Hypergraphs: Concepts, Applications and Analysis

Complex networks are a mainstream tool for understanding and modeling complex systems. Hypergraphs have been extensively studied in many fields due to its strong ability to represent higher-order group relationships among objects. In this paper, we give a comprehensive overview of hypergraphs. We first introduce the background of hypergraph and some basic terminologies. Then, we review hypergraph generation methods and representation methods combined with some downstream tasks, such as vertex classification, hyperedge prediction. Finally, we look into topological properties of some typical hypergraphs, including vertex degree distribution, hyperedge degree distribution, connectivity, etc. The paper concludes with a discussion of application and promising future directions of hypergraphs.