Nowadays the role of the computer networks became much more important, hence the goal is to increase the survivability of these networks. It is not allowed that the points of a network become unreachable caused by the failure of an element of the network. To increase this survivabilty, the networks may contain redundance, typically two-node connected. In existing networks it is not allowed to add links to the network optionally, only the given additional links can be used to reach a two-node connected physical network topology. After discussing writings in similar subject, we introduce our solution of the problem, an ILP (Integer Linear Program) to reach a two-connected topology. We use this solution on more examples and compare with existing heuristic algorithims. The results show that the results given by the ILP are better than the heuristic results, but if there is no solution to the problem and the network topology can not be two-connected, the heurstic algorithms give partly solutions while the ILP does not. The time and space demand of the ILP is much bigger than other the methods but it gives an optimal solution.