Study of the variable growth hypernetworks influence on the scaling law

Abstract

This paper presents the influence of two kinds of variable growth hypernetworks on the scaling law of hypernetworks. Our model can be degenerated to the original evolving model. On one hand, we establish the variable growth of hyperedges evolving hypernetworks model and obtain the stationary average hyperdegree distribution of the model by employing the Poisson process theory and the continuous method. The theoretical analyses in this paper agree with the conducted numerical simulations. The results show that the transient average hyperdegree distribution of the hypernetwork follows the scale-free law. However, the stationary average hyperdegree distribution does not, which indicates that the number of hyperedges at each time step affects the scaling law of hypernetworks. On the other hand, we establish the new nodes variable growth hypernetworks model and obtain analytical solutions of the transient average hyperdegree distribution. We simulate to compare the different node growth rate effect on the hyperdegree distribution characteristics. The results show that the growth rate does not affect the scaling law properties of the hypernetworks. Only when λ=1 can we obtain analytical solutions of stationary average hyperdegree distribution of the hypernetwork which is not scale-free law.