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REVIEW 4 major objections 6 minor 75 references

How do Probabilistic Graphical Models and Graph Neural Networks Look at Network Data?

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper asks when classical probabilistic graphical models (PGMs) outperform graph neural networks (GNNs) on the same network task, using link prediction as a common benchmark on synthetic and real networks.

desk verdict A useful but flawed benchmark: the PGM-vs-GNN link-prediction comparison is extensive, yet the low-dimensional feature claim is confounded by feature-source mismatch and test-edge leakage. read the letter →

arxiv 2506.11869 v3 pith:3PDXLHM3 submitted 2025-06-13 stat.ML cond-mat.dis-nncond-mat.stat-mechcs.LGphysics.soc-ph

Michela Lapenna , Caterina De Bacco This is my paper
classification stat.MLcond-mat.dis-nncond-mat.stat-mechcs.LGphysics.soc-ph
keywords probabilisticgraphicalmodelsgraphneuralnetworkslinkpredictionheterophilynodefeaturesstochasticblockmodelinterpretabilitynetworkdata
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks when classical probabilistic graphical models (PGMs) outperform graph neural networks (GNNs) on the same network task. Using link prediction as a common benchmark on synthetic and ten real networks, the authors vary the type and dimensionality of node features, the level of feature noise, and the graph's heterophily. They find that GNNs are outperformed by PGMs when input features are low-dimensional or noisy, and that PGMs also degrade less when heterophily increases. The practical message is that for link prediction, the choice of input features can matter as much as the model family.

What carries the argument

The comparison runs on a single link-prediction protocol applied to off-the-shelf models from both families: three stochastic block model variants (MULTITENSOR, MTCOV, BNP) and four GNN architectures (GAT, GAE, VGAE, H2GCN). The crux is controlled manipulation of the input features—full attribute vectors, adjacency-matrix rows, K-means-clustered one-dimensional labels, and shuffled noise—so that both families are tested under identical information conditions, with AUC on held-out edges as the shared metric.

What would settle it

Re-run the structure-feature experiment with adjacency rows built only from training edges, never touching validation or test edges; if GNNs no longer match PGMs, the reported structure-feature advantage is leakage, not signal.

Watch

Extended reading notes

Core claim

On its own terms, the paper establishes that for link prediction, stochastic-block-model PGMs are the safer choice when node attributes are sparse, low-dimensional, or corrupted. GNNs match or approach PGM performance when given high-dimensional features, whether attribute vectors or adjacency-matrix rows, but drop sharply when features are compressed to a one-dimensional cluster label or randomly shuffled. Under increasing heterophily, PGMs remain more competitive, and GNNs recover some lost ground only when fed structure-based adjacency-row features, not when a heterophily-aware architecture is used. The authors interpret this as evidence that GNNs cannot fall back on topology alone the way PGMs can, and that architectural tweaks are less decisive than feature choice.

Load-bearing premise

The conclusion that structure-based features help GNNs assumes the adjacency-row features do not accidentally reveal the held-out test edges, since the validation and test rows progressively include the very links being predicted.

Editorial extensions

If this is right

  • In practical link-prediction settings where node attributes are scalar or unreliable, a PGM should be the default choice.
  • GNN users should treat feature engineering as a first-class design step: adjacency-row features can close the gap to PGMs on heterophilic graphs.
  • Adding uninformative or noisy features can hurt GNN performance, so feature selection deserves the same attention as architecture selection.
  • A heterophily-aware GNN architecture (H2GCN) does not consistently beat PGMs, suggesting that input features are the binding constraint.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural extension is to test the same protocol with GNNs that include explicit feature-selection or denoising layers; the paper's results imply such modules could be worth more than new message-passing schemes.
  • The complexity comparison suggests a trade-off: PGM cost scales with community count K, while GNN cost scales with hidden dimension and layers, so on very large graphs the ranking could shift even if the accuracy pattern holds.
  • The link-prediction focus likely understates PGM advantages: on node classification, where labels are the target, previous work cited by the paper already shows GNNs losing to a contextual stochastic block model, so the gap may generalize.
  • Practitioners using adjacency-row features for GNNs should check for target leakage; the paper's own validation protocol is susceptible, and the structure-feature advantage may be partly an artifact.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. This paper compares three probabilistic graphical models (MULTITENSOR, MTCOV, BNP) with four graph neural networks (GAT, GAE, VGAE, H2GCN) on a link prediction task, using synthetic networks and ten real-world datasets. The three main experiments vary the type and dimensionality of input features, corrupt node features, and increase graph heterophily; a final section compares interpretability and computational complexity. The paper concludes that GNNs are outperformed by PGMs when input features are low-dimensional or noisy, that PGMs are more robust than GNNs when heterophily increases, and that feature choice can matter more than GNN architecture for heterophilic graphs.

