Network reliability is one of the most important concepts in this modern era.Reliability characteristics, component significance measures, such as the Birnbaum importance measure, critical weleda skin food 75ml best price importance measure, the risk growth factor and average risk growth factor, and network reliability stability of the communication network system have been discussed in this paper to identify the critical components in the network, and also to quantify the impact of component failures.The study also proposes an efficient algorithm to compute the reliability indices of the network.The authors explore how the universal generating function can work to solve the problems related to the network using the exponentially distributed failure rate.To illustrate the proposed algorithm, here a numerical example has been taken.