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arxiv: 2603.01388 · v1 · pith:RW4ZCYXCnew · submitted 2026-03-02 · 💻 cs.LG · stat.ML

Invariant-Stratified Propagation for Expressive Graph Neural Networks

Asela Hevapathige , Ahad N. Zehmakan , Asiri Wijesinghe , Saman Halgamuge This is my paper

Pith reviewed 2026-05-21 11:23 UTC · model grok-4.3

classification 💻 cs.LG stat.ML
keywords graph neural networksweisfeiler-lemanstructural heterogeneitygraph invariantsoversmoothingexpressivitymessage passing
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The pith

Stratifying nodes by graph invariants in hierarchical layers lets GNNs distinguish structural positions invisible to the 1-WL test.

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

The paper presents Invariant-Stratified Propagation as a way to move graph neural networks past the uniform aggregation and limited distinction power of standard message passing. It groups nodes into strata according to graph invariants and processes these strata in a hierarchy. This setup quantifies how nodes occupy distinct roles inside larger patterns instead of treating all neighbors alike. If the approach works, models gain stronger structural awareness while staying computationally practical compared with other high-expressivity techniques.

Core claim

ISP stratifies nodes according to graph invariants, processing them in hierarchical strata that reveal structural distinctions invisible to 1-WL. Through hierarchical structural heterogeneity encoding, ISP quantifies differences in nodes' structural positions within higher-order patterns, distinguishing interactions where participants occupy different roles from those with uniform participation.

What carries the argument

Invariant-Stratified Propagation (ISP) framework, including the ISP-WL variant and its neural implementation ISPGNN, that stratifies nodes by invariants and processes them hierarchically to encode structural heterogeneity.

If this is right

  • GNNs achieve formal expressivity beyond the 1-WL test.
  • Models gain resistance to oversmoothing through the hierarchical processing.
  • Convergence guarantees hold for the stratified propagation.
  • Consistent gains appear in graph classification, node classification, and influence estimation tasks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The stratification idea could transfer to dynamic graphs where invariants evolve.
  • It offers a middle path between simple 1-WL models and costly higher-order subgraph methods.
  • Role quantification may improve tasks like community detection where position differences matter.

Load-bearing premise

Stratifying nodes by graph invariants and processing them hierarchically will capture structural distinctions beyond 1-WL while staying computationally efficient.

What would settle it

A pair of non-isomorphic graphs that ISP-WL fails to distinguish despite the stratification, or a benchmark task where ISPGNN shows no gain over standard GNNs on structural role distinctions.

Figures

Figures reproduced from arXiv: 2603.01388 by Ahad N. Zehmakan, Asela Hevapathige, Asiri Wijesinghe, Saman Halgamuge.

