From Primes to Paths: Enabling Fast Multi-Relational Graph Analysis

TL;DR

This paper introduces an enhanced prime-based framework for efficiently representing and analyzing large multi-relational graphs, enabling fast computation of multi-hop relationships and versatile feature extraction for various analytics tasks.

Contribution

It extends the Prime Adjacency Matrices framework with a lossless multi-hop computation algorithm and proposes the Bag of Paths representation for improved graph analysis.

Findings

BoP models match or outperform neural models in accuracy

Framework significantly improves speed of multi-relational graph analysis

Method offers better interpretability for graph analytics

Abstract

Multi-relational networks capture intricate relationships in data and have diverse applications across fields such as biomedical, financial, and social sciences. As networks derived from increasingly large datasets become more common, identifying efficient methods for representing and analyzing them becomes crucial. This work extends the Prime Adjacency Matrices (PAMs) framework, which employs prime numbers to represent distinct relations within a network uniquely. This enables a compact representation of a complete multi-relational graph using a single adjacency matrix, which, in turn, facilitates quick computation of multi-hop adjacency matrices. In this work, we enhance the framework by introducing a lossless algorithm for calculating the multi-hop matrices and propose the Bag of Paths (BoP) representation, a versatile feature extraction methodology for various graph analytics tasks, at the node, edge, and graph level. We demonstrate the efficiency of the framework across various tasks and datasets, showing that simple BoP-based models perform comparably to or better than commonly used neural models while offering improved speed and interpretability.