophilic message passing, then examines heterophily in dynamic graphs and hypergraphs. It highlights the challenges of modeling these settings and the need for reliable evaluation.

VI. HYBRID METHODS

  • Hybrid methods extend heterophilic GNNs through local message-passing or global inter-layer incorporation, with most surveyed methods using the local approach.Local methods typically first construct a topology emphasizing local homophily, then aggregate over it; examples include WRGNN, BM-GCN, RAW-GNN, GPNN, and Deformable GCN.Source: §VI · pp. 11–12, Table III · p. 12
  • Global-level methods provide homophilic guidance through inter-layer information transfer, as H2GNN and NLGNN illustrate.H2GNN separates ego and neighbor embeddings, uses higher-order neighborhoods, and incorporates intermediate representations; NLGNN sorts non-local neighbors by attention before aggregating them in two steps.Source: §VI · p. 12

VII. DISCUSSION

  • The survey cautions that early heterophily results may be affected by dataset flaws and metrics, while well-tuned GCNs can succeed under specific conditions.It cites class imbalance and data leakage, proposes label informativeness for cross-dataset comparison, and notes GCNs succeed on some graphs, when neighborhood distributions across classes are distinguishable; it recommends reliable, high-quality datasets.Source: §VI · p. 12

A. Heterophily GNNs on Diverse Graph Types

  • Although research mainly studies static single-relational graphs, applications such as traffic dynamics and co-purchasing involve dynamic graphs and hypergraphs –.The survey describes heterophily in these graph types as an emerging research area with distinct challenges for GNNs.Source: A. Heterophily GNNs on Diverse Graph… · p. 12

1) Heterophily GNNs on Dynamic Graphs:

  • Topology-task discordance arises when fixed message-passing topologies aggregate neighbors that do not match node-level regression targets on time-varying spatial-temporal graphs.Open challenges include identifying homophily without categorical labels, using target information to reconstruct node correlations, and personalizing high-order propagation to dynamic neighborhoods.Source: 1) Heterophily GNNs on Dynamic Graphs · p. 13
  • Spatial-temporal heterophily is characterized by low intra-graph and inter-graph-transition homophily across Metr-LA, PeMS-Bay, KnowAir, and Temperature.These measurements suggest physically connected nodes may have dissimilar observations or directional changes.Source: 1) Heterophily GNNs on Dynamic Graphs · p. 13

2) Heterophily GNNs on Hypergraphs:

  • Heterophily may be more prevalent in hypergraphs than graphs because large hyperedges need not contain nodes with a common label.Li et al. initiated heterophilic hypergraph learning by addressing measurement, dataset diversity, and baseline development; hypergraph research has since emphasized performance on heterophilic data.Source: 2) Heterophily GNNs on Hypergraphs · p. 13
  • ED-HNN [110] approximates continuous equivariant hypergraph diffusion operators and reports superior heterophilic node-label prediction on four hypergraphs.Hyperedge mixtures of node categories make prediction more intricate than in graphs; the review says characterization and architecture design for specific heterophilic hypergraphs remain open challenges. Evaluated datasets are Congress, Senate, Walmart, and House.Source: 2) Heterophily GNNs on Hypergraphs · p. 13

3) Heterophily GNNs on Heterogeneous Graphs: … 3) Relation between Graph Heterophily and Graph Anomaly Detection:

The section connects heterophily to heterogeneous-graph learning, adversarial robustness, over-smoothing, and graph anomaly detection, highlighting heterophily-aware methods and unresolved dataset limitations.

