Emergence of scaling in hypernetworks

Abstract

This paper proposes a unified model for hypernetworks and complex networks, and studies the evolution mechanisms of scale-free hypernetworks and the topological properties of the hypernetwork. We have analyzed the proposed model and calculated the stationary average hyperdegree distribution of the hypernetwork by using a Poisson process theory and a continuous technique. The analytical result agrees well with the simulation. It is shown that the hyperdegree distribution of the dynamic model follows a scale-free law. This paper not only integrates the hypernetwork model, in which one new node forms an edge with some old nodes, and the hypernetwork model, in which some new nodes form an edge with one old node, but also integrates the scale-free model in complex networks.