mlsanityData to 14 Oct 2026

HodgeNet: Graph Neural Networks for Edge Data

arXiv 1912.02354 ↗First posted 5 Dec 2019eess.SP cs.SIcited by 39

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Abstract (arXiv)

Networks and network processes have emerged as powerful tools for modeling social interactions, disease propagation, and a variety of additional dynamics driven by relational structures. Recently, neural networks have been generalized to process data on graphs, thus being able to learn from the aforementioned network processes achieving cutting-edge performance in traditional tasks such as node classification and link prediction. However, these methods have all been formulated in a way suited only to data on the nodes of a graph. The application of these techniques to data supported on the edges of a graph, namely flow signals, has not been explored in detail. To bridge this gap, we propose the use of the so-called Hodge Laplacian combined with graph neural network architectures for the analysis of flow data. Specifically, we apply two graph neural network architectures to solve the problems of flow interpolation and source localization.

Key facts. Cited by 39 papers in the map (data through 14 Oct 2026). First posted on arXiv 5 Dec 2019.

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Citing papers per year: 2021: 13; 2022: 6; 2023: 8; 2024: 5; 2025: 4; 2026: 3.

39 papers.

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  1. 2021Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyondcited by 82
  2. 2021Principled Simplicial Neural Networks for Trajectory Predictioncited by 77
  3. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 66
  4. 2023Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networkscited by 43
  5. 2022Simplicial Attention Networkscited by 41
  6. 2021Simplicial Convolutional Neural Networkscited by 40
  7. 2022Explaining the Explainers in Graph Neural Networks: a Comparative Studycited by 35
  8. 2021Signal Processing on Cell Complexescited by 31
  9. 2023Convolutional Learning on Simplicial Complexescited by 27
  10. 2023Generalized Simplicial Attention Neural Networkscited by 27
  11. 2021Link Scheduling using Graph Neural Networkscited by 26
  12. 2022Simplicial Attention Neural Networkscited by 21
27 more
  1. 2022Simplicial Convolutional Filterscited by 18
  2. 2021Dist2Cycle: A Simplicial Neural Network for Homology Localizationcited by 16
  3. 2021Finite Impulse Response Filters for Simplicial Complexescited by 15
  4. 2021Untrained Graph Neural Networks for Denoisingcited by 15
  5. 2021Signal processing on simplicial complexescited by 12
  6. 2023Dirac signal processing of higher-order topological signalscited by 9
  7. 2021The decomposition of the higher-order homology embedding constructed from the k-Laplaciancited by 8
  8. 2021Data-Centric AI Requires Rethinking Data Notioncited by 8
  9. 2022Convolutional Filtering in Simplicial Complexescited by 8
  10. 2023Cycle Invariant Positional Encoding for Graph Representation Learningcited by 8
  11. 2024On the Theoretical Expressive Power and the Design Space of Higher-Order Graph Transformerscited by 8
  12. 2023Topo-MLP : A Simplicial Network Without Message Passingcited by 7
  13. 2022Graph-based Algorithm Unfolding for Energy-aware Power Allocation in Wireless Networkscited by 5
  14. 2023Representing Edge Flows on Graphs via Sparse Cell Complexescited by 5
  15. 2024Higher-Order Topological Directionality and Directed Simplicial Neural Networkscited by 5
  16. 2024Demystifying Higher-Order Graph Neural Networkscited by 4
  17. 2021Free Energy Node Embedding via Generalized Skip-gram with Negative Samplingcited by 2
  18. 2021Stability Analysis of Unfolded WMMSE for Power Allocationcited by 2
  19. 2024Graph Neural Networks for Edge Signals: Orientation Equivariance and Invariancecited by 2
  20. 2025Continuous Simplicial Neural Networkscited by 2
  21. 2023SC-MAD: Mixtures of Higher-order Networks for Data Augmentationcited by 0
  22. 2025Topological Neural Networks over the Aircited by 0
  23. 2025Directed Semi-Simplicial Learning with Applications to Brain Activity Decodingcited by 0
  24. 2025Kernel Regression of Multi-Way Data via Tensor Trains with Hadamard Overparametrization: The Dynamic Graph Flow Casecited by 0
  25. 2026TopoU-Net: a U-Net architecture for topological domainscited by 0
  26. 2026Cellular Sheaf Neural Operators for Structure-Preserving Surrogate Modeling of Constrained PDEscited by 0
  27. 2026Kernel Regression with Tensor Trains and Hadamard Overparameterizationcited by 0