Significance. The paper addresses a real gap: a direct, controlled comparison of PGM and GNN frameworks on a common task, across a reasonably broad set of datasets and architectures. The computational complexity table and the interpretability discussion are useful for practitioners. If the main empirical claims were established, the paper would be a valuable benchmark. However, the central experiments contain feature-information confounds and a test-edge leakage issue that undermine the headline conclusions. The comparison is nevertheless potentially repairable, because the issues are experimental-design problems rather than irreparable theoretical flaws.

major comments (4)
  1. [Section 6, Figure 2 and Appendix Figure 8] The low-dimensional-feature comparison is confounded by feature source and information content. On synthetic data, MTCOV receives the argmax of the ground-truth membership vector as its one-dimensional feature, whereas GNNs receive a K-means cluster label of their attribute vectors; on real data, MTCOV's scalar feature is a K-means cluster label of the adjacency-matrix row, whereas GNNs' scalar feature clusters node attributes. The observed GNN drop at F=1 could therefore be caused by lossy clustering of attributes or by label leakage in the synthetic setting, rather than by dimensionality per se. The claim that GNNs are outperformed by PGMs when input features are low-dimensional is not established by this design.
  2. [Section 6, case 1 and Figure 1] The structure-based feature experiment leaks test links into the model input. The text states that, when constructing the adjacency-matrix-row feature, 'for validation and test we progressively include the validation and test set links.' Because these rows are used as node features for GNNs, the model receives information about the very edges it is asked to predict, potentially inflating GNN performance. This invalidates the feature-type comparison in Figure 1 and the specific observation about Peptides, and it also affects the heterophily analysis in Figure 4, where structure-based features are used.
  3. [Section 7, Figure 3] The noise-robustness experiment applies different corruptions to the two frameworks. GNN features are corrupted by permuting entries of the attribute vector, while MTCOV's scalar feature is replaced by a uniformly random cluster label; moreover, MTCOV's scalar feature is itself a K-means label of the adjacency-matrix row, not the attribute feature used by GNNs. The comparison therefore measures different quantities and does not isolate robustness to feature noise. The claim that PGMs are more robust to noisy features is not cleanly supported.
  4. [Section 8, Figure 4] Including H2GCN contradicts the stated 'off-the-shelf' design principle in Section 4, since H2GCN is explicitly designed for heterophily. The conclusion that 'architectural adaptations alone may not fully address the challenges posed by heterophilic graphs' is based on a single architecture and is not supported by a controlled comparison; the reported result is also affected by the feature-source confound from Section 6. This weakens the heterophily pillar of the paper's headline claim.
minor comments (6)
  1. [Introduction, Section 1] The text refers to the 'Stochastic Block Model (SMB)'; the standard abbreviation is SBM. Please correct this typo.
  2. [Section 6, Figure 2 caption] The caption says MTCOV takes one-dimensional (Clustered) features by design, but on synthetic data the feature is the argmax of the ground-truth membership vector, not a K-means cluster label. Please clarify the caption to match the actual protocol.
  3. [References] References [13] and [39] are the same paper (Zhu et al., 'Beyond homophily in graph neural networks'); one of the two entries should be removed or cross-referenced.
  4. [Throughout] The word 'heteropilic' appears several times and should be 'heterophilic'.
  5. [Section 9.2, Table 2] The BNP complexity is listed as O(N ln(N^2)); this looks like a typo for O(N ln N), but if it is intentional, please explain the origin of the factor of 2.
  6. [General] There is no code or data availability statement. For reproducibility, please include one or state clearly whether code and data will be released.

Circularity Check

1 steps flagged · score 4.0 of 10

The structure-based feature comparison is circular because test-set edges are included in the input features; the headline low-dimensional/noisy and heterophily conclusions are not themselves forced by this step.

  1. self definitional [Section 6, 'The role of input features', case 1 (structure-based feature) cross-validation paragraph]
    "We stress that, when splitting the graph in training, validation and test set in our cross-validation link prediction routine, we take into account the masking of the edges, and we feed the node with the masked adjacency matrix row. Indeed, the training set feature only contains the links between nodes in the training set graph, while for validation and test we progressively include the validation and test set links."

