Topological Simplifications of Hypergraphs
This work addresses visualization challenges for hypergraphs, which are common in complex data analysis, but it is incremental as it builds on existing topological data analysis tools.
The paper tackles the problem of hypergraph visualization by proposing topological simplifications that combine vertices or merge hyperedges based on shared membership, using graph representations like line graphs and clique expansions. The result is a general, mathematically justifiable framework that unifies vertex and hyperedge simplification.
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.