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Community Detection on Networks with Ricci Flow

arXiv 1907.03993 ↗First posted 9 Jul 2019cs.SI physics.soc-phcited by 62

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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.

Key facts. Cited by 62 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Jul 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 4; 2022: 4; 2023: 10; 2024: 9; 2025: 15; 2026: 20.

62 papers.

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  1. 2021Understanding over-squashing and bottlenecks on graphs via curvaturecited by 471
  2. 2022Hyperbolic Graph Neural Networks: A Review of Methods and Applicationscited by 40
  3. 2023Mitigating Over-Smoothing and Over-Squashing using Augmentations of Forman-Ricci Curvaturecited by 39
  4. 2021Curvature Graph Neural Networkcited by 24
  5. 2022Heterogeneous manifolds for curvature-aware graph embeddingcited by 23
  6. 2023Contrastive Graph Clustering in Curvature Spacescited by 15
  7. 2024DeepRicci: Self-supervised Graph Structure-Feature Co-Refinement for Alleviating Over-squashingcited by 15
  8. 2023Curvature-based Clustering on Graphscited by 14
  9. 2023GRIL: A 2-parameter Persistence Based Vectorization for Machine Learningcited by 13
  10. 2023How Curvature Enhance the Adaptation Power of Framelet GCNscited by 13
  11. 2023Effective Structural Encodings via Local Curvature Profilescited by 13
  12. 2021WGCN: Graph Convolutional Networks with Weighted Structural Featurescited by 12
38 more
  1. 2022Generalized energy and gradient flow via graph frameletscited by 10
  2. 2024Graph Pooling via Ricci Flowcited by 10
  3. 2023Continuum Limits of Ollivier's Ricci Curvature on data clouds: pointwise consistency and global lower boundscited by 6
  4. 2025Spectro-Riemannian Graph Neural Networkscited by 5
  5. 2025PIORF: Physics-Informed Ollivier-Ricci Flow for Long-Range Interactions in Mesh Graph Neural Networkscited by 5
  6. 2024Deep Learning as Ricci Flowcited by 4
  7. 2023CAMEL: Curvature-Augmented Manifold Embedding and Learningcited by 3
  8. 2024Contrastive Sequential Interaction Network Learning on Co-Evolving Riemannian Spacescited by 3
  9. 2024Ricci flow-based brain surface covariance descriptors for diagnosing Alzheimer's diseasecited by 3
  10. 2024Curvature Augmented Manifold Embedding and Learningcited by 3
  11. 2024Analyzing Neural Network Robustness Using Graph Curvaturecited by 2
  12. 2025EmbedOR: Provable Cluster-Preserving Visualizations with Curvature-Based Stochastic Neighbor Embeddingscited by 2
  13. 2025Efficient Curvature-aware Graph Networkcited by 2
  14. 2026Tackling Over-smoothing on Hypergraphs: A Ricci Flow-guided Neural Diffusion Approachcited by 2
  15. 2021Smart Vectorizations for Single and Multiparameter Persistencecited by 1
  16. 2024Hypergraph clustering using Ricci curvature: an edge transport perspectivecited by 1
  17. 2025Geometry matters: insights from Ollivier Ricci Curvature and Ricci Flow into representational alignment through Ollivier-Ricci Curvature and Ricci Flowcited by 1
  18. 2025Graph and Simplicial Complex Prediction Gaussian Process via the Hodgelet Representationscited by 1
  19. 2025Adaptive Riemannian Graph Neural Networkscited by 1
  20. 2025RicciFlowRec: A Geometric Root Cause Recommender Using Ricci Curvature on Financial Graphscited by 1
  21. 2025Neural Feature Geometry Evolves as Discrete Ricci Flowcited by 1
  22. 2025Discrete scalar curvature as a weighted sum of Ollivier-Ricci curvaturescited by 1
  23. 2025Structural Invariance Matters: Rethinking Graph Rewiring through Graph Metricscited by 1
  24. 2026Dynamic Graph Structure Learning via Resistance Curvature Flowcited by 1
  25. 2026HypRAG: Hyperbolic Dense Retrieval for Retrieval Augmented Generationcited by 1
  26. 2026Diffusion Operator Geometry of Feedforward Representationscited by 1
  27. 2026Geometric Flow enhanced Graph Coarseningcited by 1
  28. 2022Ollivier-Ricci Curvature For Head Pose Estimation From a Single Imagecited by 0
  29. 2023Curvature-enhanced Graph Convolutional Network for Biomolecular Interaction Predictioncited by 0
  30. 2023Locally Stationary Graph Processescited by 0
  31. 2024Ironing the Graphs: Toward a Correct Geometric Analysis of Large-Scale Graphscited by 0
  32. 2025Transport Network, Graph, and Air Pollutioncited by 0
  33. 2025GFLC: Graph-based Fairness-aware Label Correction for Fair Classificationcited by 0
  34. 2025Graph-based Integrated Gradients for Explaining Graph Neural Networkscited by 0
  35. 2025A roadmap for curvature-based geometric data analysis and learningcited by 0
  36. 2026Post-Training Neural Network Pruning using Graph Curvaturecited by 0
  37. 2026Understanding and Improving UMAP with Geometric and Topological Priors: The JORC-UMAP Algorithmcited by 0
  38. 2026Sobolev--Ricci Curvaturecited by 0

50 most cited of 62 All 62 (JSON)