# Geometric Sampling of Networks

arXiv: https://arxiv.org/abs/2010.15221 · HTML: https://mlsanity.com/paper/2010.15221/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Oct 2020.

## Built on by (most cited first, 3 of 3)

- [Rewiring Networks for Graph Neural Network Training Using Discrete Geometry](https://mlsanity.com/paper/2207.08026/) (2022)
- [Curved Markov Chain Monte Carlo for Network Learning](https://mlsanity.com/paper/2110.03413/) (2021)
- [Ironing the Graphs: Toward a Correct Geometric Analysis of Large-Scale Graphs](https://mlsanity.com/paper/2407.21609/) (2024)

## Abstract (arXiv)

Motivated by the methods and results of manifold sampling based on Ricci curvature, we propose a similar approach for networks. To this end we make appeal to three types of discrete curvature, namely the graph Forman-, full Forman- and Haantjes-Ricci curvatures for edge-based and node-based sampling. We present the results of experiments on real life networks, as well as for square grids arising in Image Processing. Moreover, we consider fitting Ricci flows and we employ them for the detection of networks' backbone. We also develop embedding kernels related to the Forman-Ricci curvatures and employ them for the detection of the coarse structure of networks, as well as for network visualization with applications to SVM. The relation between the Ricci curvature of the original manifold and that of a Ricci curvature driven discretization is also studied.