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

arXiv: https://arxiv.org/abs/1607.08654 · HTML: https://mlsanity.com/paper/1607.08654/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jul 2016.

## Built on by (most cited first, 21 of 21)

- [Mitigating Over-Smoothing and Over-Squashing using Augmentations of Forman-Ricci Curvature](https://mlsanity.com/paper/2309.09384/) (2023)
- [Self-Supervised Continual Graph Learning in Adaptive Riemannian Spaces](https://mlsanity.com/paper/2211.17068/) (2022)
- [Curvature Graph Neural Network](https://mlsanity.com/paper/2106.15762/) (2021)
- [Curvature-based Clustering on Graphs](https://mlsanity.com/paper/2307.10155/) (2023)
- [Effective Structural Encodings via Local Curvature Profiles](https://mlsanity.com/paper/2311.14864/) (2023)
- [Ollivier-Ricci Curvature for Hypergraphs: A Unified Framework](https://mlsanity.com/paper/2210.12048/) (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)
- [Deep Learning as Ricci Flow](https://mlsanity.com/paper/2404.14265/) (2024)
- [Geometric Machine Learning on EEG Signals](https://mlsanity.com/paper/2502.05334/) (2025)
- [Efficient Curvature-aware Graph Network](https://mlsanity.com/paper/2511.01443/) (2025)
- [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)
- [Geometric Flow enhanced Graph Coarsening](https://mlsanity.com/paper/2609.14962/) (2026)
- [GFLC: Graph-based Fairness-aware Label Correction for Fair Classification](https://mlsanity.com/paper/2506.15620/) (2025)
- [A Remedy for Over-Squashing in Graph Learning via Forman-Ricci Curvature based Graph-to-Hypergraph Structural Lifting](https://mlsanity.com/paper/2508.11390/) (2025)
- [A roadmap for curvature-based geometric data analysis and learning](https://mlsanity.com/paper/2510.22599/) (2025)
- [Sandpile Economics: Theory, Identification, and Evidence](https://mlsanity.com/paper/2604.13890/) (2026)
- [Periodic Topological Deep Learning for Polymer Design and Discovery](https://mlsanity.com/paper/2605.26833/) (2026)
- [Look Before You Lift: Visual and Quantitative Diagnostics for Topological Deep Learning](https://mlsanity.com/paper/2608.15388/) (2026)
- [CurvFlow-DTA: dual-graph discrete Ricci curvature flow for drug--target affinity prediction](https://mlsanity.com/paper/2609.22862/) (2026)

## 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.