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 runngin 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. We introduce a net set of reliability preserving reductions : the $K^{4}$ (complete graph of 4-nodes)-chain reductions. The total number of the different $K^{4}$ types in R(G), is 6. We present the reduction formula for each $K^{4}$ type. But in computing R(G), it is possible that homeomorphic graphs from $K^{4}$ occur. We devide the homemorphic graphs from $K^{4}$ into 3 types. We develop the reliability preserving reductions for s types, and show that the remaining one is divided into two subgraphs which can be reduced by $K^{4}$-chain reductions 7 polygon-to-chain reductions.