  Network scientists have shown that there is great value in studying pairwise
interactions between components in a system. From a linear algebra point of
view, this involves defining and evaluating functions of the associated
adjacency matrix. Recent work indicates that there are further benefits from
accounting directly for higher order interactions, notably through a hypergraph
representation where an edge may involve multiple nodes. Building on these
ideas, we motivate, define and analyze a class of spectral centrality measures
for identifying important nodes and hyperedges in hypergraphs, generalizing
existing network science concepts. By exploiting the latest developments in
nonlinear Perron-Frobenius theory, we show how the resulting constrained
nonlinear eigenvalue problems have unique solutions that can be computed
efficiently via a nonlinear power method iteration. We illustrate the measures
on realistic data sets.
