# Edge-Based Graph Component Pooling

arXiv: https://arxiv.org/abs/2409.11856 · HTML: https://mlsanity.com/paper/2409.11856/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 30 references that are in the map.
- First posted on arXiv 18 Sep 2024.

## Builds on (most cited first, 18 of 18)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Directed Acyclic Graph Neural Networks](https://mlsanity.com/paper/2101.07965/) (2021)
- [Memory-Based Graph Networks](https://mlsanity.com/paper/2002.09518/) (2020)
- [Graph Pooling for Graph Neural Networks: Progress, Challenges, and Opportunities](https://mlsanity.com/paper/2204.07321/) (2022)
- [Topology-Aware Graph Pooling Networks](https://mlsanity.com/paper/2010.09834/) (2020)
- [The expressive power of pooling in Graph Neural Networks](https://mlsanity.com/paper/2304.01575/) (2023)
- [Distribution Knowledge Embedding for Graph Pooling](https://mlsanity.com/paper/2109.14333/) (2021)
- [Structure-Feature based Graph Self-adaptive Pooling](https://mlsanity.com/paper/2002.00848/) (2020)
- [Multi-Level Attention Pooling for Graph Neural Networks: Unifying Graph Representations with Multiple Localities](https://mlsanity.com/paper/2103.01488/) (2021)

## Built on by (most cited first, 1 of 1)

- [LGRPool: Hierarchical Graph Pooling Via Local-Global Regularisation](https://mlsanity.com/paper/2504.08530/) (2025)

## Abstract (arXiv)

Graph-structured data naturally occurs in many research fields, such as chemistry and sociology. The relational information contained therein can be leveraged to statistically model graph properties through geometrical deep learning. Graph neural networks employ techniques, such as message-passing layers, to propagate local features through a graph. However, message-passing layers can be computationally expensive when dealing with large and sparse graphs. Graph pooling operators offer the possibility of removing or merging nodes in such graphs, thus lowering computational costs. However, pooling operators that remove nodes cause data loss, and pooling operators that merge nodes are often computationally expensive. We propose a pooling operator that merges nodes so as not to cause data loss but is also conceptually simple and computationally inexpensive. We empirically demonstrate that the proposed pooling operator performs statistically significantly better than edge pool on four popular benchmark datasets while reducing time complexity and the number of trainable parameters by 70.6% on average. Compared to another maximally powerful method named Graph Isomporhic Network, we show that we outperform them on two popular benchmark datasets while reducing the number of learnable parameters on average by 60.9%.