A computer-based method for determining a probability that no path exists from a starting node to a target node within a network of nodes and directional links between pairs of nodes. The nodes and directional links form paths of a reliability graph and the method is performed using a computer coupled to a database. The method includes selecting a set of paths between the starting node and the target node that have been determined to be reliable, calculating a reliability of the union of the selected path sets, setting an upper bound for unreliability of the set of all paths, selecting a set of minimal cutsets from all cutsets that lie between the starting node and the target node, calculating the probability of the union of the minimal cutsets, and setting a lower bound for the unreliability of the set of all cutsets.