We model migration in the framework of network analysis. It allows to present all countries involved in the international migration as a graph, where nodes are countries and edges correspond to migration flows between them. The networks are constructed for each annual dataset on international migration flows. Our work is aimed to detect the countries with the highest level of importance in the international migration process. To consider all the relevant issues, we constructed our own index that accounts for the distinctive features of the problem. We apply Indices of Short-Range (SRIC) and Long-Range Interactions Centralities (LRIC). SRIC examines only first-long-range connections in the network and LRIC accounts for s-long-range routes where the parameter s can be managed. The network of migration between countries is constructed based on the annual data (from 1970 to 2013) of international migration flows provided by the United Nations Organization. The process of international migration is studied in the dynamics.