Exploring the dynamic growth mechanism of social networks using evolutionary hypergraph

An evolutionary hypernetwork model is proposed to describe the non-uniform evolution of social networks, in which nodes represent individuals while hyperedges represent relationships among individuals. The number of nodes in a hyperedge is a random integer. And the evolving process includes the addition of new nodes, linking of old nodes, and rewiring of links. By using Poisson process theory and the continuous method, we proved that the stationary average hyperdegree distribution follows the shifted power law (SPL). The theoretical analysis agree with the numerical simulations. Our model is universal, the fitness model in complex networks and scale-free model in hypernetworks can all be regarded as degradation cases of the model.