Multiterminal measures for network reliability and resilience

Network reliability, specifically k-terminal reliability, gives the probability that k specified nodes in a network are connected. Multi-terminal network resilience measures the average k-terminal reliability over all node sets of size k. This is the expectation that a randomly chosen set of k nodes is connected. One may also ask for the probability that any k nodes are connected. This leads to three ways to require a set of k nodes be connected: the nodes are provided as input to the problem (as in reliability), they are randomly chosen (as in resilience), or they can be any k nodes. Certain problems may require a set constructed by some combination of the three. We introduce new measures to cover these possibilities, and reduce all measures to two general expressions that capture them. These expressions permit the consideration of decades of work on reliability to solve them. Additionally, we introduce six component-based network measures, and demonstrate how they can be solved alongside reliability and resilience. The component based measures admit even more variability in problem definition. In the end, we have thirteen distinct measures, and solve them simultaneously. An algorithm and example results are provided.