    The structure-based feature is the adjacency-matrix row A_i, and for validation/test rows it includes the validation/test edges, which are exactly the edges the link-prediction task asks the model to predict. For a candidate edge (i,j) in the test set, the value A_ij appears in the input feature of both endpoints, so the model can read the target from its input rather than predict it. Any reported AUC gain from 'structure-based features' in Figures 1, 7, and the structure-feature panels of Figure 4 is therefore partly a lookup of the label by construction rather than a measured predictive ability. This does not force the main low-dimensional/noisy-feature results, which use attribute-based clustered features, but it is a genuine circularity in the structure-feature leg of the benchmark.

full rationale

The paper contains no formal derivation chain; its claims are empirical comparisons, so most circularity categories do not apply. The PGM models MULTITENSOR and MTCOV are self-cited, but they are used off-the-shelf from independently published work, and the GNN baselines and datasets are external, so this is ordinary self-reference rather than load-bearing circularity. The one genuine circularity is in the structure-based feature protocol in Section 6, case 1: for validation and test, the adjacency-row feature is said to 'progressively include the validation and test set links,' so the link-prediction target is present in the model input by construction; the reported AUC in Figures 1, 7, and the structure-feature panels of Figure 4 is therefore partly a lookup, not a prediction. This affects the supporting claim that structure-based features make GNNs competitive, but it works against, rather than for, the paper's headline that PGMs are more robust, so the central conclusions still have independent content from the attribute-based and noise experiments. A separate validity concern—on synthetic data MTCOV's one-dimensional feature is the argmax of the ground-truth membership vector, unlike the K-means-clustered features given to GNNs—is an experimental confound in the low-dimensional comparison, but it is not a derivational circularity under the strict definition used here. Overall circularity is partial and localized rather than pervasive.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The synthetic data comes from the authors' own PGM generative model, and the only invented entities are none. The free parameters are model hyperparameters tuned on validation data; the axioms are the domain assumptions of the benchmark design.

free parameters (3)
  • Number of communities K (MULTITENSOR, MTCOV) = cross-validated per dataset
    The number of latent communities is tuned on the validation set, and the link-prediction AUC of the PGM depends on it.
  • gamma (MTCOV) = cross-validated per dataset
    Controls the relative weight of adjacency matrix A and node features X in the MTCOV objective, affecting the reported results.
  • GNN hyperparameter set (learning rate, weight decay, dropout, hidden dimension, number of layers) = tuned by grid search on a validation split
    GNN performance was tuned over these values, so the comparison depends on the chosen grid.
assumptions (4)
  • domain assumption Synthetic networks generated from the MULTITENSOR generative model are representative of network data for comparing PGMs and GNNs.
    Section B. The synthetic evaluation assumes that data produced by the PGM's own generative family is a fair testbed, which may favor PGMs.
  • domain assumption The link-prediction task with AUC as metric is a fair common ground for comparing the two frameworks.
    Section 3. The paper argues link prediction aligns with both frameworks' capabilities, but the choice of task and metric influences the ranking.
  • ad hoc to paper Node features derived from adjacency-matrix rows do not contain information about test edges when used as model input.
    Section 6, case 1. This assumption is required for the structure-based feature experiments, but the protocol adds test edges to features, violating it.
  • standard math Standard results in graph theory and probability (e.g., SBM edge likelihood, message-passing updates) are correct.
    Used throughout Sections 4 and B without proof, these are uncontroversial background results.

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Pith. "Pith review of How do Probabilistic Graphical Models and Graph Neural Networks Look at Network Data?." pith.science (2026). https://pith.science/paper/3PDXLHM3

@misc{pith2026250611869,
  author       = {Pith},
  title        = {Pith review of: How do Probabilistic Graphical Models and Graph Neural Networks Look at Network Data?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3PDXLHM3}},
  note         = {Machine review of arXiv:2506.11869}
}
read the original abstract

Graphs are a powerful data structure for representing relational data and are widely used to describe complex real-world systems. Probabilistic Graphical Models (PGMs) and Graph Neural Networks (GNNs) can both leverage graph-structured data, but their inherent functioning is different. The question is how do they compare in capturing the information contained in networked datasets? We address this objective by solving a link prediction task and we conduct three main experiments, on both synthetic and real networks: one focuses on how PGMs and GNNs handle input features, while the other two investigate their robustness to noisy features and increasing heterophily of the graph. PGMs do not necessarily require features on nodes, while GNNs cannot exploit the network edges alone, and the choice of input features matters. We find that GNNs are outperformed by PGMs when input features are low-dimensional or noisy, mimicking many real scenarios where node attributes might be scalar or noisy. Then, we find that PGMs are more robust than GNNs when the heterophily of the graph is increased. Finally, to assess performance beyond prediction tasks, we also compare the two frameworks in terms of their computational complexity and interpretability.

Figures

Figures reproduced from arXiv: 2506.11869 by the authors.

