超网络的全终端可靠性分析

Analysis for all-terminal reliability of hypernetworks

网络的可靠性是复杂网络研究的一个重要领域,能有效刻画某些复杂系统的超网络属于复杂网络的研究范畴。基于超网络的拓扑结构——超图,提出了超网络在边失效下的全终端可靠度的定义,并给出了计算可靠度的两种基本方法,即状态枚举法和因式分解法,依据因式分解法对一些具有特殊结构的超网络进行化简。作为超网络可靠性的应用,研究了连通生成子网络的数目;在与普通复杂网络的对比中可以得知,超网络的可靠性研究不能用其转换后的普通复杂网络可靠性作替代研究,该研究是对超网络可靠性研究的初步探索,有着广阔的研究空间和应用前景。

The network reliability is an important field of the complex network research.Hypernetworks which can describe some complex systems effectively belong to the scope of the complex network research.Based on the topological structures of hypernetworks:hypergraphs,this paper presented the definition of the all-terminal reliability of hypernetworks with edge failure,and proposed two basic methods for calculating the reliability,namely state enumeration and the factorization method.According to the factorization method,some hypernetworks with special structures could be simplified.As an application of the hypernetwork reliability,this paper studied the number of connected spanning sub-networks.Compared with the ordinary complex networks,the result concludes that the reliability of hypernetworks can’t be replaced by the reliability of ordinary complex networks that transform from corresponding hypernetworks.This research is a preliminary exploration of the hypernetwork reliability,which has broad research spaces and application prospects.