Abstract
In this study, a new method is presented to evaluate the system reliability of a flow network using spanning trees with flow. The proposed method includes two main tasks: 1. Identifying the spanning trees without flow by representing each network link as a binary string of length N (N is the number of nodes) and performing all possible combinations between N − 1 links, and 2. Using the generated spanning trees without flow to find the spanning trees with flow by calculating the total flow carried by the links. The proposed method is tested on different examples from the literature to illustrate its efficiency in generating the spanning trees with flow and calculating the system reliability.
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