Figure 1
Figure 1. Figure 1: ISP-GNN architecture overview. (a) Input graph. (b) ISP coloring based on invariant values. (c) Layered propagation [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Mechanisms by which ISP-WL distinguishes graphs [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Oversmoothing comparison 5.3.2 Component Analysis. To assess each mechanism’s contri￾bution, we ablated core components of ISP-GNN: invariant-based stratification, triangle aggregation, and hierarchical structural het￾erogeneity encoding, evaluating them on four graph classification benchmarks. Results in [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Runtime and performance on ogbg-molpcba dataset. [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Gap encoding components capture complementary [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Graphs 𝐺1 and 𝐺2 with identical degree sequences but different triangle structures. However, |𝑇 (𝑢)| = 0 ≠ 1 = |𝑇 (𝑣)|. ISP-WL computes: 𝑀 struct 𝑢 = {{(𝑐ISP (𝑢 ′ ), 𝑐ISP (𝑢 ′′), 𝛿 (𝑢, 𝑢′ , 𝑢′′)) : (𝑢 ′ , 𝑢′′) ∈ 𝑇 (𝑢)}} Since |𝑀struct 𝑢 | ≠ |𝑀struct 𝑣 |, by injective hashing: 𝑐ISP (𝑢) ≠ 𝑐ISP (𝑣) Therefore,𝑐ISP-WL (𝑢) ≠ 𝑐ISP-WL (𝑣) despite 𝑐1-WL (𝑢) = 𝑐1-WL (𝑣). □ Theorem 4.3 (Invariant-Dependent Expressivi… view at source ↗
Figure 7
Figure 7. Figure 7: Structural metrics comparison across datasets. [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 10
Figure 10. Figure 10: Ablation study on hierarchical gap encoding components for graph classification. Results demonstrate the comple [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: t-SNE visualization of ISP-GNN embeddings on Cora-ML. The learnable invariant produces the most compact and [PITH_FULL_IMAGE:figures/full_fig_p019_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Hyperparameter sensitivity analysis. (a) Effect of number of strata [PITH_FULL_IMAGE:figures/full_fig_p021_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: ISP-WL computational overhead on synthetic BA graphs. (a) Time per iteration scales linearly with graph size for all [PITH_FULL_IMAGE:figures/full_fig_p021_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Preprocessing cost analysis (log scale). (a) Invariant computation time shows Degree ( [PITH_FULL_IMAGE:figures/full_fig_p022_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Triangle enumeration scalability on BA graphs. (a) Sublinear triangle growth confirms bounded degeneracy typical [PITH_FULL_IMAGE:figures/full_fig_p022_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Coloring refinement comparison of 1-WL and ISP-WL. ISP-WL with different invariants achieves 17-27% more colours [PITH_FULL_IMAGE:figures/full_fig_p024_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Pairwise complementarity between invariants measured as percentage of nodes receiving different final colors. High [PITH_FULL_IMAGE:figures/full_fig_p024_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Iterative color refinement across variants. K-Truss converges fastest, while other finer-grained invariants, such as [PITH_FULL_IMAGE:figures/full_fig_p025_18.png] view at source ↗
read the original abstract

Graph Neural Networks (GNNs) face fundamental limitations in expressivity and capturing structural heterogeneity. Standard message-passing architectures are constrained by the 1-dimensional Weisfeiler-Leman (1-WL) test, unable to distinguish graphs beyond degree sequences, and aggregate information uniformly from neighbors, failing to capture how nodes occupy different structural positions within higher-order patterns. While methods exist to achieve higher expressivity, they incur prohibitive computational costs and lack unified frameworks for flexibly encoding diverse structural properties. To address these limitations, we introduce Invariant-Stratified Propagation (ISP), a framework comprising both a novel WL variant (ISP-WL) and its efficient neural network implementation (ISPGNN). ISP stratifies nodes according to graph invariants, processing them in hierarchical strata that reveal structural distinctions invisible to 1-WL. Through hierarchical structural heterogeneity encoding, ISP quantifies differences in nodes' structural positions within higher-order patterns, distinguishing interactions where participants occupy different roles from those with uniform participation. We provide formal theoretical analysis establishing enhanced expressivity beyond 1-WL, convergence guarantees, and inherent resistance to oversmoothing. Extensive experiments across graph classification, node classification, and influence estimation demonstrate consistent improvements over standard architectures and state-of-the-art expressive baselines.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The manuscript introduces Invariant-Stratified Propagation (ISP), a framework consisting of the ISP-WL variant and its neural implementation ISPGNN. ISP stratifies nodes according to graph invariants and processes them hierarchically to encode structural heterogeneity, aiming to distinguish node roles in higher-order patterns that are invisible to the 1-WL test. The authors supply formal theoretical analysis for expressivity beyond 1-WL, convergence guarantees, and oversmoothing resistance, together with experiments on graph classification, node classification, and influence estimation that report consistent gains over standard GNNs and expressive baselines.

