The work is dedicated to routing effectiveness increasing for heterogeneous networks with dynamic variables heterogeneities. Distribution of information flows in heterogeneous networks depends on the structural heterogeneities that can dynamically change because of incorrect settings, overload, migration of virtual machines and other emergencies. These factors considerably influence the success routing, notably in large-scale networks that provide a wide range of services. We propose algorithm based on Ricci flows that allow transition from one space to another with preservation properties of conformal mapping network structure to improve the availability of nodes. A wide range of foreign scientists considers the Ricci flow in Euclidean space. This work represents the routing algorithm based on Ricci flow in hyperbolic space, which allows smoothing the verge heterogeneities. Consequently, laying circuits can be designed so that its metric is compatible with the Euclidean metric by applying Poincare disk that allows us to depict the network topology on a single canonical disk with round holes and convert nodes to form of virtual coordinates. We perform the network simulation based on comparison of routing algorithms using hyperbolic and traditional Ricci flows and GeoRou (Geometric routing), which represents the best results of geometric algorithms. The algorithm converge faster than others do, since it allows reducing the probability of errors in the curvature and ensuring effective delivery in the presence of complex dynamic structural variable heterogeneities. We also perform the simulation of distance vector routing based on real coordinates using virtual coordinates. With real coordinates, successful routing was observed in 78.66% cases, based on virtual coordinates - in 92.5% cases. Therefore, routing algorithm based on hyperbolic Ricci flow improves effectiveness compared to other routing algorithms by a slight increase in the respective Euclidean metric.