  Among various real-life emerging applications, wireless sensor networks,
Internet of Things, smart grids, social networks, communication networks,
transportation networks, and computer grid systems, etc., the binary-state
network is the fundamental network structure and model with either working or
failed binary components. The network reliability is an effective index for
assessing the network function and performance. Hence, the network reliability
between two specific nodes has been widely adopted and more efficient network
reliability algorithm is always needed. To have complete information for a
better decision, all-pairs network reliability thus arises correspondingly. In
this study, a new algorithm called the all-pairs BAT is proposed by revising
the binary-addition-tree algorithm (BAT) and the layered-search algorithm
(LSA). From both the theoretical analysis and the practical experiments
conducted on 20 benchmark problems, the proposed all-pairs BAT is more
efficient than these algorithms by trying all combinations of any pairs of
nodes.
