The Reliability of a Class of Two-Layer Networks with Unreliable Edges

It is well known that networks are dynamic graphs, and the topology of a network can be described by a graph. Thus, the reliability of a network under edge failure is defined as the probability that its corresponding topological graph remains connected under the condition that the edges fail with independent probabilities. In this paper, the reliability of a class of two-layer networks is considered, where each layer is a complete graph and the edges joining different layers are one-to-one correspondingly connected. The edge failure probability is uniform in the same layer and distinct in different layers and between layers. The recursive formula for the reliability (reliability polynomial) of the two-layer network is obtained, and the corresponding algorithm is also given. Furthermore, the reliability of several networks is computed by Python, which verifies the correctness of the algorithm.