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How different cultures evaluate a person? Is an important person in one culture is also important in the other culture? We address these questions via ranking of multilingual Wikipedia articles. With three ranking algorithms based on network structure of Wikipedia, we assign ranking to all articles in 9 multilingual editions of Wikipedia and investigate general ranking structure of PageRank, CheiRank and 2DRank. In particular, we focus on articles related to persons, identify top 30 persons for each rank among different editions and analyze distinctions of their distributions over activity fields such as politics, art, science, religion, sport for each edition. We find that local heroes are dominant but also global heroes exist and create an effective network representing entanglement of cultures. The Google matrix analysis of network of cultures shows signs of the Zipf law distribution. This approach allows to examine diversity and shared characteristics of knowledge organization between cultures. The developed computational, data driven approach highlights cultural interconnections in a new perspective.

How different cultures evaluate a person? Is an important person in one culture is also important in the other culture? We address these questions via ranking of multilingual Wikipedia articles. With three ranking algorithms based on network structure of Wikipedia, we assign ranking to all articles in 9 multilingual editions of Wikipedia and investigate general ranking structure of PageRank, CheiRank and 2DRank. In particular, we focus on articles related to persons, identify top 30 persons for each rank among different editions and analyze distinctions of their distributions over activity fields such as politics, art, science, religion, sport for each edition. We find that local heroes are dominant but also global heroes exist and create an effective network representing entanglement of cultures. The Google matrix analysis of network of cultures shows signs of the Zipf law distribution. This approach allows to examine diversity and shared characteristics of knowledge organization between cultures. The developed computational, data driven approach highlights cultural interconnections in a new perspective.

We describe a new method of reduced Google matrix which allows to establish direct and hidden links between a subset of nodes of a large directed network. This approach uses parallels with quantum scattering theory, developed for processes in nuclear and mesoscopic physics and quantum chaos. The method is applied to the Wikipedia networks in different language editions analyzing several groups of political 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

We develop the Google matrix analysis of the multiproduct world trade network obtained from the UN COMTRADE database in recent years. The comparison is done between this new approach and the usual Import-Export description of this world trade network. The Google matrix analysis takes into account the multiplicity of trade transactions thus highlighting in a better way the world influence of specific countries and products. It shows that after Brexit, the European Union of 27 countries has the leading position in the world trade network ranking, being ahead of USA and China. Our approach determines also a sensitivity of trade country balance to specific products showing the dominant role of machinery and mineral fuels in multiproduct exchanges. It also underlines the growing influence of Asian countries.

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).

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 that preserves 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 the set of 27 European Union 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).

International audience ; 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 that preserves 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 the set of 27 European Union 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).

International audience ; 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 that preserves 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 the set of 27 European Union 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).

International audience ; 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 that preserves 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 the set of 27 European Union 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).

International audience ; 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 that preserves 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 the set of 27 European Union 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).

Geopolitics focuses on political power in relation to geographic space. Interactions among world countries have been widely studied at various scales, observing economic exchanges, world history or international politics among others. This work exhibits the potential of Wikipedia mining for such studies. Indeed, Wikipedia stores valuable fine-grained dependencies among countries by linking webpages together for diverse types of interactions (not only related to economical, political or historical facts). We mine herein the Wikipedia networks of several language editions using the recently proposed method of reduced Google matrix analysis. This approach allows to establish direct and hidden links between a subset of nodes that belong to a much larger directed network. Our study concentrates on 40 major countries chosen worldwide. Our aim is to offer a multicultural perspective on their interactions by comparing networks extracted from five different Wikipedia language editions, emphasizing English, Russian and Arabic ones. We demonstrate that this approach allows to recover meaningful direct and hidden links among the 40 countries of interest.

