A Path Algebra for Multi-Relational Graphs

TL;DR

This paper introduces a comprehensive algebraic framework for traversing multi-relational graphs, combining relational algebra, path algebra, and tensor algebra to support advanced graph traversal and analysis.

Contribution

It develops a novel algebraic foundation integrating multiple algebraic structures for multi-relational graph traversal, enabling formal reasoning and engine construction.

Findings

Provides a unified algebraic framework for multi-relational graph traversal

Establishes monoid, automata, and formal language foundations

Facilitates the development of graph traversal engines

Abstract

A multi-relational graph maintains two or more relations over a vertex set. This article defines an algebra for traversing such graphs that is based on an $n$-ary relational algebra, a concatenative single-relational path algebra, and a tensor-based multi-relational algebra. The presented algebra provides a monoid, automata, and formal language theoretic foundation for the construction of a multi-relational graph traversal engine.