Emergence of scaling in evolving hypernetworks

Abstract

Based on hypernetwork theory, we construct a new evolving hypernetwork, which incorporating new nodes and new hyperedges growing, old nodes and old hyperedges disappearing, or rewiring of hyperedges from some nodes to anothers. Besides the growth of hyperedges by adding new nodes, it is also possible that a new hyperedge can be constructed between old nodes in hypernetworks. This evolving hypernetwork model with both increasing and decreasing is more realistic than the evolving model only with increasing. By employing Poisson process theory and continuous method, we obtain stationary average hyperdegree distribution and degree distribution of the hypernetwork. Analytical result shows that the evolving hypernetwork following a generalized power-law distribution, has a phenomenon of “the rich get richer” and a wide range of universality. The theoretical prediction of the stationary average hyperdegree distribution and degree distribution are in good agreement with the real numerical simulation results.