The network reliability analysis based on Binary Decision Diagram (BDD) consists of three steps: edge ordering, BDD generation and BDD evaluation. The BDD generation process using edge expansion technique should recursively decompose the network and construct the edge expansion subnet in a top-down manner. There is large number of useless or redundant subnets generated in this decomposition, which causes numerous inefficient computations. Thus, it is extremely important to optimize the edge expansion technique. In this paper, the notation of useless edge expansion and redundant edge expansion is formally defined.