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    Area of Science:

    • Computer Science
    • Data Visualization
    • Network Analysis

    Background:

    • Graphs are essential for representing relationships but are difficult to analyze due to abstractness.
    • Node-link diagrams with force-directed layouts are common but suffer from clutter and overlap.
    • Existing methods struggle to effectively reveal the global structure of complex graphs.

    Purpose of the Study:

    • To leverage persistent homology features for enhanced interactive manipulation of force-directed graph layouts.
    • To address the challenges of clutter and overlap in graph visualizations.
    • To improve the analysis and understanding of complex graph structures.

    Main Methods:

    • Efficiently extracting 0-dimensional persistent homology features from undirected graphs (weighted and unweighted).
    • Introducing an interactive persistence barcode for manipulating force-directed layouts.
    • Allowing users to add/remove forces derived from persistent homology features to refine the layout.

    Main Results:

    • Demonstrated the utility of persistent homology features in improving force-directed graph layouts.
    • Successfully reduced clutter and overlap in graph visualizations.
    • Enabled interactive selection of features that optimize layout clarity.

    Conclusions:

    • Persistent homology features offer a powerful approach for interactive graph visualization.
    • The proposed method enhances the analysis of complex relationships by improving layout clarity.
    • This technique is applicable to both synthetic and real-world graph datasets.