Powerful Graph Convolutional Networks with Adaptive Propagation Mechanism for Homophily and Heterophily

Tao WangDi JinRui WangDongxiao HeYuxiao Huang

article2022AAAI137 citations

Proposes an adaptive graph convolutional network that dynamically adjusts feature propagation weights based on topological and attribute-driven homophily estimates between node pairs, effectively overcoming standard performance drops on heterophilic graphs.

Listen

Graph Convolutional Networks are essential machine learning tools used to analyze interconnected data across diverse domains, including social network analysis, biology, and recommendation systems. However, conventional network models rely on the foundational assumption of homophily, which presumes that connected entities naturally share identical labels or characteristics. In many critical real-world systems, networks exhibit heterophily—where linked entities belong to entirely different categories, such as opposite-gender interactions in dating networks or distinct amino acids in protein structures. Standard models struggle in these heterophilic environments because their fixed information-passing mechanisms indiscriminately mix conflicting data from dissimilar neighbors.

The article develops and evaluates a new architecture, termed Homophily-Guided Graph Convolutional Network (HOG-GCN), designed to adaptively adjust its internal information propagation mechanism across both homophilic and heterophilic environments.

To address the limitations of prior techniques, the article introduces a dual-source estimation approach that measures the similarity between node pairs using both node characteristics and structural network positions. This estimated relationship matrix dynamically scales information flow: it strengthens signals between same-class nodes while dampening interference from different-class connections across two-step neighborhoods. The system trains the relationship estimation and information propagation jointly in a unified process. The article evaluates this design through semi-supervised classification experiments across seven real-world benchmark datasets—four exhibiting strong heterophily and three exhibiting traditional homophily—using standardized data splits.

The findings show that the proposed method consistently delivers superior predictive accuracy across diverse network types. In heterophilic networks, the architecture outperformed traditional graph models by an average of 24.5% to 26.5% in classification accuracy and surpassed specialized heterophily baselines by 3.9% to 19.0%. On homophilic networks, it achieved competitive or superior accuracy compared to standard models, maintaining top performance across datasets. Experimental parameter analyses established that examining two-step neighborhoods strikes the optimal balance for gathering relevant same-class signals, while broader neighborhood expansion introduces disruptive noise. Visual analysis confirmed that the approach produces sharply separated, well-defined classification boundaries.

These results demonstrate that graph learning systems can overcome structural assumptions without requiring separate model architectures for different types of relational data. For organizations relying on graph-based decision support, anomaly detection, or predictive modeling, this adaptability reduces deployment risk and lowers analytical error rates in complex environments where network relationships deviate from standard assumptions.

Technical leaders and data science teams implementing relational machine learning models should transition from rigid neighborhood aggregation pipelines to adaptive propagation frameworks when processing heterogeneous or mixed-relation graphs. Before full-scale deployment in production environments, teams should benchmark the architecture on domain-specific data and verify neighborhood search depths, as expanding beyond two-step connections risks incorporating unwanted data noise.

The study's empirical validations rely on seven standard benchmark datasets and specific semi-supervised data splits. While the empirical results and theoretical proofs provide strong confidence in the method's core effectiveness, operational performance may vary in extremely large-scale, dynamically changing networks that require specialized scaling optimizations.

George Washington University Tianjin University attention mechanism convolutional neural networks graph neural networks graph convolutional networks adaptive propagation mechanism homophilic networks

arXiv: 2112.13562

Paper: Beyond Homophily in Graph Neural Networks: Current Limitations and Effective Designs, Jiong Zhu et al. (2020). It identifies the fundamental theoretical and architectural limitations of traditional graph neural networks in heterophilous settings, establishing the key design principles that this paper directly builds upon and improves.
Paper: Geom-GCN: Geometric Graph Convolutional Networks, Hongbin Pei et al. (2020). It introduces foundational benchmarks and geometric aggregation methods for learning on disassortative and heterophilous graphs, which motivates this work's adaptive propagation framework.
Paper: Semi-Supervised Classification with Graph Convolutional Networks, Thomas N. Kipf et al. (2017). It provides the foundational graph convolutional network architecture and propagation rule under the homophily assumption that the source paper seeks to generalize.
Paper: Representation Learning on Graphs with Jumping Knowledge Networks, Keyulu Xu et al. (2018). It analyzes multi-hop aggregation depth and representation combination strategies in graph neural networks, addressing the baseline aggregation mechanisms critiqued by the source.
Paper: Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning, Qimai Li et al. (2018). It formalizes graph convolution as Laplacian smoothing and demonstrates the resulting over-smoothing and class-mixing issues that become particularly problematic under heterophily.
Paper: How Powerful are Graph Neural Networks?, Keyulu Xu et al. (2019). It establishes the theoretical framework for analyzing the expressive and distinguishing power of neighborhood aggregation in graph neural networks.

