The evaluation of the terminal reliability of a given computer communication network is an NP-hard problem. Hence, the problem of assigning reliabilities to links of a fixed computer communication network topology to optimize the system reliability is also NP-hard. We develop a heuristic method to assign links to a given topology so that the system reliability of the network is near optimal. Our method provides a way to assign reliability measures to the links of a network to increase overall reliability. The method is based on the principle that the most reliable link should be assigned to the most vulnerable edge. The method computes an importance order for the edges of the network and uses the order to assign link reliabilities. If there are less than six links in a network, it can be shown that our heuristic method, with the aid of theorem 2 gives the optimal assignment.