mlsanityData to 14 Oct 2026

Diversity Curves for Graph Representation Learning

arXiv 2605.06466 ↗First posted 7 May 2026cs.LGcited by 0

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Abstract (arXiv)

Graph-level representations are crucial tools for characterising structural differences between graphs. However, comparing graphs with different cardinalities, even when sampled from the same underlying distribution, remains challenging. Unsupervised tasks in particular require interpretable, scalable, and reliable size-aware graph representations. Our work addresses these issues by tracking the structural diversity of a graph across coarsening levels. The resulting graph embeddings, which we denote diversity curves, are interpretable by construction, efficient, and directly comparable across coarsening hierarchies. Specifically, we track the spread of graphs, a novel isometry invariant that is inherently well-suited for encoding the metric diversity and geometry of graphs. We utilise edge contraction coarsening and prove that this improves expressivity, thus leading to more powerful graph-level representations than structural descriptors alone. Demonstrating their utility over a range of baseline methods in practice, we use diversity curves to (i) cluster and visualise simulated graphs across varying sizes, (ii) distinguish the geometry of single-cell graphs, (iii) compare the structure of molecular graph datasets, and (iv) characterise geometric shapes.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 28 of its 96 references that are in the map. First posted on arXiv 7 May 2026.

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28 of 96 references.

References · 28

  1. 2020Graph Contrastive Learning with Augmentationscited by 1,208
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  11. 2018NetLSD: Hearing the Shape of a Graphcited by 52
  12. 2019Graph Kernels: A Surveycited by 44
16 more
  1. 2021Evaluation Metrics for Graph Generative Models: Problems, Pitfalls, and Practical Solutionscited by 39
  2. 2023An Empirical Study of Realized GNN Expressivenesscited by 33
  3. 2023Curvature Filtrations for Graph Generative Model Evaluationcited by 19
  4. 2023On the Expressivity of Persistent Homology in Graph Learningcited by 19
  5. 2023Metric Space Magnitude for Evaluating the Diversity of Latent Representationscited by 17
  6. 2023A Simple and Scalable Representation for Graph Generationcited by 16
  7. 2025No Metric to Rule Them All: Toward Principled Evaluations of Graph-Learning Datasetscited by 16
  8. 2024MANTRA: The Manifold Triangulations Assemblagecited by 12
  9. 2022Evaluating Graph Generative Models with Contrastively Learned Featurescited by 5
  10. 2025Geometry-Aware Edge Pooling for Graph Neural Networkscited by 5
  11. 2023Learning to Group Auxiliary Datasets for Moleculecited by 3
  12. 2025PolyGraph Discrepancy: a classifier-based metric for graph generationcited by 3
  13. 2023Fast 2-Approximate All-Pairs Shortest Pathscited by 1
  14. 2024TopER: Topological Embeddings in Graph Representation Learningcited by 1
  15. 2025Multi-Relation Graph-Kernel Strengthen Network for Graph-Level Clusteringcited by 1
  16. 2025Heat Kernel Goes Topologicalcited by 1

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