Paper: Ordered GNN: Ordering Message Passing to Deal with Heterophily and Over-smoothing, Yunchong Song et al. (2023). It extends message-passing under heterophily by structuring and ordering neuron segments according to neighborhood hierarchy to simultaneously alleviate oversmoothing.
Paper: Finding Global Homophily in Graph Neural Networks When Meeting Heterophily, Xiang Li et al. (2022). It advances beyond local pairwise homophily adjustments by identifying and aggregating globally homophilous nodes across the entire graph under heterophily in linear time.
Paper: Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs, Cristian Bodnar et al. (2022). It generalizes adaptive propagation under heterophily through continuous topological cellular sheaf diffusion, providing deeper mathematical explanations for avoiding representation collapse.
Paper: GREAD: Graph Neural Reaction-Diffusion Networks, Jeongwhan Choi et al. (2023). It continues the investigation into robust graph propagation under non-homophilous conditions by formulating neural message passing via generalized reaction-diffusion systems.

Cover for Powerful Graph Convolutional Networks with Adaptive Propagation Mechanism for Homophily and Heterophily

Abstract

Graph Convolutional Networks (GCNs) have been widely applied in various fields due to their significant power on processing graph-structured data. Typical GCN and its variants work under a homophily assumption (i.e., nodes with same class are prone to connect to each other), while ignoring the heterophily which exists in many real-world networks (i.e., nodes with different classes tend to form edges). Existing methods deal with heterophily by mainly aggregating higher-order neighborhoods or combing the immediate representations, which leads to noise and irrelevant information in the result. But these methods did not change the propagation mechanism which works under homophily assumption (that is a fundamental part of GCNs). This makes it difficult to distinguish the representation of nodes from different classes. To address this problem, in this paper we design a novel propagation mechanism, which can automatically change the propagation and aggregation process according to homophily or heterophily between node pairs. To adaptively learn the propagation process, we introduce two measurements of homophily degree between node pairs, which is learned based on topological and attribute information, respectively. Then we incorporate the learnable homophily degree into the graph convolution framework, which is trained in an end-to-end schema, enabling it to go beyond the assumption of homophily. More importantly, we theoretically prove that our model can constrain the similarity of representations between nodes according to their homophily degree. Experiments on seven real-world datasets demonstrate that this new approach outperforms the state-of-the-art methods under heterophily or low homophily, and gains competitive performance under homophily.

Topics

attention mechanism convolutional neural networks graph neural networks network architecture

Keywords

graph convolutional networks adaptive propagation mechanism homophilic networks heterophilic networks Homophily Degree Matrix Estimation feature propagation node classification collective classification

Introduction
Preliminaries
Notations and Problem Descriptions
The Framework
Overview
Homophily Degree Matrix Estimation
Homophily-guided Propagation
Optimization Objective
Theoretical Analysis
Experiments
Experimental Setup
Visualization
Node Classification
Parameter Analysis
Homophily Degree Matrix Analysis
Conclusion
Acknowledgments
References

