The Gremlin Graph Traversal Machine and Language

TL;DR

This paper introduces Gremlin, a graph traversal machine and language that provides a flexible, mathematically grounded framework for graph querying across various computing systems, supporting both imperative and declarative styles.

Contribution

It offers a formal mathematical description of Gremlin, detailing its automaton and functional properties, and introduces the concept of a Universal Gremlin Machine for broad applicability.

Findings

Supports imperative and declarative querying

Enables host language agnosticism and extensible optimization

Allows hybrid depth- and breadth-first evaluation

Abstract

Gremlin is a graph traversal machine and language designed, developed, and distributed by the Apache TinkerPop project. Gremlin, as a graph traversal machine, is composed of three interacting components: a graph $G$, a traversal $\Psi$, and a set of traversers $T$. The traversers move about the graph according to the instructions specified in the traversal, where the result of the computation is the ultimate locations of all halted traversers. A Gremlin machine can be executed over any supporting graph computing system such as an OLTP graph database and/or an OLAP graph processor. Gremlin, as a graph traversal language, is a functional language implemented in the user's native programming language and is used to define the $\Psi$ of a Gremlin machine. This article provides a mathematical description of Gremlin and details its automaton and functional properties. These properties enable Gremlin to naturally support imperative and declarative querying, host language agnosticism, user-defined domain specific languages, an extensible compiler/optimizer, single- and multi-machine execution models, hybrid depth- and breadth-first evaluation, as well as the existence of a Universal Gremlin Machine and its respective entailments.