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A global reliability measure called 'network reliability' (NR) is the probability that a call entering a probabilistic network at any originating node can reach every other node. This concept is quite useful in multiterminal networks such as computer networks and parallel processors, etc. A simple technique is presented for evaluating NR in symbolic form. The method is based on cutsets and is computationally advantageous with respect to the spanning tree approach. It requires fewer cutsets to be manipulated in the process of determining the NR expression. The number of cutsets is approximately half that of spanning trees even for a small sized computer communication network and there is a further improvement in the situation for larger networks.