This paper proposes a new and flexible approach for network reliability computation. The method is based on Propositional Directed Acyclic Graphs (PDAGs), a general graph-based language for the representation of Boolean functions. We introduce an algorithm which creates in polynomial time a generic structure function representation for reliability networks. In contrast to many existing methods, our method does not rely on the enumeration of all mincuts or minpaths, which may be infeasible in practice. From this representation, we can then derive the structure functions for different network reliability problems. Based on the compact PDAG representation, we can both compute the exact reliability or estimate the reliability by means of an approximation method.