Knowls

Knowl 1 — HOG-GCN adaptive homophily-guided propagation
model/method
HOG-GCN is a graph convolutional network for semi-supervised node classification that changes feature propagation according to a learned homophily degree matrix. For an undirected graph with adjacency matrix $A\in\mathbb{R}^{n\times n}$ , node-feature matrix $X\in\mathbb{R}^{n\times f}$ , and $C$ node classes, define the $k$ -order adjacency matrix as $A_k=\sum_{r=1}^{k}A^r$ . Let $H\in\mathbb{R}^{n\times n}$ encode the estimated homophily degree between node pairs, and let $\widehat D$ be diagonal with $\widehat D_{ii}=\sum_j(A_k\odot H)_{ij}$ , where $\odot$ denotes elementwise multiplication. The propagation layer is
$Z^{(l)}=\sigma\!\left(\mu Z^{(l-1)}W_e^{(l)}+\xi\widehat D^{-1}(A_k\odot H)Z^{(l-1)}W_n^{(l)}\right),\qquad Z^{(0)}=X.$
Here $Z^{(l)}\in\mathbb{R}^{n\times d_l}$ is the layer- $l$ representation, $W_e^{(l)}$ and $W_n^{(l)}$ are learnable ego- and neighborhood-transformation matrices, $\sigma$ is an activation function, and $\mu,\xi$ weight the ego and neighborhood representations. Thus, high-homophily pairs receive stronger feature influence, while low-homophily pairs receive weaker influence; ego features are handled separately to preserve node-specific information. The paper uses $k=2$ in its main experiments.
Knowl 2 — Attribute-based homophily estimation
model/method
HOG-GCN estimates homophily from node attributes with a graph-independent multilayer perceptron. For node features $X\in\mathbb{R}^{n\times f}$ and $C$ classes, the MLP computes
$Z_m^{(l)}=\sigma\!\left(Z_m^{(l-1)}W_m^{(l)}\right),\qquad Z_m^{(0)}=X,$
where $W_m^{(l)}$ is learnable and $Z_m$ denotes the final-layer output. A row-wise softmax produces the class-probability matrix $B\in\mathbb{R}^{n\times C}$ :
$B=\operatorname{softmax}(Z_m),$
so $B_{ic}$ is the MLP-estimated probability that node $v_i$ belongs to class $c$ . The MLP is trained on the labeled node set $V_L$ using cross-entropy between its predictions and the known one-hot labels. The attribute-derived homophily matrix is
$S=BB^{\mathsf T},\qquad S_{ij}=b_i b_j^{\mathsf T},$
where $b_i$ and $b_j$ are the class-probability vectors for nodes $v_i$ and $v_j$ . Thus, $S_{ij}$ measures the similarity of the two nodes' predicted class distributions and can provide class-aware propagation guidance even when graph edges are heterophilic.
Knowl 3 — Topology-based generalized label propagation
model/method
To estimate homophily from graph topology without assuming that adjacent nodes share a class, HOG-GCN learns edge weights through generalized label propagation. For an adjacency matrix $A$ and neighborhood order $k$ , it uses $A_k=\sum_{r=1}^{k}A^r$ . A learnable matrix $T\in\mathbb{R}^{n\times n}$ assigns weights to existing $k$ -order neighborhoods; it does not add or remove graph connections. With initial soft labels $Y^{(0)}\in\mathbb{R}^{n\times C}$ equal to one-hot labels on labeled nodes and zero vectors on unlabeled nodes, the propagation is
$Y^{(l)}=D_k^{-1}(A_k\odot T)Y^{(l-1)},$
where $D_k$ is diagonal with $(D_k)_{ii}=\sum_j(A_k\odot T)_{ij}$ . The matrix $T$ is learned by minimizing the labeled-node cross-entropy
$T^*=\arg\min_T\;\frac{1}{|V_L|}\sum_{v_a\in V_L}J(\widehat y_a^{\mathrm{lp}},y_a),$
where $\widehat y_a^{\mathrm{lp}}$ is the propagated class distribution, $y_a$ is the known one-hot label, and $J$ is cross-entropy. Because weights that improve classification of labeled nodes increase the influence of compatible class information, the learned $T$ serves as a topology-derived homophily estimate.
Knowl 4 — Combined homophily degree matrix
equation
HOG-GCN combines attribute-derived homophily $S=BB^{\mathsf T}$ with topology-derived homophily $T$ using two nonnegative weighting hyperparameters $\alpha$ and $\beta$ :
$H=\alpha S+\beta T.$
Here $H,S,T\in\mathbb{R}^{n\times n}$ , and $H_{ij}$ controls the feature-propagation weight between nodes $v_i$ and $v_j$ . The matrix $S$ can provide homophily estimates for arbitrary node pairs, whereas $T$ is learned only on the $k$ -order neighborhoods used for propagation. Entries of $H$ outside the propagation neighborhoods do not affect the graph convolution because they are removed by the elementwise product with $A_k$ .
Knowl 5 — End-to-end optimization of propagation and homophily estimation
model/method
HOG-GCN jointly trains the graph convolution parameters, the attribute MLP, and the topology-weight matrix so that homophily estimation and feature propagation improve one another. Let $Z$ be the final graph-convolution representation, $R=\operatorname{softmax}(Z)$ the node-class predictions, $\Theta_g$ the graph-convolution parameters, $\Theta_m$ the MLP parameters, and $T$ the learnable topology-weight matrix. The three supervised losses are the graph-convolution loss $L_{\mathrm{gcn}}$ , the attribute-MLP loss $L_{\mathrm{mlp}}$ , and the generalized-label-propagation loss $L_{\mathrm{lp}}$ . The complete training objective is
$(\Theta_g^*,\Theta_m^*,T^*) =\arg\min_{\Theta_g,\Theta_m,T} \left(L_{\mathrm{gcn}}+\lambda L_{\mathrm{mlp}}+\gamma L_{\mathrm{lp}}\right),$
where $\lambda$ and $\gamma$ balance the auxiliary MLP and label-propagation losses against the final node-classification loss. The learned matrix $H=\alpha BB^{\mathsf T}+\beta T$ guides feature propagation, while the resulting predictions provide supervision that updates both sources of homophily information.
Knowl 6 — Representation-similarity guarantee from homophily-weighted propagation
theoretical result
For HOG-GCN representations $Z_i$ and $Z_j$ of nodes $v_i$ and $v_j$ , the homophily-guided propagation corresponds to minimizing the weighted smoothness objective
$O=\frac{1}{2}\sum_{v_i\in V}\sum_{v_j\in N_k(v_i)}H_{ij}\lVert Z_i-Z_j\rVert_2^2,$
where $N_k(v_i)$ is the set of $k$ -order neighbors of $v_i$ , $H_{ij}$ is the learned homophily degree, and $\lVert\cdot\rVert_2$ is the Euclidean norm. Under the paper's assumption that $H$ is symmetric, the corresponding normalized propagation operator is $\widehat D^{-1}(A_k\odot H)$ , with $\widehat D_{ii}=\sum_j(A_k\odot H)_{ij}$ . Ignoring nonlinear activations and taking an initial transformed feature matrix $Z^{(0)}=XW$ , the $l$ -step propagation is
$Z^{(l)}=\left[\widehat D^{-1}(A_k\odot H)\right]^lXW.$
Consequently, pairs with larger learned homophily degrees incur a stronger penalty for dissimilar representations and are driven toward greater representation similarity, whereas low-homophily pairs exert weaker smoothing pressure. This gives HOG-GCN a mechanism for avoiding indiscriminate smoothing across heterophilic edges.
Knowl 7 — Evaluation design across homophilic and heterophilic graphs
experimental setup
HOG-GCN was evaluated on transductive node classification using seven real-world graphs: four heterophilic networks—Texas, Wisconsin, Cornell, and Film—and three homophilic citation networks—Cora, Citeseer, and Pubmed. Accuracy was averaged over 10 random train/validation/test splits; each split used 48% of nodes per class for training, 32% for validation, and the remaining nodes for testing. All compared methods used the same splits.

