mlsanityData to 7 Oct 2026

Characterizing Complex Networks with Forman-Ricci Curvature and Associated Geometric Flows

arXiv 1607.08654 ↗First posted 28 Jul 2016cs.DM cs.SI math.COcited by 21

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Abstract (arXiv)

We introduce Forman-Ricci curvature and its corresponding flow as characteristics for complex networks attempting to extend the common approach of node-based network analysis by edge-based characteristics. Following a theoretical introduction and mathematical motivation, we apply the proposed network-analytic methods to static and dynamic complex networks and compare the results with established node-based characteristics. Our work suggests a number of applications for data mining, including denoising and clustering of experimental data, as well as extrapolation of network evolution.

Key facts. Cited by 21 papers in the map (data through 7 Oct 2026). First posted on arXiv 28 Jul 2016.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 2; 2023: 4; 2024: 2; 2025: 7; 2026: 5.

21 papers.

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  1. 2023Mitigating Over-Smoothing and Over-Squashing using Augmentations of Forman-Ricci Curvaturecited by 39
  2. 2022Self-Supervised Continual Graph Learning in Adaptive Riemannian Spacescited by 32
  3. 2021Curvature Graph Neural Networkcited by 24
  4. 2023Curvature-based Clustering on Graphscited by 14
  5. 2023Effective Structural Encodings via Local Curvature Profilescited by 13
  6. 2022Ollivier-Ricci Curvature for Hypergraphs: A Unified Frameworkcited by 12
  7. 2024Graph Pooling via Ricci Flowcited by 10
  8. 2023Continuum Limits of Ollivier's Ricci Curvature on data clouds: pointwise consistency and global lower boundscited by 6
  9. 2024Deep Learning as Ricci Flowcited by 4
  10. 2025Geometric Machine Learning on EEG Signalscited by 3
  11. 2025Efficient Curvature-aware Graph Networkcited by 2
  12. 2025Removing Neural Signal Artifacts with Autoencoder-Targeted Adversarial Transformers (AT-AT)cited by 1
9 more
  1. 2025Neural Feature Geometry Evolves as Discrete Ricci Flowcited by 1
  2. 2026Geometric Flow enhanced Graph Coarseningcited by 1
  3. 2025GFLC: Graph-based Fairness-aware Label Correction for Fair Classificationcited by 0
  4. 2025A Remedy for Over-Squashing in Graph Learning via Forman-Ricci Curvature based Graph-to-Hypergraph Structural Liftingcited by 0
  5. 2025A roadmap for curvature-based geometric data analysis and learningcited by 0
  6. 2026Sandpile Economics: Theory, Identification, and Evidencecited by 0
  7. 2026Periodic Topological Deep Learning for Polymer Design and Discoverycited by 0
  8. 2026Look Before You Lift: Visual and Quantitative Diagnostics for Topological Deep Learningcited by 0
  9. 2026CurvFlow-DTA: dual-graph discrete Ricci curvature flow for drug--target affinity predictioncited by 0