# Formalising opencypher Graph Queries in Relational Algebra

## TL;DR

This paper provides a formal foundation for openCypher graph queries by defining a relational algebra extension and an algorithm for systematic query compilation, aiding standardization and interoperability.

## Contribution

It introduces relational graph algebra and maps openCypher constructs to this algebra, enabling formal analysis and systematic compilation of graph queries.

## Key findings

- Formal specification of openCypher in relational algebra
- Algorithm for systematic compilation of openCypher queries
- Supports standardization and interoperability of graph query languages

## Abstract

Graph database systems are increasingly adapted for storing and processing heterogeneous network-like datasets. However, due to the novelty of such systems, no standard data model or query language has yet emerged. Consequently, migrating datasets or applications even between related technologies often requires a large amount of manual work or ad-hoc solutions, thus subjecting the users to the possibility of vendor lock-in. To avoid this threat, vendors are working on supporting existing standard languages (e.g. SQL) or creating standardised languages. In this paper, we present a formal specification for openCypher, a high-level declarative graph query language with an ongoing standardisation effort. We introduce relational graph algebra, which extends relational operators by adapting graph-specific operators and define a mapping from core openCypher constructs to this algebra. We propose an algorithm that allows systematic compilation of openCypher queries.