We describe a new method of reduced Google matrixwhich allows to establish direct and hidden links betweena subset of nodes of a large directed network. This approach uses parallels with quantum scattering theory, developed for processes in nuclear and mesoscopic physicsand quantum chaos. The method is applied to the Wikipedia networksin different language editionsanalyzing several groups ofpolitical leaders of USA, UK, Germany, France, Russia and G20.We demonstrate that this approach allows to recover reliably direct and hidden links among political leaders.We argue that the reduced Google matrix method can form the mathematical basis for studies in social and political sciences analyzing Leader-Members eXchange (LMX).