Figure 1
Figure 1. Structure-based vs. attribute-based features. AUC scores of link prediction in real datasets when giving in [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. High vs. low dimensional features. AUC scores of link prediction in real and synthetic datasets when giving [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. AUC score variation in real datasets when increasing the percentage of nodes [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: AUC scores of link prediction in real and synthetic heterophilic datasets when using the full feature. For the [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Comparing the parameters inferred. Marker positions are extracted by applying t-SNE to either the [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: Inferred partitions on Citeseer dataset. For the PGMs we plot the membership vectors, mixed for MTCOV [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: AUC scores of link prediction in real and synthetic datasets when using [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]
Figure 8
Figure 8. Figure 8: High vs. low dimensional features. AUC scores of link prediction in real and synthetic datasets when giving [PITH_FULL_IMAGE:figures/full_fig_p016_8.png]

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Reference graph

Works this paper leans on

75 extracted references · 64 canonical work pages

  1. [1]

    An introduction to probabilistic graphical models, 2003

    Michael I Jordan. An introduction to probabilistic graphical models, 2003

    work page 2003

  2. [2]

    Holland, Kathryn Blackmond Laskey, and Samuel Leinhardt

    Paul W. Holland, Kathryn Blackmond Laskey, and Samuel Leinhardt. Stochastic blockmodels: First steps. Social Networks, 5(2):109–137, 1983

    1983

  3. [3]

    Wang and George Y

    Yuchung J. Wang and George Y . Wong. Stochastic blockmodels for directed graphs.Journal of the American Statistical Association, 82(397):8–19, 1987

    work page 1987

  4. [4]

    Estimation and prediction for stochastic blockmodels for graphs with latent block structure

    Tom Snijders and Krzysztof Nowicki. Estimation and prediction for stochastic blockmodels for graphs with latent block structure. Journal of Classification, 14:75–100, 01 1997

    work page 1997

  5. [5]

    Community detection and stochastic block models: recent developments

    Emmanuel Abbe. Community detection and stochastic block models: recent developments. J. Mach. Learn. Res., 18(1):6446–6531, January 2017

    work page 2017

  6. [6]

    The graph neural network model

    Franco Scarselli, Marco Gori, Ah Chung Tsoi, Markus Hagenbuchner, and Gabriele Monfardini. The graph neural network model. IEEE Transactions on Neural Networks, 20(1):61–80, 2009. 10 How do Probabilistic Graphical Models and Graph Neural Networks Look at Network Data?

    work page 2009

  7. [7]

    Convolutional neural networks on graphs with fast localized spectral filtering

    Micha¨el Defferrard, Xavier Bresson, and Pierre Vandergheynst. Convolutional neural networks on graphs with fast localized spectral filtering. In Proceedings of the 30th International Conference on Neural Information Processing Systems, NIPS’16, page 3844–3852, Red Hook, NY , USA, 2016. Curran Associates Inc

    work page 2016

  8. [8]

    Bronstein

    Federico Monti, Davide Boscaini, Jonathan Masci, Emanuele Rodol`a, Jan Svoboda, and Michael M. Bronstein. Geometric deep learning on graphs and manifolds using mixture model cnns. In 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 5425–5434, 2017

    work page 2017

Show all 75 references
  1. [9]

    Message passing all the way up, 2022

    Petar Veli ˇckovi´c. Message passing all the way up, 2022

    2022

  2. [10]

    Revisiting heterophily for graph neural networks

    Sitao Luan, Chenqing Hua, Qincheng Lu, Jiaqi Zhu, Mingde Zhao, Shuyuan Zhang, Xiao-Wen Chang, and Doina Precup. Revisiting heterophily for graph neural networks. In Proceedings of the 36th International Conference on Neural Information Processing Systems, NIPS ’22, Red Hook, N...

    2022

  3. [11]

    Bronstein

    Francesco Di Giovanni, James Rowbottom, Benjamin Paul Chamberlain, Thomas Markovich, and Michael M. Bronstein. Understanding convolution on graphs via energies. Transactions on Machine Learning Research, 2023

    2023

  4. [12]

    Understanding heterophily for graph neural networks

    Junfu Wang, Yuanfang Guo, Liang Yang, and Yunhong Wang. Understanding heterophily for graph neural networks. In Ruslan Salakhutdinov, Zico Kolter, Katherine Heller, Adrian Weller, Nuria Oliver, Jonathan Scarlett, and Felix Berkenkamp, editors, Proceedings of the 41st Internati...

