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This paper presents a new model to study the reliability of communication networks in which link failures are statistically dependent. The approach tries to identify and model explicitly the events that cause communication link failures. No conditional probabilities are needed, and so two major difficulties inherent to them, namely, an exponential number of conditional probabilities to deal with and a consistency requirement to satisfy, are avoided. For reliability computations, some existing algorithms for finding network reliability can be used with minor modifications and no significant increase in computational complexity.