Brand effect versus competitiveness in hypernetworks

A few of evolving models in hypernetworks have been proposed based on uniform growth. In order to better depict the growth mechanism and competitive aspect of real hypernetworks, we propose a model in term of the non-uniform growth. Besides hyperdegrees, the other two important factors are introduced to underlie preferential attachment. One dimension is the brand effect and the other is the competitiveness. Our model can accurately describe the evolution of real hypernetworks. The paper analyzes the model and calculates the stationary average hyperdegree distribution of the hypernetwork by using Poisson process theory and a continuous technique. We also address the limit in which this model has a condensation. The theoretical analyses agree with numerical simulations. Our model is universal, in that the standard preferential attachment, the fitness model in complex networks and scale-free model in hypernetworks can all be seen as degenerate cases of the model.