    2024

  5. [13]

    Beyond homophily in graph neural networks: current limitations and effective designs

    Jiong Zhu, Yujun Yan, Lingxiao Zhao, Mark Heimann, Leman Akoglu, and Danai Koutra. Beyond homophily in graph neural networks: current limitations and effective designs. In Proceedings of the 34th International Conference on Neural Information Processing Systems, NIPS ’20, Red ...

    2020

  6. [14]

    Finding global homophily in graph neural networks when meeting heterophily

    Xiang Li, Renyu Zhu, Yao Cheng, Caihua Shan, Siqiang Luo, Dongsheng Li, and Weining Qian. Finding global homophily in graph neural networks when meeting heterophily. InInternational Conference on Machine Learning, pages 13242–13256. PMLR, 2022

    2022

  7. [15]

    The heterophilic graph learning handbook: Benchmarks, models, theoretical analysis, applications and challenges

    Sitao Luan, Chenqing Hua, Qincheng Lu, Liheng Ma, Lirong Wu, Xinyu Wang, Minkai Xu, Xiao-Wen Chang, Doina Precup, Rex Ying, et al. The heterophilic graph learning handbook: Benchmarks, models, theoretical analysis, applications and challenges. arXiv preprint arXiv:2407.09618, 2024

    2024 arXiv

  8. [16]

    On the impact of feature heterophily on link prediction with graph neural networks

    Jiong Zhu, Gaotang Li, Yao-An Yang, Jing Zhu, Xuehao Cui, and Danai Koutra. On the impact of feature heterophily on link prediction with graph neural networks. arXiv preprint arXiv:2409.17475, 2024

    2024 arXiv

  9. [17]

    Insights from network science can advance deep graph learning

    Christopher Bl¨ocker, Martin Rosvall, Ingo Scholtes, and Jevin D West. Insights from network science can advance deep graph learning. arXiv preprint arXiv:2502.01177, 2025

    2025

  10. [18]

    Stochastic blockmodels meet graph neural networks

    Nikhil Mehta, Lawrence Carin, and Piyush Rai. Stochastic blockmodels meet graph neural networks. ArXiv, abs/1905.05738, 2019

    1905 arXiv

  11. [19]

    The deep latent position block model for the block clustering and latent representation of networks, 2024

    R´emi Boutin, Pierre Latouche, and Charles Bouveyron. The deep latent position block model for the block clustering and latent representation of networks, 2024

    2024

  12. [20]

    Gnninterpreter: A probabilistic generative model-level explanation for graph neural networks

    Xiaoqi Wang and Han-Wei Shen. Gnninterpreter: A probabilistic generative model-level explanation for graph neural networks. In International Conference on Learning Representations (ICLR), 2023

    2023

  13. [21]

    Inference in probabilistic graphical models by graph neural networks

    KiJung Yoon, Renjie Liao, Yuwen Xiong, Lisa Zhang, Ethan Fetaya, Raquel Urtasun, Richard Zemel, and Xaq Pitkow. Inference in probabilistic graphical models by graph neural networks. In 2019 53rd Asilomar Conference on Signals, Systems, and Computers, pages 868–875, 2019

    2019

  14. [22]

    GNNs getting comfy: Community and feature similarity guided rewiring

    Celia Rubio-Madrigal, Adarsh Jamadandi, and Rebekka Burkholz. GNNs getting comfy: Community and feature similarity guided rewiring. In The Thirteenth International Conference on Learning Representations, 2025

    2025

  15. [23]

    Revisiting graph neural networks: All we have is low-pass filters, 2019

    Hoang NT and Takanori Maehara. Revisiting graph neural networks: All we have is low-pass filters, 2019

    2019

  16. [24]

    On the bottleneck of graph neural networks and its practical implications

    Uri Alon and Eran Yahav. On the bottleneck of graph neural networks and its practical implications. In International Conference on Learning Representations (ICLR), 2021

    2021

  17. [25]

    Graph clustering with graph neural networks

    Anton Tsitsulin, John Palowitch, Bryan Perozzi, and Emmanuel M ¨uller. Graph clustering with graph neural networks. Journal of Machine Learning Research, 24(127):1–21, 2023

    2023

  18. [26]

    Duranthon and Lenka Zdeborov’a

    O. Duranthon and Lenka Zdeborov’a. Optimal inference in contextual stochastic block models. Trans. Mach. Learn. Res., 2024, 2023

    2024

  19. [27]

    The ground truth about metadata and community detection in networks

    Leto Peel, Daniel B Larremore, and Aaron Clauset. The ground truth about metadata and community detection in networks. Science advances, 3(5):e1602548, 2017

    2017

  20. [28]

    Structure and inference in annotated networks

    Mark EJ Newman and Aaron Clauset. Structure and inference in annotated networks. Nature communications, 7(1):11863, 2016. 11 How do Probabilistic Graphical Models and Graph Neural Networks Look at Network Data?

