# Curvature Filtrations for Graph Generative Model Evaluation

arXiv: https://arxiv.org/abs/2301.12906 · HTML: https://mlsanity.com/paper/2301.12906/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 75 references that are in the map.
- First posted on arXiv 30 Jan 2023.

## Builds on (most cited first, 30 of 37)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting](https://mlsanity.com/paper/2006.09252/) (2020)
- [Permutation Invariant Graph Generation via Score-Based Generative Modeling](https://mlsanity.com/paper/2003.00638/) (2020)
- [Graph Neural Network for Traffic Forecasting: A Survey](https://mlsanity.com/paper/2101.11174/) (2021)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [Can Graph Neural Networks Count Substructures?](https://mlsanity.com/paper/2002.04025/) (2020)
- [Efficient Graph Generation with Graph Recurrent Attention Networks](https://mlsanity.com/paper/1910.00760/) (2019)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [Graph Neural Tangent Kernel: Fusing Graph Neural Networks with Graph Kernels](https://mlsanity.com/paper/1905.13192/) (2019)
- [Weisfeiler and Leman go Machine Learning: The Story so far](https://mlsanity.com/paper/2112.09992/) (2021)
- [Fake News Detection on Social Media using Geometric Deep Learning](https://mlsanity.com/paper/1902.06673/) (2019)
- [Wasserstein Weisfeiler-Lehman Graph Kernels](https://mlsanity.com/paper/1906.01277/) (2019)
- [How Powerful are K-hop Message Passing Graph Neural Networks](https://mlsanity.com/paper/2205.13328/) (2022)
- [Topological Graph Neural Networks](https://mlsanity.com/paper/2102.07835/) (2021)
- [Iterative Refinement Graph Neural Network for Antibody Sequence-Structure Co-design](https://mlsanity.com/paper/2110.04624/) (2021)
- [Graph Filtration Learning](https://mlsanity.com/paper/1905.10996/) (2019)
- [Scalable Deep Generative Modeling for Sparse Graphs](https://mlsanity.com/paper/2006.15502/) (2020)
- [On Weisfeiler-Leman Invariance: Subgraph Counts and Related Graph Properties](https://mlsanity.com/paper/1811.04801/) (2018)
- [Graph Kernels: State-of-the-Art and Future Challenges](https://mlsanity.com/paper/2011.03854/) (2020)
- [Graph Neural Networks with Local Graph Parameters](https://mlsanity.com/paper/2106.06707/) (2021)
- [A Theoretical Comparison of Graph Neural Network Extensions](https://mlsanity.com/paper/2201.12884/) (2022)
- [Geodesic Exponential Kernels: When Curvature and Linearity Conflict](https://mlsanity.com/paper/1411.0296/) (2014)
- [Tree Mover's Distance: Bridging Graph Metrics and Stability of Graph Neural Networks](https://mlsanity.com/paper/2210.01906/) (2022)
- [Are Powerful Graph Neural Nets Necessary? A Dissection on Graph Classification](https://mlsanity.com/paper/1905.04579/) (2019)

## Built on by (most cited first, 19 of 19)

- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [On the Expressivity of Persistent Homology in Graph Learning](https://mlsanity.com/paper/2302.09826/) (2023)
- [Topological Neural Networks go Persistent, Equivariant, and Continuous](https://mlsanity.com/paper/2406.03164/) (2024)
- [Position: All Current Generative Fidelity and Diversity Metrics are Flawed](https://mlsanity.com/paper/2505.22450/) (2025)
- [Boosting Graph Pooling with Persistent Homology](https://mlsanity.com/paper/2402.16346/) (2024)
- [HOG-Diff: Higher-Order Guided Diffusion for Graph Generation](https://mlsanity.com/paper/2502.04308/) (2025)
- [Diss-l-ECT: Dissecting Graph Data with Local Euler Characteristic Transforms](https://mlsanity.com/paper/2410.02622/) (2024)
- [CliquePH: Higher-Order Information for Graph Neural Networks through Persistent Homology on Clique Graphs](https://mlsanity.com/paper/2409.08217/) (2024)
- [PolyGraph Discrepancy: a classifier-based metric for graph generation](https://mlsanity.com/paper/2510.06122/) (2025)
- [Fast Graph Generation via Autoregressive Noisy Filtration Modeling](https://mlsanity.com/paper/2502.02415/) (2025)
- [FlatLand: Personalized Graph Federated Learning via Tailored Lorentz Space](https://mlsanity.com/paper/2608.21096/) (2026)
- [Topology-Aware CLIP Few-Shot Learning](https://mlsanity.com/paper/2505.01694/) (2025)
- [Discrete scalar curvature as a weighted sum of Ollivier-Ricci curvatures](https://mlsanity.com/paper/2510.04936/) (2025)
- [Dynamic Vertex Replacement Grammars](https://mlsanity.com/paper/2303.11553/) (2023)
- [Characterizing Physician Referral Networks with Ricci Curvature](https://mlsanity.com/paper/2408.16022/) (2024)
- [Vertical Validation: Evaluating Implicit Generative Models for Graphs on Thin Support Regions](https://mlsanity.com/paper/2411.13358/) (2024)
- [Diversity Curves for Graph Representation Learning](https://mlsanity.com/paper/2605.06466/) (2026)
- [Higher-Order Molecular Grammars for Generative and Foundation Models in Chemistry](https://mlsanity.com/paper/2610.02186/) (2026)
- [Exact Topological Compliance: Generating Persistence-Equivalent Graphs](https://mlsanity.com/paper/2610.18856/) (2026)

## 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.