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Real-world complex networks are usually being modeled as graphs. The conceptof graphs assumes that the relations within the network are binary (forinstance, between pairs of nodes); however, this is not always true for manyreal-life scenarios, such as peer-to-peer communication schemes, paperco-authorship, or social network interactions. For such scenarios, it is oftenthe case that the underlying network is better and more naturally modeled byhypergraphs. A hypergraph is a generalization of a graph in which a single(hyper)edge can connect any number of vertices. Hypergraphs allow modelers tohave a complete representation of multi-relational (many-to-many) networks;hence, they are extremely suitable for analyzing and discovering more subtledependencies in such data structures.  Working with hypergraphs requires new software libraries that make itpossible to perform operations on them, from basic algorithms (such assearching or traversing the network) to computing significant hypergraphmeasures, to including more challenging algorithms (such as communitydetection). In this paper, we present a new software library,SimpleHypergraphs.jl, written in the Julia language and designed forhigh-performance computing on hypergraphs and propose two new algorithms foranalyzing their properties: s-betweenness and modified label propagation.  We also present various approaches for hypergraph visualization integratedinto 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 thecollaboration network built upon the Game of Thrones TV series. The results arepromising and they confirm the ability of hypergraphs to provide more insightthan standard graph-based approaches.

Analyzing, Exploring, and Visualizing Complex Networks via Hypergraphs using SimpleHypergraphs.jl