# Curvature-based Clustering on Graphs

arXiv: https://arxiv.org/abs/2307.10155 · HTML: https://mlsanity.com/paper/2307.10155/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 63 references that are in the map.
- First posted on arXiv 19 Jul 2023.

## Builds on (most cited first, 13 of 13)

- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [Networks beyond pairwise interactions: structure and dynamics](https://mlsanity.com/paper/2006.01764/) (2020)
- [Higher-order organization of complex networks](https://mlsanity.com/paper/1612.08447/) (2016)
- [Community Detection on Networks with Ricci Flow](https://mlsanity.com/paper/1907.03993/) (2019)
- [Spectral redemption: clustering sparse networks](https://mlsanity.com/paper/1306.5550/) (2013)
- [Bayesian estimation from few samples: community detection and related problems](https://mlsanity.com/paper/1710.00264/) (2017)
- [Detecting Overlapping Communities in Networks Using Spectral Methods](https://mlsanity.com/paper/1412.3432/) (2014)
- [Characterizing Complex Networks with Forman-Ricci Curvature and Associated Geometric Flows](https://mlsanity.com/paper/1607.08654/) (2016)
- [Identifying the latent space geometry of network models through analysis of curvature](https://mlsanity.com/paper/2012.10559/) (2020)
- [Forman-Ricci Curvature for Hypergraphs](https://mlsanity.com/paper/1811.07825/) (2018)
- [Neighborhood Growth Determines Geometric Priors for Relational Representation Learning](https://mlsanity.com/paper/1910.05565/) (2019)
- [Forman's Ricci curvature - From networks to hypernetworks](https://mlsanity.com/paper/1810.07749/) (2018)
- [Random line graphs and edge-attributed network inference](https://mlsanity.com/paper/2103.14726/) (2021)

## Built on by (most cited first, 14 of 14)

- [Mitigating Over-Smoothing and Over-Squashing using Augmentations of Forman-Ricci Curvature](https://mlsanity.com/paper/2309.09384/) (2023)
- [Exposition on over-squashing problem on GNNs: Current Methods, Benchmarks and Challenges](https://mlsanity.com/paper/2311.07073/) (2023)
- [Effective Structural Encodings via Local Curvature Profiles](https://mlsanity.com/paper/2311.14864/) (2023)
- [Graph Pooling via Ricci Flow](https://mlsanity.com/paper/2407.04236/) (2024)
- [Spectro-Riemannian Graph Neural Networks](https://mlsanity.com/paper/2502.00401/) (2025)
- [CurvGAD: Leveraging Curvature for Enhanced Graph Anomaly Detection](https://mlsanity.com/paper/2502.08605/) (2025)
- [Geometric Machine Learning on EEG Signals](https://mlsanity.com/paper/2502.05334/) (2025)
- [Hypergraph clustering using Ricci curvature: an edge transport perspective](https://mlsanity.com/paper/2412.15695/) (2024)
- [Removing Neural Signal Artifacts with Autoencoder-Targeted Adversarial Transformers (AT-AT)](https://mlsanity.com/paper/2502.05332/) (2025)
- [Neural Feature Geometry Evolves as Discrete Ricci Flow](https://mlsanity.com/paper/2509.22362/) (2025)
- [Lower Ricci Curvature for Hypergraphs](https://mlsanity.com/paper/2506.03943/) (2025)
- [Topology-Aware Active Learning on Graphs](https://mlsanity.com/paper/2510.25892/) (2025)
- [Sobolev--Ricci Curvature](https://mlsanity.com/paper/2603.12652/) (2026)
- [Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature](https://mlsanity.com/paper/2607.22381/) (2026)

## Abstract (arXiv)

Unsupervised node clustering (or community detection) is a classical graph learning task. In this paper, we study algorithms, which exploit the geometry of the graph to identify densely connected substructures, which form clusters or communities. Our method implements discrete Ricci curvatures and their associated geometric flows, under which the edge weights of the graph evolve to reveal its community structure. We consider several discrete curvature notions and analyze the utility of the resulting algorithms. In contrast to prior literature, we study not only single-membership community detection, where each node belongs to exactly one community, but also mixed-membership community detection, where communities may overlap. For the latter, we argue that it is beneficial to perform community detection on the line graph, i.e., the graph's dual. We provide both theoretical and empirical evidence for the utility of our curvature-based clustering algorithms. In addition, we give several results on the relationship between the curvature of a graph and that of its dual, which enable the efficient implementation of our proposed mixed-membership community detection approach and which may be of independent interest for curvature-based network analysis.