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The validation and evaluation of network reliability are significant issues in the planning, design, and control of systems. The minimal path (MP, an edge set) set is one of the main tools used in measuring network reliability. A new node-based concept to find all MPs is proposed by simply searching all of the ordered node subsets with a time complexity <inline-formula> <tex-math notation="LaTeX">$O$ </tex-math></inline-formula>(<inline-formula> <tex-math notation="LaTeX">$ne^{n}$ </tex-math></inline-formula>), where <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> is the number of nodes. The proposed concept is implemented in a newly proposed node-based MP algorithm using depth-first search (DFS). Because <inline-formula> <tex-math notation="LaTeX">$O(m)=O(n^{2})$ </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> is the number of edges, the proposed node-based MP algorithm is theoretically more efficient than conventional edge-based algorithms, which all use time complexity O(<inline-formula> <tex-math notation="LaTeX">$n 2^{m}$ </tex-math></inline-formula>) to search for all MPs. Finally, a series of numerical experiments is implemented to test the performance of the proposed algorithm.

A New Node-Based Concept for Solving the Minimal Path Problem in General Networks