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Topological Simplifications of Hypergraphs.

Youjia Zhou, Archit Rathore, Emilie Purvine

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    Summary
    This summary is machine-generated.

    We introduce a new method for simplifying complex hypergraphs using topological data analysis. This approach unifies vertex and hyperedge simplification for better hypergraph visualization.

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    Area of Science:

    • Mathematics
    • Computer Science
    • Data Analysis

    Background:

    • Hypergraphs are complex structures requiring effective visualization techniques.
    • Topological data analysis offers tools for simplifying complex data.

    Purpose of the Study:

    • To develop a unified framework for hypergraph simplification.
    • To enhance hypergraph visualization through topological methods.

    Main Methods:

    • Transforming hypergraphs into graph representations (line graph, clique expansion).
    • Applying topological simplification to these graph representations.
    • Defining criteria for vertex and hyperedge merging based on shared elements.

    Main Results:

    • A general and mathematically justifiable approach to hypergraph simplification.
    • Inducing hypergraph simplification from graph representation simplification.
    • Unifying vertex and hyperedge simplification within a single framework.

    Conclusions:

    • The proposed methods provide a robust way to simplify hypergraphs.
    • This simplification aids in the visualization and understanding of complex hypergraph structures.
    • The unified framework offers a versatile tool for hypergraph analysis.