Significance. If the theoretical claims are substantiated, the work would offer a computationally tractable route to higher expressivity that avoids the costs of existing higher-order methods while providing unified handling of diverse structural properties. The combination of a new WL variant, convergence and oversmoothing analysis, and empirical validation on multiple tasks would constitute a solid contribution to expressive GNN design.

major comments (2)
  1. [§3] §3 (ISP-WL definition): the proof that ISP-WL strictly exceeds 1-WL expressivity must exhibit at least one concrete pair of non-isomorphic graphs that 1-WL fails to separate but ISP-WL separates via the invariant stratification; without this, the central expressivity claim remains unanchored.
  2. [§5.2] §5.2 (convergence theorem): the stated convergence guarantee appears to rely on the hierarchical strata being fixed after the first layer; if strata are recomputed each layer the contraction argument needs re-derivation, as this affects the practical stability claim.
minor comments (3)
  1. [Table 2] Table 2 (node classification results): report standard deviation over the 10 runs rather than only mean accuracy to allow assessment of statistical reliability.
  2. [Notation] Notation section: the symbol for the invariant function is introduced inconsistently between the WL variant and the GNN implementation; adopt a single definition.
  3. [Figure 3] Figure 3 caption: clarify whether the visualized strata correspond to a single graph or an aggregate over the dataset.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below and indicate the revisions we will incorporate.

read point-by-point responses

  1. Referee: [§3] §3 (ISP-WL definition): the proof that ISP-WL strictly exceeds 1-WL expressivity must exhibit at least one concrete pair of non-isomorphic graphs that 1-WL fails to separate but ISP-WL separates via the invariant stratification; without this, the central expressivity claim remains unanchored.

    Authors: We agree that an explicit example would strengthen the presentation of the expressivity result. While the formal argument in §3 demonstrates that invariant stratification enables distinctions beyond 1-WL, we will revise the manuscript to include a concrete pair of non-isomorphic graphs (e.g., two graphs equivalent under 1-WL but separated by differing invariant-based node strata) to illustrate the separation directly. revision: yes

  2. Referee: [§5.2] §5.2 (convergence theorem): the stated convergence guarantee appears to rely on the hierarchical strata being fixed after the first layer; if strata are recomputed each layer the contraction argument needs re-derivation, as this affects the practical stability claim.

    Authors: We appreciate this observation. In the ISP framework, stratification is performed using graph invariants that are intrinsic structural properties computed once prior to any propagation; the resulting hierarchical strata remain fixed across layers. The convergence analysis in §5.2 is derived under this fixed-strata setting. We will add an explicit clarifying statement in the revised §5.2 to confirm that strata do not change between layers, thereby preserving the contraction argument as stated. revision: partial

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper introduces ISP-WL and ISPGNN as a novel framework that stratifies nodes by graph invariants and encodes hierarchical structural heterogeneity, with formal theoretical analysis claimed for expressivity beyond 1-WL, convergence, and oversmoothing resistance. No equations, fitted parameters, or predictions are presented that reduce by construction to inputs defined inside the paper itself. The central claims rest on independent theoretical analysis and experimental validation rather than self-definitional steps, load-bearing self-citations, or renaming of known results, rendering the derivation self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 2 invented entities

The abstract relies on standard graph-theoretic background (1-WL test, graph invariants) without introducing fitted numerical parameters or new physical entities. The main additions are the ISP-WL and ISPGNN constructs themselves.

axioms (1)
  • standard math The 1-dimensional Weisfeiler-Leman test is the relevant baseline for expressivity limits of standard message-passing GNNs
    Invoked when stating that standard architectures are constrained by 1-WL.
invented entities (2)
  • ISP-WL no independent evidence
    purpose: Novel variant of the Weisfeiler-Leman test that incorporates invariant stratification
    Introduced as the theoretical component of the framework.
  • ISPGNN no independent evidence
    purpose: Efficient neural-network realization of invariant-stratified propagation
    Introduced as the practical implementation.

