# On the expressive power of linear algebra on graphs

## TL;DR

This paper explores how linear algebra operations in the MATLANG language affect the ability to distinguish between graphs, providing a comprehensive analysis of its expressive power in graph query languages.

## Contribution

It characterizes the expressive power of linear algebra-based graph query languages, specifically MATLANG, in differentiating graphs.

## Key findings

- Linear algebra operations influence graph distinguishability.
- Complete characterization of MATLANG's expressive power.
- Implications for graph query language design.

## Abstract

Most graph query languages are rooted in logic. By contrast, in this paper we consider graph query languages rooted in linear algebra. More specifically, we consider MATLANG, a matrix query language recently introduced, in which some basic linear algebra functionality is supported. We investigate the problem of characterising equivalence of graphs, represented by their adjacency matrices, for various fragments of MATLANG. A complete picture is painted of the impact of the linear algebra operations in MATLANG on their ability to distinguish graphs.