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Algebraic connectivity of an even uniform hypergraph

Author

Listed:
  • Shenglong Hu

    (The Hong Kong Polytechnic University)

  • Liqun Qi

    (The Hong Kong Polytechnic University)

Abstract

We generalize Laplacian matrices for graphs to Laplacian tensors for even uniform hypergraphs and set some foundations for the spectral hypergraph theory based upon Laplacian tensors. Especially, algebraic connectivity of an even uniform hypergraph based on Z-eigenvalues of the corresponding Laplacian tensor is introduced and its connections with edge connectivity and vertex connectivity are discussed.

Suggested Citation

  • Shenglong Hu & Liqun Qi, 2012. "Algebraic connectivity of an even uniform hypergraph," Journal of Combinatorial Optimization, Springer, vol. 24(4), pages 564-579, November.
    • Handle: RePEc:spr:jcomop:v:24:y:2012:i:4:d:10.1007_s10878-011-9407-1
    DOI: 10.1007/s10878-011-9407-1
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    Citations

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    Cited by:

    1. Shenglong Hu & Guoyin Li & Liqun Qi, 2016. "A Tensor Analogy of Yuan’s Theorem of the Alternative and Polynomial Optimization with Sign structure," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 446-474, February.
    2. Tian Liu & Chaoyi Wang & Ke Xu, 2015. "Large hypertree width for sparse random hypergraphs," Journal of Combinatorial Optimization, Springer, vol. 29(3), pages 531-540, April.
    3. Yisheng Song & Liqun Qi, 2015. "Properties of Some Classes of Structured Tensors," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 854-873, June.
    4. Qin Ni & Liqun Qi, 2015. "A quadratically convergent algorithm for finding the largest eigenvalue of a nonnegative homogeneous polynomial map," Journal of Global Optimization, Springer, vol. 61(4), pages 627-641, April.
    5. Meilan Zeng, 2021. "Tensor Z-eigenvalue complementarity problems," Computational Optimization and Applications, Springer, vol. 78(2), pages 559-573, March.
    6. Yuning Yang & Qingzhi Yang & Liqun Qi, 2014. "Properties and methods for finding the best rank-one approximation to higher-order tensors," Computational Optimization and Applications, Springer, vol. 58(1), pages 105-132, May.

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