    2016

  21. [29]

    Community detection with node attributes in multilayer networks

    Martina Contisciani, Eleanor Power, and Caterina De Bacco. Community detection with node attributes in multilayer networks. Scientific reports, 10:15736, 09 2020

    2020

  22. [30]

    Structure and inference in hypergraphs with node attributes

    Anna Badalyan, Nicol `o Ruggeri, and Caterina De Bacco. Structure and inference in hypergraphs with node attributes. Nature Communications, 15(1):7073, 2024

    2024

  23. [31]

    Power, Daniel B

    Caterina De Bacco, Eleanor A. Power, Daniel B. Larremore, and Cristopher Moore. Community detection, link prediction, and layer interdependence in multilayer networks. Phys. Rev. E, 95:042317, Apr 2017

    2017

  24. [32]

    Efficient monte carlo and greedy heuristic for the inference of stochastic block models

    Tiago P Peixoto. Efficient monte carlo and greedy heuristic for the inference of stochastic block models. Physical Review E, 89(1):012804, 2014

    2014

  25. [33]

    Pairre: Knowledge graph embeddings via paired relation vectors

    Linlin Chao, Jianshan He, Taifeng Wang, and Wei Chu. Pairre: Knowledge graph embeddings via paired relation vectors. In Annual Meeting of the Association for Computational Linguistics, 2020

    2020

  26. [34]

    Automated concatenation of embeddings for structured prediction

    Xinyu Wang, Yong Jiang, Nguyen Bach, Tao Wang, Zhongqiang Huang, Fei Huang, and Kewei Tu. Automated concatenation of embeddings for structured prediction. In Annual Meeting of the Association for Computational Linguistics, 2020

    2020

  27. [35]

    MacQueen

    J. MacQueen. Some methods for classification and analysis of multivariate observations. In Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability, pages 281–297, 1967

    1967

  28. [36]

    S. Lloyd. Least squares quantization in pcm. IEEE Transactions on Information Theory, 28(2):129–137, 1982

    1982

  29. [37]

    Graph Attention Networks

    Petar Veliˇckovi´c, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Li`o, and Yoshua Bengio. Graph Attention Networks. International Conference on Learning Representations, 2018

    2018

  30. [38]

    Kipf and Max Welling

    Thomas N. Kipf and Max Welling. Variational graph autoencoders. In Proceedings of the NeurIPS Workshop on Bayesian Deep Learning, 2016

    2016

  31. [39]

    Beyond homophily in graph neural networks: Current limitations and effective designs

    Jiong Zhu, Yujun Yan, Lingxiao Zhao, Mark Heimann, Leman Akoglu, and Danai Koutra. Beyond homophily in graph neural networks: Current limitations and effective designs. In Proceedings of the 34th International Conference on Neural Information Processing Systems, NIPS ’20, Red ...

    2020

  32. [40]

    Konstantin Rusch, Michael M

    T. Konstantin Rusch, Michael M. Bronstein, and Siddhartha Mishra. A survey on oversmoothing in graph neural networks, 2023

    2023

  33. [41]

    Demystifying oversmoothing in attention-based graph neural networks

    Xinyi Wu, Amir Ajorlou, Zihui Wu, and Ali Jadbabaie. Demystifying oversmoothing in attention-based graph neural networks. In Proceedings of the 37th International Conference on Neural Information Processing Systems, NIPS ’23, Red Hook, NY , USA, 2023. Curran Associates Inc

    2023

  34. [42]

    Graph neural networks exponentially lose expressive power for node classification

    Kenta Oono and Taiji Suzuki. Graph neural networks exponentially lose expressive power for node classification. arXiv: Learning, 2019

    2019

  35. [43]

    A note on over-smoothing for graph neural networks

    Chen Cai and Yusu Wang. A note on over-smoothing for graph neural networks. ArXiv, abs/2006.13318, 2020

    2006 arXiv

  36. [44]

    Cohen, and Ruslan Salakhutdinov

    Zhilin Yang, William W. Cohen, and Ruslan Salakhutdinov. Revisiting semi-supervised learning with graph embeddings. In Proceedings of the 33rd International Conference on International Conference on Machine Learning - Volume 48, ICML’16, page 40–48. JMLR.org, 2016

    2016

  37. [45]

    Predicting multicellular function through multi-layer tissue networks

    Marinka Zitnik, Monu Agrawal, and Jure Leskovec. Predicting multicellular function through multi-layer tissue networks. Bioinformatics, 33(14):1916–1923, 2017

    1916

  38. [46]

    Long range graph benchmark

    Vijay Prakash Dwivedi, Ladislav Ramp´aˇsek, Mikhail Galkin, Ali Parviz, Guy Wolf, Anh Tuan Luu, and Dominique Beaini. Long range graph benchmark. In Proceedings of the 36th International Conference on Neural Information Processing Systems, NIPS ’22, Red Hook, NY , USA, 2022. C...

