Evolving hypernetwork model

Complex hypernetworks are ubiquitous in real-life systems. While a substantial body of previous research has only focused on the applications of hypernetworks, relatively little work has investigated the evolving models of hypernetworks. Considering the formations of many real world networks, we propose two evolving mechanisms of the hyperedge growth and the hyperedge preferential attachment, then construct an evolving hypernetwork model. We introduce some basic topological quantities, such as a variety of degree distributions, clustering coefficients as well as average path length. We numerically investigate these quantities in the limit of large hypernetwork size and find that our hypernetwork model shares similar qualitative features with the majority of complex networks that have been previously studied, such as the scale-free property of the degree distribution and a high degree of clustering, as well as the small-world property. It is expected that our attempt in the hypernetwork model can bring the upsurge in the study of the hypernetwork model in further.