3) Heterophily GNNs on Heterogeneous Graphs:

  • Lin et al. [117] show heterophilic patterns in homogeneous graphs and homophilic structures in heterogeneous graphs, and introduce H2GB; Shen et al. define semantic heterophily and propose LatGRL.LatGRL uses latent graph-guided reinforcement learning for hierarchical feature disentanglement; existing benchmarks remain limited in scale and scenario coverage.Source: 3) Heterophily GNNs on Heterogeneous… · p. 13

1) Relation between Graph Heterophily and Adversarial Robustness:

  • Structural attacks on GNNs exhibit heterophily, and research describes two defense paradigms: explicit adversarial filtering and implicit robustness from heterophily-adaptive architectures.Theoretical work establishes homophily–heterophily dynamics under structural attacks and argues heterophily-aware designs enhance robustness.Source: 1) Relation between Graph Heterophily… · p. 14
  • GNNGUARD filters adversarial heterophilic edges using feature–structure correlations, while GARNET and ATDGIA treat heterophilic connections as adversarial edges.These methods use antiinterference mechanisms to support robust message propagation.Source: 1) Relation between Graph Heterophily… · p. 14

2) Relation between Graph Heterophily and OverSmoothing:

  • Heterophilic aggregation can dissipate information in deep architectures, while heterophilic GNNs such as FAGCN and NLGNN exhibit anti-over-smoothing properties.Some over-smoothing mitigation strategies also improve heterophilic learning.Source: 2) Relation between Graph Heterophily… · p. 14
  • Cellular sheaf theory links heterophily and over-smoothing; negative signed edges [28], support FAGCN, and unified frameworks address the depth-performance trade-off.These frameworks improve performance across heterophilic benchmarks while maintaining stable higher-layer performance.Source: 2) Relation between Graph Heterophily… · p. 14

3) Relation between Graph Heterophily and Graph Anomaly Detection:

  • Fraudulent nodes typically form minority clusters surrounded by normal nodes and have higher heterophily ratios than legitimate entities, while homophilic GAD methods amplify heterophily-induced noise.This noise is associated with significant performance degradation on real-world fraud detection benchmarks.Source: 3) Relation between Graph Heterophily… · p. 14
  • Gong et al. prune heterophilic edges while preserving homophilic dependencies, and Gao’s SDS uses adversarial topology regularization to mitigate structural distribution shifts between imbalanced classes.Source: 3) Relation between Graph Heterophily… · p. 14
  • Hybrid methods, combine low- and high-frequency signals through adaptive graph filtering, improving performance over conventional GAD baselines for heterophilic anomalies.The survey identifies heterophily suppression as critical for robust fraud detection systems.Source: 3) Relation between Graph Heterophily… · p. 14

4) Relation between Graph Heterophily and Uncertainty Modeling: · VIII. FUTURE DIRECTIONS · IX. CONCLUSION

The survey organizes heterophilic GNNs into three method classes, reviews their links to other graph-learning domains, and identifies open directions for advancing the field.

4) Relation between Graph Heterophily and Uncertainty Modeling:

  • Heterophilic mixed neighborhoods create topological uncertainty and expose homophily bias, motivating uncertainty-aware prediction and topology augmentation.Liu’s framework uses epistemic uncertainty to identify heterophilic nodes, while GraphTU uses neighborhood variance for non-parametric topology perturbation that enhances minor-class representation.Source: 4) Relation between Graph Heterophily… · p. 14
  • Self-supervised heterophilic GNNs adapt contrastive learning to identify intra-class neighbors or discriminate edge homophily, extending beyond standard augmentation.He et al. combine GCL sampling with homophily discrimination; PairE preserves homophilic and heterophilic information through higher-level entities; GREET learns from contrastive views of both edge types.Source: 4) Relation between Graph Heterophily… · p. 15

