The migration phenomena of human populations is a well-known issue in social, economic, and sociophysics studies. A common effect of non-forced migration is the fact that important cities gain population over the first years and become overpopulated. Therefore, neighboring cities receive all migration and end up geographically merging with the important ones. Several studies have addressed the social and economic reasons behind this effect, but a mathematical model has been lacking. Here, we construct a migration complex network with population and migration dynamics and carry out an indirect influences analysis of those dynamics. Using this, we can measure the effect of migration on population growth across cities. The results show that the analysis of the indirect influences reveals interesting facts about the mentioned migration effect and address the measurement of this. Given this, urban planners and city administrations can make use of these findings to improve their migratory research.