Topological Simplifications of Hypergraphs

Zhou, Youjia; Rathore, Archit; Purvine, Emilie; Wang, Bei

doi:10.1109/tvcg.2022.3153895

Title: Topological Simplifications of Hypergraphs

Journal Article · 24 February 2022 · IEEE Transactions on Visualization and Computer Graphics

DOI: https://doi.org/10.1109/tvcg.2022.3153895 · OSTI ID:2369460

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Univ. of Utah, Salt Lake City, UT (United States). Scientific Computing & Imaging (SCI) Institute; University of Utah
Univ. of Utah, Salt Lake City, UT (United States). Scientific Computing & Imaging (SCI) Institute
Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Here 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.

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Research Organization:: Univ. of Utah, Salt Lake City, UT (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: SC0021015

OSTI ID:: 2369460

Journal Information:: IEEE Transactions on Visualization and Computer Graphics, Journal Name: IEEE Transactions on Visualization and Computer Graphics Journal Issue: 7 Vol. 29; ISSN 1077-2626

Publisher:: IEEECopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
graph simplification
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Title: Topological Simplifications of Hypergraphs

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