VIII. FUTURE DIRECTIONS

  • Explaining heterophilic GNN predictions remains under-explored because explanations may require proximal and distant structures and must account for complex ego-neighbor similarities.Open questions include extracting explainable subgraphs from the data-centric view and explaining model predictions across different degrees of heterophily; ShapeGGen provides a benchmark dataset generator with ground-truth explanations.Source: §VIII · p. 15
  • Scaling heterophilic GNNs remains difficult: minibatch sampling can undermine heterophilic relationships, while preserving heterophily during sampling is still open.LINKX shows an MLP-based model can outperform GNNs in minibatch training on large heterophilic graphs, and HopGNN uses preprocessed multi-hop features to address scalability and over-smoothing.Source: §VIII · p. 16
  • Theoretical work is needed to substantiate heterophilic GNNs’ empirical efficacy and clarify how heterophily affects generalization bounds and homophilic GNN performance.Ma et al. showed that GCN can perform remarkably on heterophilic graphs under specific conditions, challenging prevailing design rationales.Source: §VIII · p. 16
  • Heterophilic learning research should expand beyond node-level tasks; link- and graph-level learning still need suitable benchmarks and architectures.DisenLink [141] models links as shaped by latent factors that can make linked nodes similar in some respects but dissimilar in others, challenging homophily-based prediction.Source: §VIII · p. 16
  • Heterophilic GNN research should extend beyond social and web graphs into fields including biomedicine, chemistry, finance, network security, and community detection.The paper notes heterophilic protein interactions and drug-drug networks, and describes fraud detection methods DRAG [151] and GAGA for binary heterophilic graph classification.Source: §VIII · p. 16

IX. CONCLUSION

  • The survey’s taxonomy groups heterophilic GNN methods into non-local neighbor extension, architecture refinement, and hybrid approaches, while reviewing progress, challenges, and future opportunities.It also discusses links between heterophily and model robustness, over-smoothing, and graph anomaly detection.Source: §IX · p. 16

APPENDIX A MEASURE OF HETEROPHILY & HOMOPHILY … E TIMELINE OF HETEROPHILY GNNS

The appendices explain homophily measures and benchmark datasets, compare models on high-quality benchmarks, list available implementations, and trace heterophilic GNN development.

APPENDIX A MEASURE OF HETEROPHILY & HOMOPHILY

  • Higher Hnode, Hedge, Hclass, Hadj, and Hun indicate stronger homophily, but Hnode and Hedge depend on class count and balance, while Hclass misses degree variation and heterophilic connectivity.Hadj can be negative when Hedge is below PC; the survey notes Hadj and Hun as alternatives advised by and.Source: Appendix A · p. 21

APPENDIX B REAL-WORLD BENCHMARKS

  • The survey organizes real-world heterophilic graph benchmarks into standard, large-scale, and high-quality dataset categories.Source: Appendix B · p. 21

A. Standard Datasets

  • Standard benchmarks include WebKB subdatasets Cornell, Texas, and Wisconsin, Wikipedia web-page datasets Chameleon and Squirrel [154], and the actor co-occurrence network Actor.These are among the first six datasets used in many empirical evaluations, originally presented in.Source: A. Standard Datasets · p. 21

B. Large-Scale Datasets

  • Large-scale benchmarks include ArXiv-Year, Snap-Patents, Penn94, Pokec, Genius, Deezer-Europe, Twitch-Gamers, and YelpChi, collected and released by and.They cover citation, online social, and web-page hotel and restaurant review data.Source: B. Large-Scale Datasets · p. 21

C. High-Quality Datasets

  • Duplicate nodes in standard datasets such as Squirrel and Chameleon can cause train-test leakage, motivating reliable benchmarks including Roman-Empire, Amazon-Ratings, Minesweeper, Tolokers, and Questions.Removing duplicates strongly affects GNN performance on Squirrel and Chameleon.Source: C. High-Quality Datasets · p. 21

C PERFORMANCE COMPARISON

  • On five high-quality benchmarks, ACM-GCN, AGS-GNN, and PD-GNN consistently outperform traditional baselines, though some earlier specialized models are occasionally surpassed.The survey presents these evaluations as a more realistic assessment of the models’ utility.Source: C PERFORMANCE COMPARISON · p. 21, Table VIII · p. 22

D OPEN-SOURCE IMPLEMENTATIONS

E TIMELINE OF HETEROPHILY GNNS

  • The timeline traces early layer-inter-combination, non-local-neighbor, and hybrid methods, followed by adaptive aggregation and later dynamic routing, self-supervision, and memory-based attention.Examples include JK-Net, GPR-GNN, GCNII, MixHop, Geom-GCN, H2GCN, FAGCN, NCGNN, GREET, and MMP.Source: E TIMELINE OF HETEROPHILY GNNS · pp. 22, 24, Figure 12 · p. 23

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