# EdgeNets:Edge Varying Graph Neural Networks

arXiv: https://arxiv.org/abs/2001.07620 · HTML: https://mlsanity.com/paper/2001.07620/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jan 2020.

## Built on by (most cited first, 30 of 36)

- [FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective](https://mlsanity.com/paper/2311.06190/) (2023)
- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Simplicial Convolutional Neural Networks](https://mlsanity.com/paper/2110.02585/) (2021)
- [Rewiring with Positional Encodings for Graph Neural Networks](https://mlsanity.com/paper/2201.12674/) (2022)
- [Graph Neural Networks with Learnable and Optimal Polynomial Bases](https://mlsanity.com/paper/2302.12432/) (2023)
- [Cell Attention Networks](https://mlsanity.com/paper/2209.08179/) (2022)
- [Topology-aware Graph Neural Networks for Learning Feasible and Adaptive ac-OPF Solutions](https://mlsanity.com/paper/2205.10129/) (2022)
- [Generalized Simplicial Attention Neural Networks](https://mlsanity.com/paper/2309.02138/) (2023)
- [Tangent Bundle Convolutional Learning: from Manifolds to Cellular Sheaves and Back](https://mlsanity.com/paper/2303.11323/) (2023)
- [ES-GNN: Generalizing Graph Neural Networks Beyond Homophily with Edge Splitting](https://mlsanity.com/paper/2205.13700/) (2022)
- [Learning to Count Isomorphisms with Graph Neural Networks](https://mlsanity.com/paper/2302.03266/) (2023)
- [Synthesizing Decentralized Controllers with Graph Neural Networks and Imitation Learning](https://mlsanity.com/paper/2012.14906/) (2020)
- [GRATIS: Deep Learning Graph Representation with Task-specific Topology and Multi-dimensional Edge Features](https://mlsanity.com/paper/2211.12482/) (2022)
- [Tangent Bundle Filters and Neural Networks: from Manifolds to Cellular Sheaves and Back](https://mlsanity.com/paper/2210.15058/) (2022)
- [Graph-Time Convolutional Neural Networks](https://mlsanity.com/paper/2103.01730/) (2021)
- [Convolutional Filtering in Simplicial Complexes](https://mlsanity.com/paper/2201.12584/) (2022)
- [Unsupervised Learning of Sampling Distributions for Particle Filters](https://mlsanity.com/paper/2302.01174/) (2023)
- [A Bipartite Graph Neural Network Approach for Scalable Beamforming Optimization](https://mlsanity.com/paper/2207.05364/) (2022)
- [Graph Neural Networks for Learning Real-Time Prices in Electricity Market](https://mlsanity.com/paper/2106.10529/) (2021)
- [Learning Graph Representation of Person-specific Cognitive Processes from Audio-visual Behaviours for Automatic Personality Recognition](https://mlsanity.com/paper/2110.13570/) (2021)
- [Attentional Graph Neural Network Is All You Need for Robust Massive Network Localization](https://mlsanity.com/paper/2311.16856/) (2023)
- [Learning Stable Graph Neural Networks via Spectral Regularization](https://mlsanity.com/paper/2211.06966/) (2022)
- [Covariance Density Neural Networks](https://mlsanity.com/paper/2505.11139/) (2025)
- [HGCN(O): A Self-Tuning GCN HyperModel Toolkit for Outcome Prediction in Event-Sequence Data](https://mlsanity.com/paper/2507.22524/) (2025)
- [Edge-Varying Fourier Graph Networks for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2210.03093/) (2022)
- [Graph Neural Networks over the Air for Decentralized Tasks in Wireless Networks](https://mlsanity.com/paper/2302.08447/) (2023)
- [Fairness-aware Optimal Graph Filter Design](https://mlsanity.com/paper/2310.14432/) (2023)
- [On the Trade-Off between Stability and Representational Capacity in Graph Neural Networks](https://mlsanity.com/paper/2312.02372/) (2023)
- [TSGDiff: Rethinking Synthetic Time Series Generation from a Pure Graph Perspective](https://mlsanity.com/paper/2511.12174/) (2025)
- [Graph Convolutional Neural Networks Sensitivity under Probabilistic Error Model](https://mlsanity.com/paper/2203.07831/) (2022)

## Abstract (arXiv)

Driven by the outstanding performance of neural networks in the structured Euclidean domain, recent years have seen a surge of interest in developing neural networks for graphs and data supported on graphs. The graph is leveraged at each layer of the neural network as a parameterization to capture detail at the node level with a reduced number of parameters and computational complexity. Following this rationale, this paper puts forth a general framework that unifies state-of-the-art graph neural networks (GNNs) through the concept of EdgeNet. An EdgeNet is a GNN architecture that allows different nodes to use different parameters to weigh the information of different neighbors. By extrapolating this strategy to more iterations between neighboring nodes, the EdgeNet learns edge- and neighbor-dependent weights to capture local detail. This is a general linear and local operation that a node can perform and encompasses under one formulation all existing graph convolutional neural networks (GCNNs) as well as graph attention networks (GATs). In writing different GNN architectures with a common language, EdgeNets highlight specific architecture advantages and limitations, while providing guidelines to improve their capacity without compromising their local implementation. An interesting conclusion is the unification of GCNNs and GATs -- approaches that have been so far perceived as separate. In particular, we show that GATs are GCNNs on a graph that is learned from the features. This particularization opens the doors to develop alternative attention mechanisms for improving discriminatory power.