# Community Detection on Networks with Ricci Flow

arXiv: https://arxiv.org/abs/1907.03993 · HTML: https://mlsanity.com/paper/1907.03993/

## Key facts

- Cited by 62 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jul 2019.

## Built on by (most cited first, 30 of 62)

- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Mitigating Over-Smoothing and Over-Squashing using Augmentations of Forman-Ricci Curvature](https://mlsanity.com/paper/2309.09384/) (2023)
- [Hyperbolic Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/2202.13852/) (2022)
- [Curvature Graph Neural Network](https://mlsanity.com/paper/2106.15762/) (2021)
- [Heterogeneous manifolds for curvature-aware graph embedding](https://mlsanity.com/paper/2202.01185/) (2022)
- [DeepRicci: Self-supervised Graph Structure-Feature Co-Refinement for Alleviating Over-squashing](https://mlsanity.com/paper/2401.12780/) (2024)
- [Contrastive Graph Clustering in Curvature Spaces](https://mlsanity.com/paper/2305.03555/) (2023)
- [Curvature-based Clustering on Graphs](https://mlsanity.com/paper/2307.10155/) (2023)
- [GRIL: A 2-parameter Persistence Based Vectorization for Machine Learning](https://mlsanity.com/paper/2304.04970/) (2023)
- [How Curvature Enhance the Adaptation Power of Framelet GCNs](https://mlsanity.com/paper/2307.09768/) (2023)
- [Effective Structural Encodings via Local Curvature Profiles](https://mlsanity.com/paper/2311.14864/) (2023)
- [WGCN: Graph Convolutional Networks with Weighted Structural Features](https://mlsanity.com/paper/2104.14060/) (2021)
- [Generalized energy and gradient flow via graph framelets](https://mlsanity.com/paper/2210.04124/) (2022)
- [Graph Pooling via Ricci Flow](https://mlsanity.com/paper/2407.04236/) (2024)
- [Continuum Limits of Ollivier's Ricci Curvature on data clouds: pointwise consistency and global lower bounds](https://mlsanity.com/paper/2307.02378/) (2023)
- [Spectro-Riemannian Graph Neural Networks](https://mlsanity.com/paper/2502.00401/) (2025)
- [PIORF: Physics-Informed Ollivier-Ricci Flow for Long-Range Interactions in Mesh Graph Neural Networks](https://mlsanity.com/paper/2504.04052/) (2025)
- [Deep Learning as Ricci Flow](https://mlsanity.com/paper/2404.14265/) (2024)
- [CAMEL: Curvature-Augmented Manifold Embedding and Learning](https://mlsanity.com/paper/2303.02561/) (2023)
- [Contrastive Sequential Interaction Network Learning on Co-Evolving Riemannian Spaces](https://mlsanity.com/paper/2401.01243/) (2024)
- [Ricci flow-based brain surface covariance descriptors for diagnosing Alzheimer's disease](https://mlsanity.com/paper/2403.06645/) (2024)
- [Curvature Augmented Manifold Embedding and Learning](https://mlsanity.com/paper/2403.14813/) (2024)
- [Tackling Over-smoothing on Hypergraphs: A Ricci Flow-guided Neural Diffusion Approach](https://mlsanity.com/paper/2603.15696/) (2026)
- [Analyzing Neural Network Robustness Using Graph Curvature](https://mlsanity.com/paper/2410.19607/) (2024)
- [RicciFlowRec: A Geometric Root Cause Recommender Using Ricci Curvature on Financial Graphs](https://mlsanity.com/paper/2508.09334/) (2025)
- [EmbedOR: Provable Cluster-Preserving Visualizations with Curvature-Based Stochastic Neighbor Embeddings](https://mlsanity.com/paper/2509.03703/) (2025)
- [Efficient Curvature-aware Graph Network](https://mlsanity.com/paper/2511.01443/) (2025)
- [Smart Vectorizations for Single and Multiparameter Persistence](https://mlsanity.com/paper/2104.04787/) (2021)
- [Hypergraph clustering using Ricci curvature: an edge transport perspective](https://mlsanity.com/paper/2412.15695/) (2024)
- [Geometry matters: insights from Ollivier Ricci Curvature and Ricci Flow into representational alignment through Ollivier-Ricci Curvature and Ricci Flow](https://mlsanity.com/paper/2501.00919/) (2025)

## Abstract (arXiv)

Many complex networks in the real world have community structures -- groups of well-connected nodes with important functional roles. It has been well recognized that the identification of communities bears numerous practical applications. While existing approaches mainly apply statistical or graph theoretical/combinatorial methods for community detection, in this paper, we present a novel geometric approach which enables us to borrow powerful classical geometric methods and properties. By considering networks as geometric objects and communities in a network as a geometric decomposition, we apply curvature and discrete Ricci flow, which have been used to decompose smooth manifolds with astonishing successes in mathematics, to break down communities in networks. We tested our method on networks with ground-truth community structures, and experimentally confirmed the effectiveness of this geometric approach.