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Reference graph

Works this paper leans on

86 extracted references · 86 canonical work pages · 1 internal anchor

  1. [1]

    Peter Allen, Julia Böttcher, and Anita Liebenau. 2023. Universality for graphs of bounded degeneracy.arXiv preprint arXiv:2309.05468(2023)

    work page arXiv 2023

  2. [2]

    Waiss Azizian et al. 2021. Expressive Power of Invariant and Equivariant Graph Neural Networks. InInternational Conference on Learning Representations

    work page 2021

  3. [3]

    Waïss Azizian and Marc Lelarge. 2021. Expressive Power of Invariant and Equi- variant Graph Neural Networks. InInternational Conference on Learning Repre- sentations

    work page 2021

  4. [4]

    Albert-László Barabási and Réka Albert. 1999. Emergence of scaling in random networks.science286, 5439 (1999), 509–512

    work page 1999

  5. [5]

    Marc Barthelemy. 2004. Betweenness centrality in large complex networks.The European physical journal B38, 2 (2004), 163–168

    work page 2004

  6. [6]

    Nesrine Ben Yahia. 2024. Enhancing social and collaborative learning using a stacked GNN-based community detection.Social Network Analysis and Mining 14, 1 (2024), 205

    work page 2024

  7. [7]

    Beatrice Bevilacqua, Fabrizio Frasca, Derek Lim, Balasubramaniam Srinivasan, Chen Cai, Gopinath Balamurugan, Michael M Bronstein, and Haggai Maron

    work page

  8. [8]

    Equivariant subgraph aggregation networks.International Conference on Learning Representations(2022)

    work page 2022

  9. [9]

    Filippo Maria Bianchi, Daniele Grattarola, and Cesare Alippi. 2020. Spectral clus- tering with graph neural networks for graph pooling. InInternational conference on machine learning. PMLR, 874–883

    work page 2020

  10. [10]

    Aleksandar Bojchevski and Stephan Günnemann. 2018. Deep Gaussian Embed- ding of Graphs: Unsupervised Inductive Learning via Ranking. InInternational Conference on Learning Representations

    work page 2018

  11. [11]

    Phillip Bonacich. 1987. Power and centrality: A family of measures.American journal of sociology92, 5 (1987), 1170–1182

    work page 1987

  12. [12]

    Giorgos Bouritsas, Fabrizio Frasca, Stefanos P Zafeiriou, and Michael Bronstein

    work page

  13. [13]

    Improving graph neural network expressivity via subgraph isomorphism counting.IEEE Transactions on Pattern Analysis and Machine Intelligence(2022)

    work page 2022

  14. [14]

    Michail Chatzianastasis, Johannes Lutzeyer, George Dasoulas, and Michalis Vazir- giannis. 2023. Graph ordering attention networks. InProceedings of the AAAI Conference on Artificial Intelligence, Vol. 37. 7006–7014

    work page 2023

  15. [15]

    Rongqin Chen, Yan Li, Dan Wu, Fan Mo, Shenghui Zhang, Pak Lon Ip, Hoi Cheong Iam, Ye Li, and Leong Hou U. 2025. Enhanced Subgraph Learning in 2-FWL GNNs via Local Connectivity, Spectral, and Distance Encodings. InProceedings of the 31st ACM SIGKDD Conference on Knowledge Discovery and Data Mining V. 2. 227–238

    work page 2025

  16. [16]

    Leonardo Cotta, Christopher Morris, and Bruno Ribeiro. 2021. Reconstruction for powerful graph representations.Advances in Neural Information Processing Systems(2021)

    work page 2021

  17. [17]

    Erik D Demaine, Felix Reidl, Peter Rossmanith, Fernando Sánchez Villaamil, Somnath Sikdar, and Blair D Sullivan. 2019. Structural sparsity of complex networks: Bounded expansion in random models and real-world graphs.J. Comput. System Sci.105 (2019), 199–241

    work page 2019

  18. [18]

