Topological Simplifications of Hypergraphs

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 into 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 and mathematically justifiable, and put vertex simplification and hyperedge simplification in a unifying framework.

Automated summary

We explore hypergraph visualization through topological simplification using tools from topological data analysis. By transforming a hypergraph into its graph representations, we can simplify the hypergraph based on the simplification of the graph representation. Our proposed approaches allow for the combination of vertices belonging to similar sets of hyperedges and the merging of hyperedges sharing similar sets of vertices. These approaches are general, mathematically justifiable, and provide a unified framework for both vertex and hyperedge simplification.