# Learning Resource Allocation Policy: Vertex-GNN or Edge-GNN?

arXiv: https://arxiv.org/abs/2307.12480 · HTML: https://mlsanity.com/paper/2307.12480/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 28 references that are in the map.
- First posted on arXiv 24 Jul 2023.

## Builds on (most cited first, 16 of 16)

- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [A Survey on The Expressive Power of Graph Neural Networks](https://mlsanity.com/paper/2003.04078/) (2020)
- [Optimal Wireless Resource Allocation with Random Edge Graph Neural Networks](https://mlsanity.com/paper/1909.01865/) (2019)
- [Graph Neural Networks for Scalable Radio Resource Management: Architecture Design and Theoretical Analysis](https://mlsanity.com/paper/2007.07632/) (2020)
- [Theory of Graph Neural Networks: Representation and Learning](https://mlsanity.com/paper/2204.07697/) (2022)
- [Edge Representation Learning with Hypergraphs](https://mlsanity.com/paper/2106.15845/) (2021)
- [Graph Embedding based Wireless Link Scheduling with Few Training Samples](https://mlsanity.com/paper/1906.02871/) (2019)
- [Graph Edge Convolutional Neural Networks for Skeleton Based Action Recognition](https://mlsanity.com/paper/1805.06184/) (2018)
- [Learning to Reflect and to Beamform for Intelligent Reflecting Surface with Implicit Channel Estimation](https://mlsanity.com/paper/2009.14404/) (2020)
- [Scalable Power Control/Beamforming in Heterogeneous Wireless Networks with Graph Neural Networks](https://mlsanity.com/paper/2104.05463/) (2021)
- [Graph Neural Networks Meet Wireless Communications: Motivation, Applications, and Future Directions](https://mlsanity.com/paper/2212.04047/) (2022)
- [A Bipartite Graph Neural Network Approach for Scalable Beamforming Optimization](https://mlsanity.com/paper/2207.05364/) (2022)
- [Multidimensional Graph Neural Networks for Wireless Communications](https://mlsanity.com/paper/2212.11531/) (2022)
- [Improving Learning Efficiency for Wireless Resource Allocation with Symmetric Prior](https://mlsanity.com/paper/2005.08510/) (2020)
- [GBLinks: GNN-Based Beam Selection and Link Activation for Ultra-dense D2D mmWave Networks](https://mlsanity.com/paper/2107.02412/) (2021)

## Built on by (most cited first, 2 of 2)

- [Revisiting Outage for Edge Inference Systems](https://mlsanity.com/paper/2504.03686/) (2025)
- [MANET-GNN: Learned Decentralized Optimization of Power Allocation in Multi-Channel MANETs](https://mlsanity.com/paper/2609.40170/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs) update the hidden representations of vertices (called Vertex-GNNs) or hidden representations of edges (called Edge-GNNs) by processing and pooling the information of neighboring vertices and edges and combining to exploit topology information. When learning resource allocation policies, GNNs cannot perform well if their expressive power is weak, i.e., if they cannot differentiate all input features such as channel matrices. In this paper, we analyze the expressive power of the Vertex-GNNs and Edge-GNNs for learning three representative wireless policies: link scheduling, power control, and precoding policies. We find that the expressive power of the GNNs depends on the linearity and output dimensions of the processing and combination functions. When linear processors are used, the Vertex-GNNs cannot differentiate all channel matrices due to the loss of channel information, while the Edge-GNNs can. When learning the precoding policy, even the Vertex-GNNs with non-linear processors may not be with strong expressive ability due to the dimension compression. We proceed to provide necessary conditions for the GNNs to well learn the precoding policy. Simulation results validate the analyses and show that the Edge-GNNs can achieve the same performance as the Vertex-GNNs with much lower training and inference time.