  We study hypergraph visualization via its topological simplification. We
explore both vertex simplification and hyperedge simplification of hypergraphs
using tools from topological data analysis. In particular, we transform a
hypergraph to its graph representations known as the line graph and clique
expansion. A topological simplification of such a graph representation induces
a simplification of the hypergraph. In simplifying a hypergraph, we allow
vertices to be combined if they belong to almost the same set of hyperedges,
and hyperedges to be merged if they share almost the same set of vertices. Our
proposed approaches are general, mathematically justifiable, and they put
vertex simplification and hyperedge simplification in a unifying framework.
