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All-terminal hypernetwork reliability synthesis of a kind of semi-deterministic hypergraphs

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  • Ke Zhang

    (School of Information Engineering, Huzhou University, Huzhou 313000, Zhejiang, P. R. China†Zhejiang Province Key Laboratory of Smart Management & Application of Modern Agricultural Resources, Huzhou University, Huzhou 313000, Zhejiang, P. R. China)

  • Haixing Zhao

    (��School of Computer, Qinghai Normal University, Xining 810800, P. R. China)

  • Zhonglin Ye

    (��School of Computer, Qinghai Normal University, Xining 810800, P. R. China)

  • Wenjun Hu

    (School of Information Engineering, Huzhou University, Huzhou 313000, Zhejiang, P. R. China†Zhejiang Province Key Laboratory of Smart Management & Application of Modern Agricultural Resources, Huzhou University, Huzhou 313000, Zhejiang, P. R. China)

  • Minmin Miao

    (School of Information Engineering, Huzhou University, Huzhou 313000, Zhejiang, P. R. China†Zhejiang Province Key Laboratory of Smart Management & Application of Modern Agricultural Resources, Huzhou University, Huzhou 313000, Zhejiang, P. R. China)

Abstract

Network reliability plays an important role in analysis, synthesis and detection of real-world networks. In this paper, we first propose the concept of hypernetwork reliability, which generalizes the concept of network reliability. The model for hypernetwork reliability studies consists of a hypergraph with perfect reliable vertices and equal and independent hyperedge failure probability 1−p. The measure of reliability is defined as the probability that a hypergraph is connected. Let H be an r-uniform hypergraph with the number of vertices n and the number of hyperedges m, where every hyperedge connects r vertices. We confirm the possibility of the existence of a fixed hypergraph that is optimal or least for all hyperedges same survival possible p. It is simple to verify that such hypergraph exists if m=[n−1r−1]. For a kind of 2-regular 3-uniform hypergraphs, we calculate the upper and lower bounds on the all-terminal reliability, and describe the class of hypergraphs that reach the boundary.

Suggested Citation

  • Ke Zhang & Haixing Zhao & Zhonglin Ye & Wenjun Hu & Minmin Miao, 2021. "All-terminal hypernetwork reliability synthesis of a kind of semi-deterministic hypergraphs," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 32(11), pages 1-13, November.
    • Handle: RePEc:wsi:ijmpcx:v:32:y:2021:i:11:n:s0129183121501539
    DOI: 10.1142/S0129183121501539
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