International audience ; La géopolitique étudie les relations entre des puissances politiques par rapport à leur situation géographique. Les interactions entre les pays du monde ont été largement étudiées à différentes échelles, en analysant par exemple des informations issues des échanges économiques, des faits historiques ou l'évolution des réglementations internationales. Cette étude propose d'exploiter les connaissances encyclopédiques de Wikipédia pour extraire les interactions entre un ensemble de pays choisis. Wikipédia enregistre ses connaissances sous la forme d'une réseau de pages Internet reliées entre elles par des hyperliens. La structure de ce réseau est porteuse d'informations très précieuses car elle représente les inter-dépendances entre les sujets étudiés. Wikipedia est édité en plusieurs langues, la plus volumineuse étant la langue anglaise. L'édition anglaise comporte plusieurs millions de pages et une étude minutieuse des interactions entre certaines pages passe par la définition d'outils mathématiques efficaces et qui capturent les inter-dépendances qui existent dans un nombre limité de pages. Dans cet article, nous utilisons la méthode d'analyse de la matrice réduite de Google récemment proposée pour extraire les interactions entre 40 pays au niveau mondial. Cette étude est menée pour 5 éditions de pages Wikipédia. Cette approche permet d'extraire du réseau, en plus des liens directs, des relations indirectes (ou cachées) entre les 40 pays sélectionnés. Ces relations indirectes sont particulièrement intéressantes car elles ne sont pas influencées par la mesure de PageRank et proposent ainsi un axe d'étude supplémentaire pertinent.

International audience ; Geopolitics focuses on political power in relation to geographic space. Interactions among world countries have been widely studied at various scales, observing economic exchanges, world history or international politics among others. This work exhibits the potential of Wikipedia mining for such studies. Indeed, Wikipedia stores valuable fine-grained dependencies among countries by linking webpages together for diverse types of interactions (not only related to economical, political or historical facts). We mine herein the Wikipedia networks of several language editions using the recently proposed method of reduced Google matrix analysis. This approach allows to establish direct and hidden links between a subset of nodes that belong to a much larger directed network. Our study concentrates on 40 major countries chosen worldwide. Our aim is to offer a multicultural perspective on their interactions by comparing networks extracted from five different Wikipedia language editions, emphasizing English, Russian and Arabic ones. We demonstrate that this approach allows to recover meaningful direct and hidden links among the 40 countries of interest.

International audience ; Geopolitics focuses on political power in relation to geographic space. Interactions among world countries have been widely studied at various scales, observing economic exchanges, world history or international politics among others. This work exhibits the potential of Wikipedia mining for such studies. Indeed, Wikipedia stores valuable fine-grained dependencies among countries by linking webpages together for diverse types of interactions (not only related to economical, political or historical facts). We mine herein the Wikipedia networks of several language editions using the recently proposed method of reduced Google matrix analysis. This approach allows to establish direct and hidden links between a subset of nodes that belong to a much larger directed network. Our study concentrates on 40 major countries chosen worldwide. Our aim is to offer a multicultural perspective on their interactions by comparing networks extracted from five different Wikipedia language editions, emphasizing English, Russian and Arabic ones. We demonstrate that this approach allows to recover meaningful direct and hidden links among the 40 countries of interest.

International audience ; La géopolitique étudie les relations entre des puissances politiques par rapport à leur situation géographique. Les interactions entre les pays du monde ont été largement étudiées à différentes échelles, en analysant par exemple des informations issues des échanges économiques, des faits historiques ou l'évolution des réglementations internationales. Cette étude propose d'exploiter les connaissances encyclopédiques de Wikipédia pour extraire les interactions entre un ensemble de pays choisis. Wikipédia enregistre ses connaissances sous la forme d'une réseau de pages Internet reliées entre elles par des hyperliens. La structure de ce réseau est porteuse d'informations très précieuses car elle représente les inter-dépendances entre les sujets étudiés. Wikipedia est édité en plusieurs langues, la plus volumineuse étant la langue anglaise. L'édition anglaise comporte plusieurs millions de pages et une étude minutieuse des interactions entre certaines pages passe par la définition d'outils mathématiques efficaces et qui capturent les inter-dépendances qui existent dans un nombre limité de pages. Dans cet article, nous utilisons la méthode d'analyse de la matrice réduite de Google récemment proposée pour extraire les interactions entre 40 pays au niveau mondial. Cette étude est menée pour 5 éditions de pages Wikipédia. Cette approche permet d'extraire du réseau, en plus des liens directs, des relations indirectes (ou cachées) entre les 40 pays sélectionnés. Ces relations indirectes sont particulièrement intéressantes car elles ne sont pas influencées par la mesure de PageRank et proposent ainsi un axe d'étude supplémentaire pertinent.