Real-world complex networks are usually being modeled as graphs. The concept of graphs assumes that the relations within the network are binary (for instance, between pairs of nodes); however, this is not always true for many real-life scenarios, such as peer-to-peer communication schemes, paper co-authorship, or social network interactions. For such scenarios, it is often the case that the underlying network is better and more naturally modeled by hypergraphs. A hypergraph is a generalization of a graph in which a single (hyper)edge can connect any number of vertices. Hypergraphs allow modelers to have a complete representation of multi-relational (many-to-many) networks; hence, they are extremely suitable for analyzing and discovering more subtle dependencies in such data structures. Working with hypergraphs requires new software libraries that make it possible to perform operations on them, from basic algorithms (such as searching or traversing the network) to computing significant hypergraph measures, to including more challenging algorithms (such as community detection). In this paper, we present a new software library, SimpleHypergraphs.jl, written in the Julia language and designed for high-performance computing on hypergraphs and propose two new algorithms for analyzing their properties: s-betweenness and modified label propagation. We also present various approaches for hypergraph visualization integrated into our tool. In order to demonstrate how to exploit the library in practice, we discuss two case studies based on the 2019 Yelp Challenge dataset and the collaboration network built upon the Game of Thrones TV series. The results are promising and they confirm the ability of hypergraphs to provide more insight than standard graph-based approaches.

中文翻译：

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使用 SimpleHypergraphs.jl 通过超图分析、探索和可视化复杂网络

现实世界的复杂网络通常被建模为图。图的概念假设网络内的关系是二元的（例如，节点对之间）；然而，对于许多现实生活场景而言，情况并非总是如此，例如点对点通信方案、论文合着或社交网络交互。对于此类场景，通常情况下底层网络通过超图更好、更自然地建模。超图是图的泛化，其中单个（超）边可以连接任意数量的顶点。超图使建模者可以完整地表示多关系（多对多）网络；因此，它们非常适合分析和发现此类数据结构中更微妙的依赖关系。使用超图需要新的软件库来对它们执行操作，从基本算法（例如搜索或遍历网络）到计算重要的超图度量，再到包括更具挑战性的算法（例如社区检测）。在本文中，我们提出了一个新的软件库 SimpleHypergraphs.jl，它是用 Julia 语言编写的，专为超图的高性能计算而设计，并提出了两种用于分析其属性的新算法：s-betweenness 和修正标签传播。我们还介绍了集成到我们工具中的各种超图可视化方法。为了演示如何在实践中利用该库，我们讨论了两个基于 2019 年 Yelp 挑战数据集和基于权力的游戏电视剧的协作网络的案例研究。结果是有希望的，它们证实了超图比标准的基于图的方法提供更多洞察力的能力。