The comparison included attribute-only MLP, topology-only DeepWalk, homophily-oriented GCN and GAT, and heterophily-oriented H2GCN, CPGNN-MLP, CPGNN-Cheby, GPR-GNN, AM-GCN, and Geom-GCN. HOG-GCN used a two-layer 512-hidden-unit MLP, a two-layer graph convolution with 256 hidden units, $\alpha=1$ , $\beta=0.1$ , $\gamma=1$ , and $\mu=1$ , optimized with Adam and PyTorch's default initialization. The dataset statistics were:
Could not parse LaTeX table
Knowl 8 — Node-classification performance
data/table
The following values are mean test accuracy (%) $\pm$ standard deviation over the 10 splits. The table compares HOG-GCN with attribute-only, topology-only, conventional GNN, and heterophily-oriented baselines across four heterophilic and three homophilic datasets. HOG-GCN obtains the best overall mean accuracy and mean rank, and its strongest advantage is on the heterophilic graphs.
Could not parse LaTeX table
On the four heterophilic graphs, HOG-GCN is the best-performing method on every dataset, with mean accuracy $73.245\%$ , compared with $46.75\%$ for GCN and $48.7975\%$ for GAT; the corresponding improvements are $26.49$ and $24.47$ percentage points. On the homophilic graphs, HOG-GCN is best on Citeseer, second-best on Cora and Pubmed, and remains competitive with methods designed for strong homophily.
Knowl 9 — Effect of propagation order and homophily-source weights
empirical result
The paper varied the neighborhood order $k$ from 1 through 6 for both generalized label propagation and homophily-guided feature propagation. On the heterophilic Texas and Cornell graphs, accuracy improved substantially when moving from $k=1$ to $k=2$ . On homophilic Cora and Citeseer, the improvement at $k=2$ was slight, and accuracy decreased as $k$ increased from 2 to 6. These results support using a small receptive field: two-hop neighborhoods can recover useful same-class information in heterophilic graphs, whereas larger neighborhoods increasingly introduce irrelevant or noisy information.

