  The use of graph centrality measures applied to biological networks, such as
protein interaction networks, underpins much research into identifying key
players within biological processes. This approach however is restricted to
dyadic interactions and it is well-known that in many instances interactions
are polyadic. In this study we illustrate the merit of using hypergraph
centrality applied to a hypernetwork as an alternative. Specifically, we review
and propose an extension to a recently introduced node and edge nonlinear
hypergraph centrality model which provides mutually dependent node and edge
centralities. A Saccharomyces Cerevisiae protein complex hypernetwork is used
as an example application with nodes representing proteins and hyperedges
representing protein complexes. The resulting rankings of the nodes and edges
are considered to see if they provide insight into the essentiality of the
proteins and complexes. We find that certain variations of the model predict
essentiality more accurately and that the degree-based variation illustrates
that the centrality-lethality rule extends to a hypergraph setting. In
particular, through exploitation of the models flexibility, we identify small
sets of proteins densely populated with essential proteins.
