The problems of risk management are considered from different points of view. Most often, they are investigated as part of organizational management. The results obtained within this approach are widely used, but their validity is debated. On the other hand, risk management can be considered as a system of mathematical models. In this form, it is discussed in the mechanism design section of control theory. The results obtained with this approach have rigorous substantiation, but also require a large number of conditions to be met, which is often hard to achieve in practice. Therefore, the convergence of these approaches is an important practical problem. The proposed paper attempts to put a formal solution to building a risk-minimizing topology of a computer network into the risk management framework. When choosing the optimal set of countermeasures to protect a computer network, the possibility of modifying the network topology is usually not considered. At the same time, topology rebuilding is a natural process for some classes of networks (in particular, wireless mesh networks). This study considers the problem of designing the topology of computer networks that minimizes risk. The proposed solution is based on the results obtained previously in research on the influence of the structure of complex systems on their integral risk. The article considers a particular case of the exact solution of the problem for a peer-to-peer distributed network of the ’bus’ topology. In addition, it proposes an algorithm to design a risk-minimizing topology in attack scenarios of a simple chain structure.