  To depict the complex relationship among nodes and the evolving process of a
complex system, a Bose-Einstein hypernetwork is proposed in this paper. Based
on two basic evolutionary mechanisms, growth and preference jumping, the
distribution of hyperedge cardinalities is studied. The Poisson process theory
is used to describe the arrival process of new node batches. And, by using the
Poisson process theory and a continuity technique, the hypernetwork is analyzed
and the characteristic equation of hyperedge cardinalities is obtained.
Additionally, an analytical expression for the stationary average hyperedge
cardinality distribution is derived by employing the characteristic equation,
from which Bose-Einstein condensation in the hypernetwork is obtained. The
theoretical analyses in this paper agree with the conducted numerical
simulations. This is the first study on the hyperedge cardinality in
hypernetworks, where Bose-Einstein condensation can be regarded as a special
case of hypernetworks. Moreover, a condensation degree is also discussed with
which Bose-Einstein condensation can be classified.
