All known methods for calculating the connection probability for two vertices of an unreliable network take time exponential in the size of the network. A method is presented for reducing network size by transforming three‐terminal subnetworks into Y‐shaped networks, thus reducing terminal degrees and possibly creating series combinations which can be reduced to a single edge. Previously defined transformations were approximate, restricted to triangles, and required perfect terminals. The transformations given here are exact, apply to any three‐terminal subnetwork with perfect terminals, and permit the inclusion of unreliable terminals which are incident to one external edge. In addition, transformations for reducing certain networks with directed edges, and transformations for eliminating positive failure correlations are discussed.
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Rosenthal et al. (1977) studied this question.