# Efficient multi-relational network representation using primes

arXiv: https://arxiv.org/abs/2209.06575 · HTML: https://mlsanity.com/paper/2209.06575/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 64 references that are in the map.
- First posted on arXiv 14 Sep 2022.

## Builds on (most cited first, 23 of 23)

- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Convolutional 2D Knowledge Graph Embeddings](https://mlsanity.com/paper/1707.01476/) (2017)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [A Survey on Knowledge Graphs: Representation, Acquisition and Applications](https://mlsanity.com/paper/2002.00388/) (2020)
- [DeepPath: A Reinforcement Learning Method for Knowledge Graph Reasoning](https://mlsanity.com/paper/1707.06690/) (2017)
- [DRUM: End-To-End Differentiable Rule Mining On Knowledge Graphs](https://mlsanity.com/paper/1911.00055/) (2019)
- [A Survey on Graph Kernels](https://mlsanity.com/paper/1903.11835/) (2019)
- [A Survey on The Expressive Power of Graph Neural Networks](https://mlsanity.com/paper/2003.04078/) (2020)
- [CoDEx: A Comprehensive Knowledge Graph Completion Benchmark](https://mlsanity.com/paper/2009.07810/) (2020)
- [Multilayer Networks](https://mlsanity.com/paper/1309.7233/) (2013)
- [Graph Kernels: State-of-the-Art and Future Challenges](https://mlsanity.com/paper/2011.03854/) (2020)
- [Relational Message Passing for Knowledge Graph Completion](https://mlsanity.com/paper/2002.06757/) (2020)
- [GraKeL: A Graph Kernel Library in Python](https://mlsanity.com/paper/1806.02193/) (2018)
- [The structure and dynamics of multilayer networks](https://mlsanity.com/paper/1407.0742/) (2014)
- [On Valid Optimal Assignment Kernels and Applications to Graph Classification](https://mlsanity.com/paper/1606.01141/) (2016)
- [Reinforced Anytime Bottom Up Rule Learning for Knowledge Graph Completion](https://mlsanity.com/paper/2004.04412/) (2020)
- [Explainable Biomedical Recommendations via Reinforcement Learning Reasoning on Knowledge Graphs](https://mlsanity.com/paper/2111.10625/) (2021)
- [Multilayer motif analysis of brain networks](https://mlsanity.com/paper/1606.09115/) (2016)

## Built on by (most cited first, 1 of 1)

- [Analysing Biomedical Knowledge Graphs using Prime Adjacency Matrices](https://mlsanity.com/paper/2305.10467/) (2023)

## Abstract (arXiv)

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.