  While network science has become an indispensable tool for studying complex
systems, the conventional use of pairwise links often shows limitations in
describing high-order interactions properly. Hypergraphs, where each edge can
connect more than two nodes, have thus become a new paradigm in network
science. Yet, we are still in lack of models linking network growth and
hyperedge expansion, both of which are commonly observable in the real world.
Here, we propose a generative hypergraph model by employing the preferential
attachment mechanism in both nodes and hyperedge formation. The model can
produce bi-heterogeneity, exhibiting scale-free distributions in both
hyperdegree and hyperedge size. We provide a mean-field treatment that gives
the expression of the two scaling exponents, which agree with the numerical
simulations. Our model may help to understand the networked systems showing
both types of heterogeneity and facilitate the study of complex dynamics
thereon.