The paper also varied $\alpha$ and $\beta$ , the weights of attribute-derived and topology-derived homophily, respectively, between 0 and 1. On Texas, performance was poor when either source was ignored ( $\alpha=0$ or $\beta=0$ ), and the best observed setting was $\alpha=0.4$ , $\beta=0.6$ . On homophilic Cora, performance was comparatively stable across the weight settings. Thus, combining attributes and topology is particularly important for fine-grained propagation control in heterophilic graphs.
Knowl 10 — Learned homophily separates same-class and different-class edges
empirical result
The learned homophily degree matrix was analyzed on two-hop neighborhoods of the heterophilic Texas graph and the homophilic Cora graph. In both graphs, node pairs belonging to the same class received higher homophily degrees than node pairs belonging to different classes. HOG-GCN therefore assigns larger propagation weights to same-class edges and smaller weights to different-class edges, regardless of whether the overall graph is heterophilic or homophilic. This empirical separation indicates that the learned matrix captures local class compatibility rather than merely reproducing the graph's global homophily level.
Knowl 11 — Representation visualization on Citeseer
empirical result
Two-dimensional t-SNE projections of learned Citeseer node representations were compared for GCN, H2GCN, CPGNN, GPR-GNN, and HOG-GCN. HOG-GCN produced the clearest class-separated clusters and the highest apparent within-class similarity. GCN and CPGNN showed dispersed same-class points with mixing between different classes, while H2GCN and GPR-GNN produced intermediate separation with less distinct class boundaries. The visualization is consistent with HOG-GCN's homophily-weighted smoothness mechanism: it encourages similarity for compatible node pairs while reducing mixing across incompatible pairs.

Coverage note — No substantial contributed material was omitted; proof derivations, background, related work, acknowledgements, and references were excluded as non-knowls.

