Equivalence of a Nonoriented Line and a Pair of Oriented Lines in a Network

Equivalence of a nonoriented line and a pair of oriented lines (in the reliability-sene) is examined for four types of networks. Type I has one input node and one output node; type II has one input node and two or more output nodes; type II' has two or more input nodes and one input node; type III has two or more input nodes and two or more output nodes. For types I, II, II', every non-oriented line is equivalent to a pair of oriented lines with equal line-reliability. The result corresponds to the presumption that almost every one has taken for granted. However equivalence of such a replacement is not true for a type III network.