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    Area of Science:

    • Network analysis
    • Graph theory
    • Machine learning

    Background:

    • Graph isomorphism is vital for network analysis but struggles with high-order relationships.
    • Traditional hypergraph methods are memory-intensive and inaccurate.
    • Existing graph algorithms do not fully capture complex hypergraph structures.

    Purpose of the Study:

    • To develop an efficient and accurate hypergraph isomorphism algorithm.
    • To extend the Weisfeiler-Lehman (WL) test to hypergraphs.
    • To introduce a hypergraph WL kernel framework for improved network analysis.

    Main Methods:

    • Introduced a hypergraph Weisfeiler-Lehman (WL) test algorithm.
    • Developed a hypergraph WL kernel framework with two variants: Hypergraph WL Subtree Kernel and Hypergraph WL Hyperedge Kernel.
    • Conducted experiments on seven graph and 12 hypergraph classification datasets.

    Main Results:

    • The Hypergraph WL Subtree Kernel achieved comparable performance to the classical Graph WL Subtree Kernel on graph datasets.
    • Proposed methods showed significant improvements over traditional kernel-based methods on hypergraph datasets.
    • The new methods demonstrated over 80x faster runtime on complex hypergraph structures.

    Conclusions:

    • The proposed hypergraph WL test and kernel framework effectively capture high-order structural information.
    • These methods offer a significant speed advantage for analyzing complex hypergraphs.
    • The framework shows great potential for real-world applications in network analysis and related fields.