    2022

  39. [47]

    Vishwanathan

    Pinar Yanardag and S.V .N. Vishwanathan. Deep graph kernels. In Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’15, page 1365–1374, New York, NY , USA, 2015. Association for Computing Machinery

    2015

  40. [48]

    Adamic and Natalie Glance

    Lada A. Adamic and Natalie Glance. The political blogosphere and the 2004 u.s. election: divided they blog. In Proceedings of the 3rd International Workshop on Link Discovery, LinkKDD ’05, page 36–43, New York, NY , USA, 2005. Association for Computing Machinery

    2004

  41. [49]

    Benson, Jure Leskovec, and David F

    Hao Yin, Austin R. Benson, Jure Leskovec, and David F. Gleich. Local higher-order graph clustering. In Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’17, page 555–564, New York, NY , USA, 2017. Association for Computing...

    2017

  42. [50]

    Geom-gcn: Geometric graph convolutional networks

    Hongbin Pei, Bingzhen Wei, Kevin Chen-Chuan Chang, Yu Lei, and Bo Yang. Geom-gcn: Geometric graph convolutional networks. ArXiv, abs/2002.05287, 2020. 12 How do Probabilistic Graphical Models and Graph Neural Networks Look at Network Data?

    2002 arXiv

  43. [51]

    Kingma and Jimmy Ba

    Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization. CoRR, abs/1412.6980, 2014

    2014 arXiv

  44. [52]

    The expressive power of graph neural networks

    Pan Li and Jure Leskovec. The expressive power of graph neural networks. Graph Neural Networks: Foundations, Frontiers, and Applications, pages 63–98, 2022

    2022

  45. [53]

    A fair comparison of graph neural networks for graph classification

    Federico Errica, Marco Podda, Davide Bacciu, and Alessio Micheli. A fair comparison of graph neural networks for graph classification. ArXiv, abs/1912.09893, 2019

    1912 arXiv

  46. [54]

    Hamilton, Rex Ying, and Jure Leskovec

    William L. Hamilton, Rex Ying, and Jure Leskovec. Inductive representation learning on large graphs. In Proceedings of the 31st International Conference on Neural Information Processing Systems , NIPS’17, page 1025–1035, Red Hook, NY , USA, 2017. Curran Associates Inc

    2017

  47. [55]

    How powerful are graph neural networks? ArXiv, abs/1810.00826, 2018

    Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. How powerful are graph neural networks? ArXiv, abs/1810.00826, 2018

    2018 arXiv

  48. [56]

    On positional and structural node features for graph neural networks on non-attributed graphs

    Hejie Cui, Zijie Lu, Pan Li, and Carl Yang. On positional and structural node features for graph neural networks on non-attributed graphs. In Proceedings of the 31st ACM International Conference on Information & Knowledge Management, CIKM ’22, page 3898–3902, New York, NY , US...

    2022

  49. [57]

    Tenorio, Madeline Navarro, Santiago Segarra, and Antonio G

    Victor M. Tenorio, Madeline Navarro, Santiago Segarra, and Antonio G. Marques. Recovering missing node features with local structure-based embeddings. In ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 9931–9935, 2024

    2024

  50. [58]

    Graph convolutional networks for graphs containing missing features

    Hibiki Taguchi, Xin Liu, and Tsuyoshi Murata. Graph convolutional networks for graphs containing missing features. Future Generation Computer Systems, 117:155–168, 2021

    2021

  51. [59]

    Graph neural networks can recover the hidden features solely from the graph structure

    Ryoma Sato. Graph neural networks can recover the hidden features solely from the graph structure. In Proceedings of the 40th International Conference on Machine Learning, ICML’23. JMLR.org, 2023

    2023

  52. [60]

    Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications

    Aurelien Decelle, Florent Krzakala, Cristopher Moore, and Lenka Zdeborov ´a. Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications. Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 84(6):066106, 2011

    2011

  53. [61]

    Community detection in large hypergraphs

    Nicol`o Ruggeri, Martina Contisciani, Federico Battiston, and Caterina De Bacco. Community detection in large hypergraphs. Science Advances, 9(28):eadg9159, 2023

    2023

  54. [62]

