Efficient multi-relational network representation using primes

TL;DR

This paper introduces Prime Adjacency Matrices (PAMs), a novel, compact, and efficient method for representing and analyzing large multi-relational networks using prime numbers, enabling fast computations and lossless data representation.

Contribution

The paper presents a new prime-based matrix representation for multi-relational networks that improves efficiency and enables lossless, compact storage and rapid multi-hop analysis.

Findings

PAMs provide a lossless, compact network representation.

Prime-based approach enables fast multi-hop adjacency computations.

Demonstrated effectiveness on various network analysis tasks.

Abstract

In this work, we propose a novel representation of complex multi-relational networks, which is compact and allows very efficient network analysis. Multi-relational networks capture complex data relationships and have a variety of applications, ranging from biomedical to financial, social, etc. As they get to be used with ever larger quantities of data, it is crucial to find efficient ways to represent and analyse such networks. This paper introduces the concept of Prime Adjacency Matrices (PAMs), which utilize prime numbers, to represent the relations of the network. Due to the fundamental theorem of arithmetic, this allows for a lossless, compact representation of a complete multi-relational graph, using a single adjacency matrix. Moreover, this representation enables the fast computation of multi-hop adjacency matrices, which can be useful for a variety of downstream tasks. We illustrate the benefits of using the proposed approach through various simple and complex network analysis tasks.