  The largest eigenvalue of the matrix describing a network's contact structure
is often important in predicting the behavior of dynamical processes. We extend
this notion to hypergraphs and motivate the importance of an analogous
eigenvalue, the expansion eigenvalue, for hypergraph dynamical processes. Using
a mean-field approach, we derive an approximation to the expansion eigenvalue
in terms of the degree sequence for uncorrelated hypergraphs. We introduce a
generative model for hypergraphs that includes degree assortativity, and use a
perturbation approach to derive an approximation to the expansion eigenvalue
for assortative hypergraphs. We define the dynamical assortativity, a
dynamically sensible definition of assortativity for uniform hypergraphs, and
describe how reducing the dynamical assortativity of hypergraphs through
preferential rewiring can extinguish epidemics. We validate our results with
both synthetic and empirical datasets.
