The authors introduce a method of calculating the coefficients of the reliability polynomial of a network when the probabilities of link failure are independent and identical, having a value 1-p. This method involves calculation of the simple paths in the network, forming all combinations of their unions, classifying the unions, and counting and appropriately summing up the numbers of members of these classes. The method is then extended to the calculation of the expected number of operational paths in a network, defined as the connectivity polynomial. The relation of the reliability polynomial to the probabilistic capacity of a network is shown.
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