  In the field of complex networks, hypergraph models have so far received
significantly less attention than graphs. However, many real-life networks
feature multiary relations (co-authorship, protein reactions) may therefore be
modeled way better by hypergraphs. Also, a recent study by Broido and Clauset
suggests that a power-law degree distribution is not as ubiquitous in the
natural systems as it was thought so far. They experimentally confirm that a
majority of networks (56% of around 1000 networks that undergone the test)
favor a power-law with an exponential cutoff over other distributions. We
address the two above observations by introducing a preferential attachment
hypergraph model which allows for vertex deactivations. The phenomenon of
vertex deactivations is rare in existing theoretical models and omnipresent in
real-life scenarios (social network accounts which are not maintained forever,
collaboration networks in which people retire, technological networks in which
devices break down). We prove that the degree distribution of the proposed
model follows a power-law with an exponential cutoff. We also check
experimentally that a Scopus collaboration network has the same characteristic.
We believe that our model will predict well the behavior of systems from a
variety of domains.
