# Graph Neural Modeling of Network Flows

arXiv: https://arxiv.org/abs/2209.05208 · HTML: https://mlsanity.com/paper/2209.05208/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 54 references that are in the map.
- First posted on arXiv 12 Sep 2022.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Combinatorial optimization and reasoning with graph neural networks](https://mlsanity.com/paper/2102.09544/) (2021)
- [A Fair Comparison of Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/1912.09893/) (2019)
- [What Can Neural Networks Reason About?](https://mlsanity.com/paper/1905.13211/) (2019)
- [Relational Graph Attention Networks](https://mlsanity.com/paper/1904.05811/) (2019)
- [Experience-driven Networking: A Deep Reinforcement Learning based Approach](https://mlsanity.com/paper/1801.05757/) (2018)
- [Maximum Flow and Minimum-Cost Flow in Almost-Linear Time](https://mlsanity.com/paper/2203.00671/) (2022)
- [Unveiling the potential of Graph Neural Networks for network modeling and optimization in SDN](https://mlsanity.com/paper/1901.08113/) (2019)
- [Neural Bipartite Matching](https://mlsanity.com/paper/2005.11304/) (2020)
- [Why (and How) Networks Should Run Themselves](https://mlsanity.com/paper/1710.11583/) (2017)
- [CFR-RL: Traffic Engineering with Reinforcement Learning in SDN](https://mlsanity.com/paper/2004.11986/) (2020)
- [GDDR: GNN-based Data-Driven Routing](https://mlsanity.com/paper/2104.09919/) (2021)
- [R-GCN: The R Could Stand for Random](https://mlsanity.com/paper/2203.02424/) (2022)
- [REPETITA: Repeatable Experiments for Performance Evaluation of Traffic-Engineering Algorithms](https://mlsanity.com/paper/1710.08665/) (2017)
- [Towards Real-Time Routing Optimization with Deep Reinforcement Learning: Open Challenges](https://mlsanity.com/paper/2106.09754/) (2021)

## Built on by (most cited first, 3 of 3)

- [Graph Reinforcement Learning for Combinatorial Optimization: A Survey and Unifying Perspective](https://mlsanity.com/paper/2404.06492/) (2024)
- [A Theoretical Framework for Graph-based Digital Twins for Supply Chain Management and Optimization](https://mlsanity.com/paper/2504.03692/) (2025)
- [Beyond the Graph: An Adaptive Meta-Learner Fuses Explainability, Weather, and Dynamics for Robust Bus ETA Prediction](https://mlsanity.com/paper/2609.31667/) (2026)

## Abstract (arXiv)

Network flow problems, which involve distributing traffic such that the underlying infrastructure is used effectively, are ubiquitous in transportation and logistics. Among them, the general Multi-Commodity Network Flow (MCNF) problem concerns the distribution of multiple flows of different sizes between several sources and sinks, while achieving effective utilization of the links. Due to the appeal of data-driven optimization, these problems have increasingly been approached using graph learning methods. In this paper, we propose a novel graph learning architecture for network flow problems called Per-Edge Weights (PEW). This method builds on a Graph Attention Network and uses distinctly parametrized message functions along each link. We extensively evaluate the proposed solution through an Internet flow routing case study using 17 Service Provider topologies and 2 routing schemes. We show that PEW yields substantial gains over architectures whose global message function constrains the routing unnecessarily. We also find that an MLP is competitive with other standard architectures. Furthermore, we analyze the relationship between graph structure and predictive performance for data-driven routing of flows, an aspect that has not been considered by existing work in the area.