# Community detection and percolation of information in a geometric setting

arXiv: https://arxiv.org/abs/2006.15574 · HTML: https://mlsanity.com/paper/2006.15574/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jun 2020.

## Built on by (most cited first, 5 of 5)

- [Spectral clustering in the Gaussian mixture block model](https://mlsanity.com/paper/2305.00979/) (2023)
- [Detection-Recovery Gap for Planted Dense Cycles](https://mlsanity.com/paper/2302.06737/) (2023)
- [Information-Theoretic Thresholds for Planted Dense Cycles](https://mlsanity.com/paper/2402.00305/) (2024)
- [Impossibility of latent inner product recovery via rate distortion](https://mlsanity.com/paper/2407.11932/) (2024)
- [Recovery of latent inner products from an anisotropic Gaussian random geometric graph](https://mlsanity.com/paper/2607.23723/) (2026)

## Abstract (arXiv)

We make the first steps towards generalizing the theory of stochastic block models, in the sparse regime, towards a model where the discrete community structure is replaced by an underlying geometry. We consider a geometric random graph over a homogeneous metric space where the probability of two vertices to be connected is an arbitrary function of the distance. We give sufficient conditions under which the locations can be recovered (up to an isomorphism of the space) in the sparse regime. Moreover, we define a geometric counterpart of the model of flow of information on trees, due to Mossel and Peres, in which one considers a branching random walk on a sphere and the goal is to recover the location of the root based on the locations of leaves. We give some sufficient conditions for percolation and for non-percolation of information in this model.