# What relations are reliably embeddable in Euclidean space?

## TL;DR

This paper investigates the conditions under which various types of relations, modeled as directed graphs, can be embedded into Euclidean space, providing characterizations, dimensionality bounds, and precision requirements.

## Contribution

It offers new characterizations and bounds for embedding relations as directed graphs into Euclidean space, advancing understanding in knowledge graph embeddings.

## Key findings

- Characterizations of embeddable relations
- Bounds on minimal embedding dimensionality
- Requirements for embedding precision

## Abstract

We consider the problem of embedding a relation, represented as a directed graph, into Euclidean space. For three types of embeddings motivated by the recent literature on knowledge graphs, we obtain characterizations of which relations they are able to capture, as well as bounds on the minimal dimensionality and precision needed.