  A family of models of growing hypergraphs with preferential rules of new
linking is introduced and studied. The model hypergraphs evolve via the
hyperedge-based growth as well as the node-based one, thus generalizing the
preferential-attachment models of scale-free networks. We obtain the degree
distribution and hyperedge size distribution for various combinations of node-
and hyperedge-based growth modes. We find that the introduction of
hyperedge-based growth can give rise to power-law degree distribution $P(k)\sim
k^{-\gamma}$ even without node-wise preferential-attachments. The hyperedge
size distribution $P(s)$ can take diverse functional forms, ranging from
exponential to power-law to a nonstationary one, depending on the specific
hyperedge-based growth rule. Numerical simulations support the mean-field
theoretical analytical predictions.
