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

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 − 1 r − 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. [ABSTRACT FROM AUTHOR]