학술논문
Topological Simplifications of Hypergraphs
Document Type
Periodical
Author
Source
IEEE Transactions on Visualization and Computer Graphics IEEE Trans. Visual. Comput. Graphics Visualization and Computer Graphics, IEEE Transactions on. 29(7):3209-3225 Jul, 2023
Subject
Language
ISSN
1077-2626
1941-0506
2160-9306
1941-0506
2160-9306
Abstract
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.