# Geometric Flow enhanced Graph Coarsening

arXiv: https://arxiv.org/abs/2609.14962 · HTML: https://mlsanity.com/paper/2609.14962/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 52 references that are in the map.
- First posted on arXiv 14 Sep 2026.

## Builds on (most cited first, 29 of 29)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [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)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [A Comprehensive Survey of Graph Embedding: Problems, Techniques and Applications](https://mlsanity.com/paper/1709.07604/) (2017)
- [Deep Convolutional Networks on Graph-Structured Data](https://mlsanity.com/paper/1506.05163/) (2015)
- [Graph Convolutional Networks with EigenPooling](https://mlsanity.com/paper/1904.13107/) (2019)
- [Understanding Pooling in Graph Neural Networks](https://mlsanity.com/paper/2110.05292/) (2021)
- [Community Detection on Networks with Ricci Flow](https://mlsanity.com/paper/1907.03993/) (2019)
- [Structural Entropy Guided Graph Hierarchical Pooling](https://mlsanity.com/paper/2206.13510/) (2022)
- [Hierarchical Representation Learning in Graph Neural Networks with Node Decimation Pooling](https://mlsanity.com/paper/1910.11436/) (2019)
- [Curvature Graph Neural Network](https://mlsanity.com/paper/2106.15762/) (2021)
- [Characterizing Complex Networks with Forman-Ricci Curvature and Associated Geometric Flows](https://mlsanity.com/paper/1607.08654/) (2016)
- [Graph Representation Learning via Hard and Channel-Wise Attention Networks](https://mlsanity.com/paper/1907.04652/) (2019)
- [Network Alignment by Discrete Ollivier-Ricci Flow](https://mlsanity.com/paper/1809.00320/) (2018)
- [Graph Pooling via Ricci Flow](https://mlsanity.com/paper/2407.04236/) (2024)
- [Forman-Ricci flow for change detection in large dynamic data sets](https://mlsanity.com/paper/1604.06634/) (2016)
- [An efficient alternative to Ollivier-Ricci curvature based on the Jaccard metric](https://mlsanity.com/paper/1710.01724/) (2017)
- [Geometry-Aware Edge Pooling for Graph Neural Networks](https://mlsanity.com/paper/2506.11700/) (2025)
- [On Exploring Node-feature and Graph-structure Diversities for Node Drop Graph Pooling](https://mlsanity.com/paper/2306.12726/) (2023)
- [Seeing All From a Few: Nodes Selection Using Graph Pooling for Graph Clustering](https://mlsanity.com/paper/2105.05320/) (2021)

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

- [Scalable Subgraph Sampling via Resistance Curvature](https://mlsanity.com/paper/2609.27209/) (2026)

## Abstract (arXiv)

Recently, researchers have proposed a graph pooling operation, akin to the pooling process in conventional convolutional neural networks (CNN), aimed at reducing the computation cost of Graph convolutional neural networks (GCNNs). While most GCNN-based methods treat graph pooling as a node clustering problem and propose learning a cluster assignment matrix, existing clustering-based pooling methods tend to focus solely on the rough topology information of graphs, neglecting the exploitation of higher-order mutual connections among neighbors. In terms of message passing on graph, the ease of information passing on edges reflects the closeness between neighboring nodes, which significantly relies on the interconnectivity among neighbors. In this study, we address this gap by considering such local connection information and introducing a novel graph pooling method named RicciPool. We introduce discrete graph curvature, particularly Ollivier-Ricci curvature, as a measure of higher-order connectivity around an edge. Subsequently, we construct an Ollivier-Ricci flow formula to reweigh edge weights, leveraging the crucial information provided by Ricci curvature, particularly vital for extracting clusters in graphs. Building upon this foundation, we utilize the spectral clustering technique to learn a new cluster assignment matrix. Experimental results on multiple bioinformatics protein datasets and social networks underscore the effectiveness of our proposed method.