mlsanityData to 7 Oct 2026

On topological descriptors for graph products

arXiv 2511.08846 ↗First posted 12 Nov 2025cs.LG math.AT stat.MLcited by 2

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Abstract (arXiv)

Topological descriptors have been increasingly utilized for capturing multiscale structural information in relational data. In this work, we consider various filtrations on the (box) product of graphs and the effect on their outputs on the topological descriptors - the Euler characteristic (EC) and persistent homology (PH). In particular, we establish a complete characterization of the expressive power of EC on general color-based filtrations. We also show that the PH descriptors of (virtual) graph products contain strictly more information than the computation on individual graphs, whereas EC does not. Additionally, we provide algorithms to compute the PH diagrams of the product of vertex- and edge-level filtrations on the graph product. We also substantiate our theoretical analysis with empirical investigations on runtime analysis, expressivity, and graph classification performance. Overall, this work paves way for powerful graph persistent descriptors via product filtrations. Code is available at https://github.com/Aalto-QuML/tda_graph_product.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 34 of its 54 references that are in the map. First posted on arXiv 12 Nov 2025.

Builds on

34 of 54 references.

References · 34

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22 more
  1. 2019PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signaturescited by 125
  2. 2021Weisfeiler and Leman go Machine Learning: The Story so farcited by 121
  3. 2021Topological Graph Neural Networkscited by 86
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  8. 2019Persistence Homology of Networks: Methods and Applicationscited by 30
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  12. 2023Differentiable Euler Characteristic Transforms for Shape Classificationcited by 18
  13. 2024Topological Neural Networks go Persistent, Equivariant, and Continuouscited by 15
  14. 2020Product Graph Learning from Multi-domain Data with Sparsity and Rank Constraintscited by 10
  15. 2022Graph-Time Convolutional Neural Networks: Architecture and Theoretical Analysiscited by 10
  16. 2024Topological Blindspots: Understanding and Extending Topological Deep Learning Through the Lens of Expressivitycited by 9
  17. 2024Continuous Product Graph Neural Networkscited by 8
  18. 2024A Flexible, Equivariant Framework for Subgraph GNNs via Graph Products and Graph Coarseningcited by 8
  19. 2024Diss-l-ECT: Dissecting Graph Data with Local Euler Characteristic Transformscited by 6
  20. 2024Topology meets Machine Learning: An Introduction using the Euler Characteristic Transformcited by 4
  21. 2024CliquePH: Higher-Order Information for Graph Neural Networks through Persistent Homology on Clique Graphscited by 3
  22. 2025Persistent Homology-induced Graph Ensembles for Time Series Regressionscited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 1; 2026: 1.

2 papers.

  1. 2025Frequent subgraph-based persistent homology for graph classificationcited by 0
  2. 2026Contraction and Hourglass Persistence for Learning on Graphs, Simplices, and Cellscited by 0