Preferential attachment hypergraph with vertex deactivation

In the area of complex networks so far hypergraph models have received significantly less attention than the graphs. However, many real-life networks feature multiary relations (co-authorship, protein reactions) thus may be modeled way better by hypergraphs. Also, 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 majority of networks (56% of around 1000 social, biological, technological, transportation, and information networks that undergone the test) favor a power-law with an exponential cutoff over other distributions. We address two above observations by introducing a preferential attachment hypergraph model which allows for a vertex deactivation. The phenomenon of a vertex deactivation is rare in existing theoretical models and omnipresent in real-life scenarios (think of social network accounts which are not maintained forever, collaboration networks in which people eventually retire or technological networks in which devices may break down). We prove that the degree distribution of a 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 the systems from variety of domains.