    Vijay Prakash Dwivedi and Xavier Bresson. 2020. A generalization of transformer networks to graphs.arXiv preprint arXiv:2012.09699(2020)

    work page arXiv 2020

  19. [19]

    Jiarui Feng, Yixin Chen, Fuhai Li, Anindya Sarkar, and Muhan Zhang. 2022. How powerful are k-hop message passing graph neural networks.Advances in Neural Information Processing Systems35 (2022), 4776–4790

    work page 2022

  20. [20]

    Yaniv Galron, Fabrizio Frasca, Haggai Maron, Eran Treister, and Moshe Eliasof

    work page

  21. [21]

    InJoint European Conference on Machine Learning and Knowledge Discovery in Databases

    Understanding and improving laplacian positional encodings for temporal gnns. InJoint European Conference on Machine Learning and Knowledge Discovery in Databases. Springer, 420–437

    work page

  22. [22]

    Hongyang Gao and Shuiwang Ji. 2019. Graph u-nets. Ininternational conference on machine learning. PMLR, 2083–2092

    work page 2019

  23. [23]

    Johannes Gasteiger, Aleksandar Bojchevski, and Stephan Günnemann. 2018. Predict then Propagate: Graph Neural Networks meet Personalized PageRank. In International Conference on Learning Representations

    work page 2018

  24. [24]

    Justin Gilmer, Samuel S Schoenholz, Patrick F Riley, Oriol Vinyals, and George E Dahl. 2017. Neural message passing for quantum chemistry. InInternational conference on machine learning. PMLR, 1263–1272

    work page 2017

  25. [25]

    Will Hamilton, Zhitao Ying, and Jure Leskovec. 2017. Inductive representation learning on large graphs.Advances in neural information processing systems30 (2017)

    work page 2017

  26. [26]

    Laurent Hébert-Dufresne, Joshua A Grochow, and Antoine Allard. 2016. Multi- scale structure and topological anomaly detection via a new network statistic: The onion decomposition.Scientific reports6, 1 (2016), 31708

    work page 2016

  27. [27]

    Asela Hevapathige. 2025. Curvature-augmented graph neural networks for molecular representation learning.Physica Scripta100, 9 (2025), 096010

    work page 2025

  28. [28]

    Asela Hevapathige, Qing Wang, and Ahad N Zehmakan. 2025. DeepSN: A Sheaf Neural Framework for Influence Maximization. InProceedings of the AAAI Conference on Artificial Intelligence, Vol. 39. 17177–17185

    work page 2025

  29. [29]

    Asela Hevapathige, Ahad N Zehmakan, and Qing Wang. 2025. Depth-Adaptive Graph Neural Networks via Learnable Bakry-Émery Curvature. InProceedings of the 31st ACM SIGKDD Conference on Knowledge Discovery and Data Mining V. 2. 944–955

    work page 2025

  30. [30]

    Weihua Hu, Matthias Fey, Marinka Zitnik, Yuxiao Dong, Hongyu Ren, Bowen Liu, Michele Catasta, and Jure Leskovec. 2020. Open graph benchmark: Datasets for machine learning on graphs.Advances in neural information processing systems 33 (2020), 22118–22133

    work page 2020

  31. [31]

    Ningyuan Teresa Huang and Soledad Villar. 2021. A short tutorial on the weisfeiler-lehman test and its variants. InICASSP 2021-2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 8533–8537

    work page 2021

  32. [32]

    Kedar Karhadkar, Pradeep Kr Banerjee, and Guido Montufar. 2023. FoSR: First- order spectral rewiring for addressing oversquashing in GNNs. InThe Eleventh International Conference on Learning Representations

    work page 2023

  33. [33]

    Sung Jin Kim and Sang Ho Lee. 2002. An improved computation of the pagerank algorithm. InEuropean Conference on Information Retrieval. Springer, 73–85

    work page 2002

  34. [34]

    DP Kingma. 2015. Adam: a method for stochastic optimization. InInternational Conference on Learning Representations

    work page 2015

  35. [35]

