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Topological Simplifications of Hypergraphs
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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.
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Cited by 1 Pith paper
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Stability of Hypergraph Invariants and Transformations
Introduces a Gromov-Hausdorff style metric on hypernetworks and proves Lipschitz stability for graphifications, invariant lower bounds, and optimal-transport cost limits.
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