  Hypergraphs have emerged as a powerful modeling framework to represent
systems with multiway interactions, that is systems where interactions may
involve an arbitrary number of agents. Here we explore the properties of
real-world hypergraphs, focusing on the encapsulation of their hyperedges,
which is the extent that smaller hyperedges are subsets of larger hyperedges.
Building on the concept of line graphs, our measures quantify the relations
existing between hyperedges of different sizes and, as a byproduct, the
compatibility of the data with a simplicial complex representation -- whose
encapsulation would be maximum. We then turn to the impact of the observed
structural patterns on diffusive dynamics, focusing on a variant of threshold
models, called encapsulation dynamics, and demonstrate that non-random patterns
can accelerate the spreading in the system.