    Thomas N Kipf and Max Welling. 2017. Semi-Supervised Classification with Graph Convolutional Networks. InInternational Conference on Learning Repre- sentations

    work page 2017

  36. [36]

    2012.The graph isomorphism problem: its structural complexity

    Johannes Kobler, Uwe Schöning, and Jacobo Torán. 2012.The graph isomorphism problem: its structural complexity. Springer Science & Business Media

    work page 2012

  37. [37]

    Sanjay Kumar, Abhishek Mallik, Anavi Khetarpal, and Bhawani Sankar Panda

    work page

  38. [38]

    Influence maximization in social networks using graph embedding and graph neural network.Information Sciences607 (2022), 1617–1636

    work page 2022

  39. [39]

    Hao Li, Hao Jiang, Yuke Zheng, Hao Sun, and Wenying Gong. 2025. UniGO: A Unified Graph Neural Network for Modeling Opinion Dynamics on Graphs. In Proceedings of the ACM on Web Conference 2025. 530–540

    work page 2025

  40. [40]

    Yusheng Li, Yilun Shang, and Yiting Yang. 2017. Clustering coefficients of large networks.Information Sciences382 (2017), 350–358

    work page 2017

  41. [41]

    Ke Liang, Lingyuan Meng, Meng Liu, Yue Liu, Wenxuan Tu, Siwei Wang, Sihang Zhou, Xinwang Liu, Fuchun Sun, and Kunlun He. 2024. A survey of knowledge graph reasoning on graph types: Static, dynamic, and multi-modal.IEEE Trans- actions on Pattern Analysis and Machine Intelligence46, 12 (2024), 9456–9478

    work page 2024

  42. [42]

    Chen Ling, Junji Jiang, Junxiang Wang, My T Thai, Renhao Xue, James Song, Meikang Qiu, and Liang Zhao. 2023. Deep graph representation learning and optimization for influence maximization. InInternational conference on machine learning. PMLR, 21350–21361

    work page 2023

  43. [43]

    Meng Liu, Haiyang Yu, and Shuiwang Ji. 2024. Empowering GNNs via Edge- Aware Weisfeiler-Leman Algorithm.Transactions on Machine Learning Research (2024)

    work page 2024

  44. [44]

    Laurens van der Maaten and Geoffrey Hinton. 2008. Visualizing data using t-SNE. Journal of machine learning research9, Nov (2008), 2579–2605

    work page 2008

  45. [45]

    Fragkiskos D Malliaros, Christos Giatsidis, Apostolos N Papadopoulos, and Michalis Vazirgiannis. 2020. The core decomposition of networks: Theory, algo- rithms and applications.The VLDB Journal29, 1 (2020), 61–92

    work page 2020

  46. [46]

    Christopher Morris, Nils Morten Kriege, Franka Bause, Kristian Kersting, Petra Mutzel, and Marion Neumann. 2020. TUDataset: A collection of benchmark datasets for learning with graphs. InICML 2020 Workshop on Graph Representation Learning and Beyond (GRL+ 2020)

    work page 2020

  47. [47]

    Christopher Morris, Martin Ritzert, Matthias Fey, William L Hamilton, Jan Eric Lenssen, Gaurav Rattan, and Martin Grohe. 2019. Weisfeiler and leman go neural: Higher-order graph neural networks. InProceedings of the AAAI conference on artificial intelligence, Vol. 33. 4602–4609

    work page 2019

  48. [48]

    Sunil Nishad, Shubhangi Agarwal, Arnab Bhattacharya, and Sayan Ranu. 2021. Graphreach: Position-aware graph neural network using reachability estimations. Thirtieth International Joint Conference on Artificial Intelligence(2021). Conference’17, July 2017, Washington, DC, USA Asela Hevapathige, Ahad N. Zehmakan, Asiri Wijesinghe, and Saman Halgamuge

    work page 2021

  49. [49]

