mlsanityData to 7 Oct 2026

Curvature Filtrations for Graph Generative Model Evaluation

arXiv 2301.12906 ↗First posted 30 Jan 2023cs.LG math.AT stat.MLcited by 18

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Abstract (arXiv)

Graph generative model evaluation necessitates understanding differences between graphs on the distributional level. This entails being able to harness salient attributes of graphs in an efficient manner. Curvature constitutes one such property that has recently proved its utility in characterising graphs. Its expressive properties, stability, and practical utility in model evaluation remain largely unexplored, however. We combine graph curvature descriptors with emerging methods from topological data analysis to obtain robust, expressive descriptors for evaluating graph generative models.

Key facts. Cited by 18 papers in the map (data through 7 Oct 2026). Builds on 37 of its 75 references that are in the map. First posted on arXiv 30 Jan 2023.

Builds on

37 of 75 references.

References · 37

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2018How Powerful are Graph Neural Networks?cited by 4,355
  3. 2018Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networkscited by 878
  4. 2020TUDataset: A collection of benchmark datasets for learning with graphscited by 718
  5. 2018Junction Tree Variational Autoencoder for Molecular Graph Generationcited by 647
  6. 2021Understanding over-squashing and bottlenecks on graphs via curvaturecited by 471
  7. 2018GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Modelscited by 406
  8. 2020Improving Graph Neural Network Expressivity via Subgraph Isomorphism Countingcited by 312
  9. 2020Permutation Invariant Graph Generation via Score-Based Generative Modelingcited by 263
  10. 2021Graph Neural Network for Traffic Forecasting: A Surveycited by 260
  11. 2015Persistence Images: A Stable Vector Representation of Persistent Homologycited by 235
  12. 2020Can Graph Neural Networks Count Substructures?cited by 235
25 more
  1. 2019Efficient Graph Generation with Graph Recurrent Attention Networkscited by 231
  2. 2021Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networkscited by 219
  3. 2019Graph Neural Tangent Kernel: Fusing Graph Neural Networks with Graph Kernelscited by 160
  4. 2021Weisfeiler and Leman go Machine Learning: The Story so farcited by 121
  5. 2019Fake News Detection on Social Media using Geometric Deep Learningcited by 115
  6. 2019Wasserstein Weisfeiler-Lehman Graph Kernelscited by 104
  7. 2022How Powerful are K-hop Message Passing Graph Neural Networkscited by 90
  8. 2021Topological Graph Neural Networkscited by 86
  9. 2021Iterative Refinement Graph Neural Network for Antibody Sequence-Structure Co-designcited by 82
  10. 2019Graph Filtration Learningcited by 68
  11. 2018On Weisfeiler-Leman Invariance: Subgraph Counts and Related Graph Propertiescited by 63
  12. 2020Scalable Deep Generative Modeling for Sparse Graphscited by 63
  13. 2020Graph Kernels: State-of-the-Art and Future Challengescited by 63
  14. 2021Graph Neural Networks with Local Graph Parameterscited by 51
  15. 2014Geodesic Exponential Kernels: When Curvature and Linearity Conflictcited by 47
  16. 2022A Theoretical Comparison of Graph Neural Network Extensionscited by 47
  17. 2019Are Powerful Graph Neural Nets Necessary? A Dissection on Graph Classificationcited by 39
  18. 2022Tree Mover's Distance: Bridging Graph Metrics and Stability of Graph Neural Networkscited by 39
  19. 2021Evaluation Metrics for Graph Generative Models: Problems, Pitfalls, and Practical Solutionscited by 38
  20. 2020Let's Agree to Degree: Comparing Graph Convolutional Networks in the Message-Passing Frameworkcited by 24
  21. 2022Affinity-Aware Graph Networkscited by 17
  22. 2022Ollivier-Ricci Curvature for Hypergraphs: A Unified Frameworkcited by 12
  23. 2019Topological Machine Learning with Persistence Indicator Functionscited by 11
  24. 2021Graphon based Clustering and Testing of Networks: Algorithms and Theorycited by 6
  25. 2019A Hierarchy of Graph Neural Networks Based on Learnable Local Featurescited by 5

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 7; 2025: 6; 2026: 3.

18 papers.

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  1. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 65
  2. 2023On the Expressivity of Persistent Homology in Graph Learningcited by 18
  3. 2024Topological Neural Networks go Persistent, Equivariant, and Continuouscited by 15
  4. 2025Position: All Current Generative Fidelity and Diversity Metrics are Flawedcited by 12
  5. 2024Boosting Graph Pooling with Persistent Homologycited by 9
  6. 2024Diss-l-ECT: Dissecting Graph Data with Local Euler Characteristic Transformscited by 6
  7. 2025HOG-Diff: Higher-Order Guided Diffusion for Graph Generationcited by 6
  8. 2024CliquePH: Higher-Order Information for Graph Neural Networks through Persistent Homology on Clique Graphscited by 3
  9. 2025Fast Graph Generation via Autoregressive Noisy Filtration Modelingcited by 2
  10. 2025PolyGraph Discrepancy: a classifier-based metric for graph generationcited by 2
  11. 2026FlatLand: Personalized Graph Federated Learning via Tailored Lorentz Spacecited by 2
  12. 2025Topology-Aware CLIP Few-Shot Learningcited by 1
6 more
  1. 2025Discrete scalar curvature as a weighted sum of Ollivier-Ricci curvaturescited by 1
  2. 2023Dynamic Vertex Replacement Grammarscited by 0
  3. 2024Characterizing Physician Referral Networks with Ricci Curvaturecited by 0
  4. 2024Vertical Validation: Evaluating Implicit Generative Models for Graphs on Thin Support Regionscited by 0
  5. 2026Diversity Curves for Graph Representation Learningcited by 0
  6. 2026Higher-Order Molecular Grammars for Generative and Foundation Models in Chemistrycited by 0