# HodgeNet: Graph Neural Networks for Edge Data

arXiv: https://arxiv.org/abs/1912.02354 · HTML: https://mlsanity.com/paper/1912.02354/

## Key facts

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

## Built on by (most cited first, 30 of 39)

- [Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond](https://mlsanity.com/paper/2101.05510/) (2021)
- [Principled Simplicial Neural Networks for Trajectory Prediction](https://mlsanity.com/paper/2102.10058/) (2021)
- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networks](https://mlsanity.com/paper/2304.10031/) (2023)
- [Simplicial Attention Networks](https://mlsanity.com/paper/2204.09455/) (2022)
- [Simplicial Convolutional Neural Networks](https://mlsanity.com/paper/2110.02585/) (2021)
- [Explaining the Explainers in Graph Neural Networks: a Comparative Study](https://mlsanity.com/paper/2210.15304/) (2022)
- [Signal Processing on Cell Complexes](https://mlsanity.com/paper/2110.05614/) (2021)
- [Convolutional Learning on Simplicial Complexes](https://mlsanity.com/paper/2301.11163/) (2023)
- [Generalized Simplicial Attention Neural Networks](https://mlsanity.com/paper/2309.02138/) (2023)
- [Link Scheduling using Graph Neural Networks](https://mlsanity.com/paper/2109.05536/) (2021)
- [Simplicial Attention Neural Networks](https://mlsanity.com/paper/2203.07485/) (2022)
- [Simplicial Convolutional Filters](https://mlsanity.com/paper/2201.11720/) (2022)
- [Dist2Cycle: A Simplicial Neural Network for Homology Localization](https://mlsanity.com/paper/2110.15182/) (2021)
- [Finite Impulse Response Filters for Simplicial Complexes](https://mlsanity.com/paper/2103.12587/) (2021)
- [Untrained Graph Neural Networks for Denoising](https://mlsanity.com/paper/2109.11700/) (2021)
- [Signal processing on simplicial complexes](https://mlsanity.com/paper/2106.07471/) (2021)
- [Dirac signal processing of higher-order topological signals](https://mlsanity.com/paper/2301.10137/) (2023)
- [The decomposition of the higher-order homology embedding constructed from the k-Laplacian](https://mlsanity.com/paper/2107.10970/) (2021)
- [Data-Centric AI Requires Rethinking Data Notion](https://mlsanity.com/paper/2110.02491/) (2021)
- [Convolutional Filtering in Simplicial Complexes](https://mlsanity.com/paper/2201.12584/) (2022)
- [Cycle Invariant Positional Encoding for Graph Representation Learning](https://mlsanity.com/paper/2311.14333/) (2023)
- [On the Theoretical Expressive Power and the Design Space of Higher-Order Graph Transformers](https://mlsanity.com/paper/2404.03380/) (2024)
- [Topo-MLP : A Simplicial Network Without Message Passing](https://mlsanity.com/paper/2312.11862/) (2023)
- [Graph-based Algorithm Unfolding for Energy-aware Power Allocation in Wireless Networks](https://mlsanity.com/paper/2201.11799/) (2022)
- [Representing Edge Flows on Graphs via Sparse Cell Complexes](https://mlsanity.com/paper/2309.01632/) (2023)
- [Higher-Order Topological Directionality and Directed Simplicial Neural Networks](https://mlsanity.com/paper/2409.08389/) (2024)
- [Demystifying Higher-Order Graph Neural Networks](https://mlsanity.com/paper/2406.12841/) (2024)
- [Free Energy Node Embedding via Generalized Skip-gram with Negative Sampling](https://mlsanity.com/paper/2105.09182/) (2021)
- [Stability Analysis of Unfolded WMMSE for Power Allocation](https://mlsanity.com/paper/2110.07471/) (2021)

## 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.