    George Panagopoulos, Nikolaos Tziortziotis, Michalis Vazirgiannis, Jun Pang, and Fragkiskos D Malliaros. 2024. Learning graph representations for influence maximization.Social Network Analysis and Mining14, 1 (2024), 203

    work page 2024

  50. [50]

    Pál András Papp, Karolis Martinkus, Lukas Faber, and Roger Wattenhofer. 2021. DropGNN: Random dropouts increase the expressiveness of graph neural net- works.Advances in Neural Information Processing Systems34 (2021), 21997–22009

    work page 2021

  51. [51]

    Hongbin Pei, Bingzhe Wei, Kevin Chen Chuan Chang, Yu Lei, and Bo Yang. 2020. GEOM-GCN: GEOMETRIC GRAPH CONVOLUTIONAL NETWORKS. In8th International Conference on Learning Representations

    work page 2020

  52. [52]

    Oleg Platonov, Denis Kuznedelev, Michael Diskin, Artem Babenko, and Liudmila Prokhorenkova. 2023. A critical look at the evaluation of GNNs under heterophily: Are we really making progress?. InThe Eleventh International Conference on Learning Representations

    work page 2023

  53. [53]

    Chendi Qian, Gaurav Rattan, Floris Geerts, Mathias Niepert, and Christopher Morris. 2022. Ordered subgraph aggregation networks.Advances in Neural Information Processing Systems35 (2022), 21030–21045

    work page 2022

  54. [54]

    Emanuele Rossi, Bertrand Charpentier, Francesco Di Giovanni, Fabrizio Frasca, Stephan Günnemann, and Michael M Bronstein. 2024. Edge directionality im- proves learning on heterophilic graphs. InLearning on graphs conference. PMLR, 25–1

    work page 2024

  55. [55]

    Ryan Rossi and Nesreen Ahmed. 2015. The network data repository with inter- active graph analytics and visualization. InProceedings of the AAAI conference on artificial intelligence, Vol. 29

    work page 2015

  56. [56]

    Ketan Rajshekhar Shahapure and Charles Nicholas. 2020. Cluster quality analysis using silhouette score. In2020 IEEE 7th international conference on data science and advanced analytics (DSAA). IEEE, 747–748

    work page 2020

  57. [57]

    Oleksandr Shchur, Maximilian Mumme, Aleksandar Bojchevski, and Stephan Günnemann. 2018. Pitfalls of graph neural network evaluation.arXiv preprint arXiv:1811.05868(2018)

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  58. [58]

    Balasubramaniam Srinivasan and Bruno Ribeiro. 2020. On the Equivalence between Positional Node Embeddings and Structural Graph Representations. In International Conference on Learning Representations

    work page 2020

  59. [59]

    Jake Topping, Francesco Di Giovanni, Benjamin Paul Chamberlain, Xiaowen Dong, and Michael M Bronstein. 2022. Understanding over-squashing and bot- tlenecks on graphs via curvature. InInternational Conference on Learning Repre- sentations

    work page 2022

  60. [60]

    Petar Veličković, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Liò, and Yoshua Bengio. 2018. Graph Attention Networks. InInternational Con- ference on Learning Representations

    work page 2018

  61. [61]

    Yuyang Wang, Zijie Li, and Amir Barati Farimani. 2023. Graph neural networks for molecules. InMachine learning in molecular sciences. Springer, 21–66

    work page 2023

  62. [62]

    Yanbo Wang and Muhan Zhang. 2024. An empirical study of realized GNN expressiveness. InProceedings of the 41st International Conference on Machine Learning. 52134–52155

    work page 2024

  63. [63]

    Yasida Insika Wanigatunga and Asela Hevapathige. 2025. Uncovering Structural Hierarchies in Molecules with Rich Club-Informed Representation Learning. In 2025 15th International Conference on Advanced Computer Information Technologies (ACIT). IEEE, 987–991

    work page 2025

  64. [64]