    Broad spectrum structure discovery in large-scale higher-order networks, 2025

    John Hood, Caterina De Bacco, and Aaron Schein. Broad spectrum structure discovery in large-scale higher-order networks, 2025

    2025

  55. [63]

    Link prediction under heterophily: A physics-inspired graph neural network approach

    Andrea Giuseppe Di Francesco, Francesco Caso, Maria Sofia Bucarelli, and Fabrizio Silvestri. Link prediction under heterophily: A physics-inspired graph neural network approach. arXiv, 2024

    2024

  56. [64]

    Is homophily a necessity for graph neural networks? arXiv preprint arXiv:2106.06134, 2021

    Yao Ma, Xiaorui Liu, Neil Shah, and Jiliang Tang. Is homophily a necessity for graph neural networks? arXiv preprint arXiv:2106.06134, 2021

    2021 arXiv

  57. [65]

    Ordered gnn: Ordering message passing to deal with heterophily and over-smoothing, 02 2023

    Song Yunchong, Chenghu Zhou, Xinbing Wang, and Zhouhan Lin. Ordered gnn: Ordering message passing to deal with heterophily and over-smoothing, 02 2023

    2023

  58. [66]

    Bastian Epping, Alexandre Ren´e, Moritz Helias, and Michael T. Schaub. Graph neural networks do not always oversmooth. In Proceedings of the 38th International Conference on Neural Information Processing Systems, NIPS ’24, Red Hook, NY , USA, 2025. Curran Associates Inc

    2025

  59. [67]

    Interpretable deep learning: Interpretation, interpretability, trustworthiness, and beyond

    Xuhong Li, Haoyi Xiong, Xingjian Li, Xuanyu Wu, Xiao Zhang, Ji Liu, Jiang Bian, and Dejing Dou. Interpretable deep learning: Interpretation, interpretability, trustworthiness, and beyond. Knowledge and Information Systems, 64(12):3197–3234, 2022

    2022

  60. [68]

    Graphlime: Local interpretable model explanations for graph neural networks

    Qiang Huang, Makoto Yamada, Yuan Tian, Dinesh Singh, and Yi Chang. Graphlime: Local interpretable model explanations for graph neural networks. IEEE Transactions on Knowledge and Data Engineering, 35(7):6968– 6972, 2022

    2022

  61. [69]

    Learning deep representations for graph clustering

    Fei Tian, Bin Gao, Qing Cui, Enhong Chen, and Tie-Yan Liu. Learning deep representations for graph clustering. In Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence, AAAI’14, page 1293–1299. AAAI Press, 2014

    2014

  62. [70]

    Attributed graph clustering: a deep attentional embedding approach

    Chun Wang, Shirui Pan, Ruiqi Hu, Guodong Long, Jing Jiang, and Chengqi Zhang. Attributed graph clustering: a deep attentional embedding approach. In Proceedings of the 28th International Joint Conference on Artificial Intelligence, IJCAI’19, page 3670–3676. AAAI Press, 2019

    2019

  63. [71]

    Deep k-means clustering based on graph neural networks: Leveraging cohesion and separation in graph nodes

    Hyesoo Shin and Ki Yong Lee. Deep k-means clustering based on graph neural networks: Leveraging cohesion and separation in graph nodes. In 2024 IEEE International Conference on Big Data and Smart Computing (BigComp), pages 190–193, 2024. 13 How do Probabilistic Graphical Model...

    2024

  64. [72]

    Viualizing data using t-sne.Journal of Machine Learning Research, 9:2579–2605, 11 2008

    Laurens van der Maaten and Geoffrey Hinton. Viualizing data using t-sne.Journal of Machine Learning Research, 9:2579–2605, 11 2008

    2008

  65. [73]

    Flexible inference in heterogeneous and attributed multilayer networks

    Martina Contisciani, Marius Hobbhahn, Eleanor A Power, Philipp Hennig, and Caterina De Bacco. Flexible inference in heterogeneous and attributed multilayer networks. PNAS Nexus, 4(1):pgaf005, 01 2025

    2025

  66. [74]

    How powerful are spectral graph neural networks

    Xiyuan Wang and Muhan Zhang. How powerful are spectral graph neural networks. In International conference on machine learning, pages 23341–23362. PMLR, 2022

    2022

  67. [75]

    On the equivalence between positional node embeddings and structural graph representations

    Balasubramaniam Srinivasan and Bruno Ribeiro. On the equivalence between positional node embeddings and structural graph representations. arXiv preprint arXiv:1910.00452, 2019. 14 How do Probabilistic Graphical Models and Graph Neural Networks Look at Network Data? A Additiona...

    1910 arXiv

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Reviewed August 7, 2026 · model on record in the stance chip above.