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.

翻译：本文提出了一种新颖的多关系网络表示方法，该方法紧凑且能实现高效的网络分析。多关系网络能够捕捉复杂的数据关系，在生物医学、金融、社交等领域具有多种应用。随着该网络处理的数据量日益庞大，寻找高效表示和分析此类网络的方法变得至关重要。本文引入了素数邻接矩阵（PAMs）的概念，通过利用素数来表示网络中的关系。基于算术基本定理，该表示能用单一邻接矩阵对完整的多关系图实现无损、紧凑的存储。此外，这种表示还能快速计算多跳邻接矩阵，这对各种下游任务非常有用。我们通过多种简单及复杂的网络分析任务，展示了所提方法的优势。