  Interactions between countries originate from diverse aspects such as
geographic proximity, trade, socio-cultural habits, language, religions, etc.
Geopolitics studies the influence of a country's geographic space on its
political power and its relationships with other countries.
  This work reveals the potential of Wikipedia mining for geopolitical study.
Actually, Wikipedia offers solid knowledge and strong correlations among
countries by linking web pages together for different types of information
(e.g. economical, historical, political, and many others). The major finding of
this paper is to show that meaningful results on the influence of country ties
can be extracted from the hyperlinked structure of Wikipedia. We leverage a
novel stochastic matrix representation of Markov chains of complex directed
networks called the reduced Google matrix theory. For a selected small size set
of nodes, the reduced Google matrix concentrates direct and indirect links of
the million-node sized Wikipedia network into a small Perron-Frobenius matrix
keeping the PageRank probabilities of the global Wikipedia network. We perform
a novel sensitivity analysis that leverages this reduced Google matrix to
characterize the influence of relationships between countries from the global
network. We apply this analysis to two chosen sets of countries (i.e. the set
of 27 European Union countries and a set of 40 top worldwide countries). We
show that with our sensitivity analysis we can exhibit easily very meaningful
information on geopolitics from five different Wikipedia editions (English,
Arabic, Russian, French and German).
