For an undirected stochastic network G, the 2-terminal reliability of G, R(G) is the probability that the specific two nodes (called as terminal nodes) are connected in G. A typical network reliability problem is to compute R(G). It has been shown that the computation problem of R(G) is NP-hard. So, any algorithm to compute R(G) has a running time which is exponential in the size of G. If by some means, the problem size, G, is reduced, it can result in immense savings. The means to reduce the size of the problem are the reliability preserving reductions and graph decompositions. The paper introduces a net set of reliability preserving reductions; the K4 (complete graph of 4-nodes) chain reductions. The total number of the different K4 types in R(G), is 6. The paper presents the reduction formula for each K4 type. But in computing R(G), it is possible that homeomorphic graphs from K4 occur. The paper divides the homeomorphic graphs from K4 into 3 types. It develops the reliability preserving reductions for 2 types, and shows that the remaining one is divided into two subgraphs which can be reduced by K4-chain reductions and polygon-to-chain reductions. [In Korean.]
