  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.
