# Random Projections of Sparse Adjacency Matrices

arXiv: https://arxiv.org/abs/2309.01360 · HTML: https://mlsanity.com/paper/2309.01360/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 20 references that are in the map.
- First posted on arXiv 4 Sep 2023.

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

- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Holographic Embeddings of Knowledge Graphs](https://mlsanity.com/paper/1510.04935/) (2015)
- [A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part II: Applications, Cognitive Models, and Challenges](https://mlsanity.com/paper/2112.15424/) (2021)
- [Fast and Accurate Network Embeddings via Very Sparse Random Projection](https://mlsanity.com/paper/1908.11512/) (2019)
- [GraphHD: Efficient graph classification using hyperdimensional computing](https://mlsanity.com/paper/2205.07826/) (2022)
- [Graph Embeddings via Tensor Products and Approximately Orthonormal Codes](https://mlsanity.com/paper/2208.10917/) (2022)

## Abstract (arXiv)

We analyze a random projection method for adjacency matrices, studying its utility in representing sparse graphs. We show that these random projections retain the functionality of their underlying adjacency matrices while having extra properties that make them attractive as dynamic graph representations. In particular, they can represent graphs of different sizes and vertex sets in the same space, allowing for the aggregation and manipulation of graphs in a unified manner. We also provide results on how the size of the projections need to scale in order to preserve accurate graph operations, showing that the size of the projections can scale linearly with the number of vertices while accurately retaining first-order graph information. We conclude by characterizing our random projection as a distance-preserving map of adjacency matrices analogous to the usual Johnson-Lindenstrauss map.