References

1.Abu-El-Haija, S.; Perozzi, B.; Kapoor, A.; Alipourfard, N.; Lerman, K.; Harutyunyan, H.; Steeg, G. V.; and Galstyan, A. 2019. MixHop: Higher-order graph convolutional architectures via sparsified neighborhood mixing. In Proceedings of the 36th International Conference on Machine Learning, 21–29.
2.Cao, Z.; Xu, Q.; Yang, Z.; Cao, X.; and Huang, Q. 2021. Dual quaternion knowledge graph embeddings. In Proceedings of the AAAI Conference on Artificial Intelligence, 6894–6902.
3.Chien, E.; Peng, J.; Li, P.; and Milenkovic, O. 2021. Adaptive universal generalized pagerank graph neural network. In Proceeding of the 9th International Conference on Learning Representations.
4.Gao, S.; Denoyer, L.; and Gallinari, P. 2011. Temporal link prediction by integrating content and structure information. In International Conference on Information and Knowledge Management, 1169–1174.
5.Gong, D.; Liu, L.; Le, V.; Saha, B.; Mansour, M. R.; Venkatesh, S.; and van den Hengel, A. 2019. Memorizing normality to detect anomaly: Memory-augmented deep autoencoder for unsupervised anomaly detection. In Proceedings of the 2019 International Conference on Computer Vision, 1705–1714.
6.Hamilton, W. L.; Ying, Z.; and Leskovec, J. 2017. Inductive representation learning on large graphs. In Advances in Neural Information Processing Systems 30, 1024–1034.
7.He, D.; Wang, T.; Zhai, L.; Jin, D.; Yang, L.; Huang, Y.; Feng, Z.; and Yu, P. S. 2021. Adversarial representation mechanism learning for network embedding. IEEE Transactions on Knowledge and Data Engineering, https://doi.org/10.1109/TKDE.2021.3103193.
8.Hinton, G. E. 2008. Visualizing high-dimensional data using t-sne. Vigiliae Christianae, 9: 2579–2605.
9.Jin, D.; Huo, C.; Liang, C.; and Yang, L. 2021a. Heterogeneous graph neural network via attribute completion. In Proceedings of the Web Conference, 391–400.
10.Jin, D.; Yu, Z.; Jiao, P.; Pan, S.; Yu, P. S.; and Zhang, W. 2021b. A survey of community detection approaches: From statistical modeling to deep learning. IEEE Transactions on Knowledge and Data Engineering, https://doi.org/10.1109/TKDE.2021.3104155.
11.Kingma, D. P.; and Ba, J. 2015. Adam: A Method for stochastic optimization. In Proceedings of the 3rd International Conference on Learning Representations.
12.Kipf, T. N.; and Welling, M. 2017. Semi-supervised classification with graph convolutional networks. In Proceeding of the 5th International Conference on Learning Representations.
13.Li, C.; and Goldwasser, D. 2019. Encoding social information with graph convolutional networks for political perspective detection in news media. In Proceedings of the 57th Conference of the Association for Computational Linguistics, 2594–2604.
14.Namata, G. M.; London, B.; Getoor, L.; and Huang, B. 2012. Query-driven active surveying for collective classification. In Workshop on Mining and Learning with Graphs (MLG).
15.Pei, H.; Wei, B.; Chang, K. C.; Lei, Y.; and Yang, B. 2020. Geom-GCN: Geometric graph convolutional networks. In Proceeding of the 8th International Conference on Learning Representations.
16.Perozzi, B.; Al-Rfou, R.; and Skiena, S. 2014. DeepWalk: Online learning of social representations. In Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, 701–710.
17.Sen, P.; Namata, G.; Bilgic, M.; Getoor, L.; Gallagher, B.; and Eliassi-Rad, T. 2008. Collective classification in network data. AI Magazine., 29(3): 93–106.
18.Tang, J.; Aggarwal, C. C.; and Liu, H. 2016. Node classification in signed social networks. In Proceedings of the 2016 SIAM International Conference on Data Mining, 54–62.
19.Tang, J.; Sun, J.; Wang, C.; and Yang, Z. 2009. Social influence analysis in large-scale networks. In Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, 807–816.
20.Tian, F.; Gao, B.; Cui, Q.; Chen, E.; and Liu, T. 2014. Learning deep representations for graph clustering. In Proceedings of the 28th AAAI Conference on Artificial Intelligence, 1293–1299.
21.Velickovic, P.; Cucurull, G.; Casanova, A.; Romero, A.; Lio,` P.; and Bengio, Y. 2018. Graph attention networks. In Proceeding of the 6th International Conference on Learning Representations.
22.Wang, C.; Wang, H.; Zhou, C.; Li, J.; and Gao, H. 2019. ECOQUG: An effective ensemble community scoring function. In Proceedings of the 35th International Conference on Data Engineering, 1702–1705.
23.Wang, X.; Zhu, M.; Bo, D.; Cui, P.; Shi, C.; and Pei, J. 2020. AM-GCN: Adaptive multi-channel graph convolutional networks. In Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, 1243–1253.
24.Wang, Z.; Wang, C.; Pei, J.; Ye, X.; and Yu, P. S. 2016. Causality based propagation history ranking in social networks. In Proceedings of the 25th International Joint Conference on Artificial Intelligence, 3917–3923.
25.Xu, K.; Hu, W.; Leskovec, J.; and Jegelka, S. 2019. How powerful are graph neural networks? In Proceedings of the 7th International Conference on Learning Representations.
26.Yan, Y.; Hashemi, M.; Swersky, K.; Yang, Y.; and Koutra, D. 2021. Two sides of the same coin: Heterophily and oversmoothing in graph convolutional neural networks. arXiv preprint arXiv:2102.06462.
27.Yan, Y.; Zhu, J.; Duda, M.; Solarz, E.; Sripada, C. S.; and Koutra, D. 2019. GroupINN: Grouping-based interpretable neural network for classification of limited, noisy brain data. In Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, 772–782.
28.Yu, X.; and Han, J. 2014. Personalized entity recommendation: A heterogeneous information network approach. In Proceedings of the 7th ACM International Conference on Web Search and Data Mining, 283–292.
29.Zhu, J.; Rossi, R. A.; Rao, A. B.; Mai, T.; Lipka, N.; Ahmed, N. K.; and Koutra, D. 2021. Graph neural networks with heterophily. In Proceedings of the 35th AAAI Conference on Artificial Intelligence.
30.Zhu, J.; Yan, Y.; Zhao, L.; Heimann, M.; Akoglu, L.; and Koutra, D. 2020. Beyond homophily in graph neural networks: Current limitations and effective designs. In Advances in Neural Information Processing Systems 33.

