# Models for information propagation on graphs

arXiv: https://arxiv.org/abs/2201.07577 · HTML: https://mlsanity.com/paper/2201.07577/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 54 references that are in the map.
- First posted on arXiv 19 Jan 2022.

## Builds on (most cited first, 6 of 6)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Continuum limit of total variation on point clouds](https://mlsanity.com/paper/1403.6355/) (2014)
- [Large Data and Zero Noise Limits of Graph-Based Semi-Supervised Learning Algorithms](https://mlsanity.com/paper/1805.09450/) (2018)
- [A comparison among various notions of viscosity solutions for Hamilton-Jacobi equations on networks](https://mlsanity.com/paper/1301.0194/) (2013)
- [On anisotropic diffusion equations for label propagation](https://mlsanity.com/paper/2007.12516/) (2020)

## Built on by (most cited first, 1 of 1)

- [Momentum-based minimization of the Ginzburg-Landau functional on Euclidean spaces and graphs](https://mlsanity.com/paper/2501.00389/) (2024)

## Abstract (arXiv)

We propose and unify classes of different models for information propagation over graphs. In a first class, propagation is modelled as a wave which emanates from a set of known nodes at an initial time, to all other unknown nodes at later times with an ordering determined by the arrival time of the information wave front. A second class of models is based on the notion of a travel time along paths between nodes. The time of information propagation from an initial known set of nodes to a node is defined as the minimum of a generalised travel time over subsets of all admissible paths. A final class is given by imposing a local equation of an eikonal form at each unknown node, with boundary conditions at the known nodes. The solution value of the local equation at a node is coupled to those of neighbouring nodes with lower values. We provide precise formulations of the model classes and prove equivalences between them. Finally we apply the front propagation models on graphs to semi-supervised learning via label propagation and information propagation on trust networks.