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The network structure entropy has served as one of the index measuring network heterogeneity, but it gives no considerations to the impact of isolated nodes on the network structure. In addition, the all-terminal reliability is zero and is unable to compare it between disconnected networks. Therefore, the concept of network connectivity entropy is suggested to remove the current bottleneck and helps facilitate new index in terms of network connectivity reliability. This study fully proves the rules as follows: when the edges of network are diminishing, the newly-established network connectivity reliability will remain unchanged or become weaker; conversely, when the edges of network are increasing, the network connectivity reliability will remain unchanged or become stronger. Thus, the proposed index of network connectivity reliability is proved reasonable. Furthermore, the impaired metro network of Nanjing city is exemplified to demonstrate the validity and practicability of network connectivity reliability. The result shows that this new approach is in good position to compute network connectivity reliability quickly and effectively, and also to compare it between different networks.