Wikipedia mining of hidden links between political leaders

We describe a new method of reduced Google matrix which allows to establish direct andhidden links between a subset of nodes of a large directed network. This approach usesparallels with quantum scattering theory, developed for processes in nuclear andmesoscopic physics and quantum chaos. The method is applied to the Wikipedia networks indifferent language editions analyzing several groups of political leaders of USA, UK,Germany, France, Russia and G20. We demonstrate that this approach allows to recoverreliably direct and hidden links among political leaders. We argue that the reduced Googlematrix method can form the mathematical basis for studies in social and political sciencesanalyzing Leader-Members eXchange (LMX).