Citation

MLA

Wang, T., et al. “Powerful Graph Convolutioal Networks with Adaptive Propagation Mechanism for Homophily and Heterophily”. arXiv, 2021, http://arxiv.org/abs/2112.13562v1.

APA

Wang, T., Wang, R., Jin, D., He, D., & Huang, Y. (2021). Powerful Graph Convolutioal Networks with Adaptive Propagation Mechanism for Homophily and Heterophily. arXiv. http://arxiv.org/abs/2112.13562v1

Chicago

Wang, T., R. Wang, D. Jin, D. He, and Y. Huang. 2021. “Powerful Graph Convolutioal Networks with Adaptive Propagation Mechanism for Homophily and Heterophily”. arXiv. http://arxiv.org/abs/2112.13562v1.

Harvard

Wang, T. et al. (2021) “Powerful Graph Convolutioal Networks with Adaptive Propagation Mechanism for Homophily and Heterophily”, arXiv [Preprint]. Available at: http://arxiv.org/abs/2112.13562v1.

Vancouver

1. Wang T, Wang R, Jin D, He D, Huang Y (2021) Powerful Graph Convolutioal Networks with Adaptive Propagation Mechanism for Homophily and Heterophily. arXiv

BibTeX

@article{wang2021powerful,
  title = {Powerful Graph Convolutioal Networks with Adaptive Propagation Mechanism for Homophily and Heterophily},
  author = {Wang, Tao and Wang, Rui and Jin, Di and He, Dongxiao and Huang, Yuxiao},
  year = {2021},
  journal = {arXiv},
  url = {http://arxiv.org/abs/2112.13562v1},
  eprint = {2112.13562}
}

Metadata:arXiv

Access the Paper

This paper is available from its original source. Click below to access the PDF.

Open PDF

Powerful Graph Convolutional Networks with Adaptive Propagation Mechanism for Homophily and Heterophily

Abstract

Topics

Keywords

Table of Contents

Knowls

Knowl 1 — HOG-GCN adaptive homophily-guided propagation

Knowl 2 — Attribute-based homophily estimation

Knowl 3 — Topology-based generalized label propagation

Knowl 4 — Combined homophily degree matrix

Knowl 5 — End-to-end optimization of propagation and homophily estimation

Knowl 6 — Representation-similarity guarantee from homophily-weighted propagation

Knowl 7 — Evaluation design across homophilic and heterophilic graphs

Knowl 8 — Node-classification performance

Knowl 9 — Effect of propagation order and homophily-source weights

Knowl 10 — Learned homophily separates same-class and different-class edges

Knowl 11 — Representation visualization on Citeseer

References

Citation

BibTeX

Access the Paper