  The random graph model has recently been extended to a random preferential
attachment graph model, in order to enable the study of general asymptotic
properties in network types that are better represented by the preferential
attachment evolution model than by the ordinary (uniform) evolution lodel.
Analogously, this paper extends the random {\em hypergraph} model to a random
{\em preferential attachment hypergraph} model. We then analyze the degree
distribution of random preferential attachment hypergraphs and show that they
possess heavy tail degree distribution properties similar to those of random
preferential attachment graphs. However, our results show that the exponent of
the degree distribution is sensitive to whether one considers the structure as
a hypergraph or as a graph.
