Efficient multi-relational network representation using primes

Multi-relational networks play an important role in today's world and are utilized to capture complex relationships between the data. Their applications span many domains such as biomedical, financial, social, etc., and because of their increasing usability, it becomes crucial to find efficient ways to deal with the added complexity of multiple layers. In this work, we propose a novel approach to represent these complex networks using a single aggregated adjacency matrix, by utilizing primes as surrogates for the relations. Due to the fundamental theorem of arithmetic, this allows for a lossless, compact representation of the whole multi-relational graph, using a single adjacency matrix. Moreover, this representation enables the fast computation of multi-hop adjacency matrices, that can be useful for a variety of downstream tasks. We present simple and complex tasks in which this representation can be useful and showcase its efficiency and performance. Finally, we also provide insights on the advantages and the open challenges that still need to be addressed and motivate future work.