    Boris Weisfeiler and Andrei Leman. 1968. The reduction of a graph to canonical form and the algebra which appears therein.nti, Series2, 9 (1968), 12–16

    work page 1968

  65. [65]

    Oliver Wieder, Stefan Kohlbacher, Mélaine Kuenemann, Arthur Garon, Pierre Ducrot, Thomas Seidel, and Thierry Langer. 2020. A compact review of molec- ular property prediction with graph neural networks.Drug Discovery Today: Technologies37 (2020), 1–12

    work page 2020

  66. [66]

    Asiri Wijesinghe and Qing Wang. 2022. A new perspective on how graph neural networks go beyond weisfeiler-lehman?. InInternational Conference on Learning Representations

    work page 2022

  67. [67]

    Ron Wilson and Alexander Din. 2018. Calculating varying scales of clustering among locations.Cityscape20, 1 (2018), 215–232

    work page 2018

  68. [68]

    Dengsheng Wu, Huidong Wu, and Jianping Li. 2024. Hierarchy-aware adaptive graph neural network.IEEE Transactions on Knowledge and Data Engineering (2024)

    work page 2024

  69. [69]

    Jian Wu, Alison Goshulak, Venkatesh Srinivasan, and Alex Thomo. 2018. K-truss decomposition of large networks on a single consumer-grade machine. In2018 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM). IEEE, 873–880

    work page 2018

  70. [70]

    Wenwen Xia, Yuchen Li, Jun Wu, and Shenghong Li. 2021. Deepis: Susceptibility estimation on social networks. InProceedings of the 14th ACM International Conference on Web Search and Data Mining. 761–769

    work page 2021

  71. [71]

    Jiaxing Xu, Aihu Zhang, Qingtian Bian, Vijay Prakash Dwivedi, and Yiping Ke

    work page

  72. [72]

    InProceedings of the AAAI conference on artificial intelligence, Vol

    Union subgraph neural networks. InProceedings of the AAAI conference on artificial intelligence, Vol. 38. 16173–16183

    work page

  73. [73]

    Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. 2018. How Powerful are Graph Neural Networks?. InInternational Conference on Learning Representa- tions

    work page 2018

  74. [74]

    Zhitao Ying, Jiaxuan You, Christopher Morris, Xiang Ren, Will Hamilton, and Jure Leskovec. 2018. Hierarchical graph representation learning with differentiable pooling.Advances in neural information processing systems31 (2018)

    work page 2018

  75. [75]

    Jiaxuan You, Jonathan M Gomes-Selman, Rex Ying, and Jure Leskovec. 2021. Identity-aware graph neural networks. InProceedings of the AAAI conference on artificial intelligence

    work page 2021

  76. [76]

    Jiaxuan You, Rex Ying, and Jure Leskovec. 2019. Position-aware graph neural networks. InInternational conference on machine learning. PMLR, 7134–7143

    work page 2019

  77. [77]

    Shengzhong Zhang, Yimin Zhang, Bisheng Li, Wenjie Yang, Min Zhou, and Zengfeng Huang. 2025. Graph Batch Coarsening framework for scalable graph neural networks.Neural Networks183 (2025), 106931

    work page 2025

  78. [78]

    Xu Zhang, Yonghui Xu, Wei He, Wei Guo, and Lizhen Cui. 2023. A comprehensive review of the oversmoothing in graph neural networks. InCCF Conference on Computer Supported Cooperative Work and Social Computing. Springer, 451–465

    work page 2023

  79. [79]

    Yongqi Zhang and Quanming Yao. 2022. Knowledge graph reasoning with relational digraph. InProceedings of the ACM web conference 2022. 912–924

    work page 2022

  80. [80]

    Lingxiao Zhao, Wei Jin, Leman Akoglu, and Neil Shah. 2022. From stars to subgraphs: Uplifting any GNN with local structure awareness.International Conference on Learning Representations(2022)

    work page 2022

Showing first 80 references.