Three methods of analysis of a communication network in which the communication links are assigned finite probabilities of failure are presented. The methods are applied to the computation of the terminal reliabilities for all pairs of nodes. The terminal reliability between a pair of nodes is defined as the probability that there exists at least one path with these nodes as termini. The first method requires the examination of the set of all subgraphs of the graph that represents the network. The second method examines the set of all subgraphs that are not connected and the third is based on the Monte Carlo method.
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Wing et al. (1964) studied this question.