Time evolution of Wikipedia network ranking

We study the time evolution of ranking and spectral properties of the Google matrix of English Wikipedia hyperlink network during years 2003 - 2011. The statistical properties of ranking of Wikipedia articles via PageRank and CheiRank probabilities, as well as the matrix spectrum, are shown to be stabilized for 2007 - 2011. A special emphasis is done on ranking of Wikipedia personalities and universities. We show that PageRank selection is dominated by politicians while 2DRank, which combines PageRank and CheiRank, gives more accent on personalities of arts. The Wikipedia PageRank of universities recovers 80 percents of top universities of Shanghai ranking during the considered time period.Comment: 10 pages, 11 figures. Accepted for publication in EPJ

Google matrix analysis of directed networks

In past ten years, modern societies developed enormous communication and social networks. Their classification and information retrieval processing become a formidable task for the society. Due to the rapid growth of World Wide Web, social and communication networks, new mathematical methods have been invented to characterize the properties of these networks on a more detailed and precise level. Various search engines are essentially using such methods. It is highly important to develop new tools to classify and rank enormous amount of network information in a way adapted to internal network structures and characteristics. This review describes the Google matrix analysis of directed complex networks demonstrating its efficiency on various examples including World Wide Web, Wikipedia, software architecture, world trade, social and citation networks, brain neural networks, DNA sequences and Ulam networks. The analytical and numerical matrix methods used in this analysis originate from the fields of Markov chains, quantum chaos and Random Matrix theory.Comment: 56 pages, 58 figures. Missed link added in network example of Fig3

Google matrix of the world trade network

Using the United Nations Commodity Trade Statistics Database [http://comtrade.un.org/db/] we construct the Google matrix of the world trade network and analyze its properties for various trade commodities for all countries and all available years from 1962 to 2009. The trade flows on this network are classified with the help of PageRank and CheiRank algorithms developed for the World Wide Web and other large scale directed networks. For the world trade this ranking treats all countries on equal democratic grounds independent of country richness. Still this method puts at the top a group of industrially developed countries for trade in {\it all commodities}. Our study establishes the existence of two solid state like domains of rich and poor countries which remain stable in time, while the majority of countries are shown to be in a gas like phase with strong rank fluctuations. A simple random matrix model provides a good description of statistical distribution of countries in two-dimensional rank plane. The comparison with usual ranking by export and import highlights new features and possibilities of our approach.Comment: 14 pages, 13 figures. More detailed data and high definition figures are available on the website: http://www.quantware.ups-tlse.fr/QWLIB/tradecheirank/index.htm

Highlighting Entanglement of Cultures via Ranking of Multilingual Wikipedia Articles

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.Comment: Published in PLoS ONE (http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0074554). Supporting information is available on the same webpag

Google matrix analysis of the multiproduct world trade network

Using the United Nations COMTRADE database \cite{comtrade} we construct the Google matrix $G$ of multiproduct world trade between the UN countries and analyze the properties of trade flows on this network for years 1962 - 2010. This construction, based on Markov chains, treats all countries on equal democratic grounds independently of their richness and at the same time it considers the contributions of trade products proportionally to their trade volume. We consider the trade with 61 products for up to 227 countries. The obtained results show that the trade contribution of products is asymmetric: some of them are export oriented while others are import oriented even if the ranking by their trade volume is symmetric in respect to export and import after averaging over all world countries. The construction of the Google matrix allows to investigate the sensitivity of trade balance in respect to price variations of products, e.g. petroleum and gas, taking into account the world connectivity of trade links. The trade balance based on PageRank and CheiRank probabilities highlights the leading role of China and other BRICS countries in the world trade in recent years. We also show that the eigenstates of $G$ with large eigenvalues select specific trade communities.Comment: 19 pages, 25 figure

Mining Missing Hyperlinks from Human Navigation Traces: A Case Study of Wikipedia

Hyperlinks are an essential feature of the World Wide Web. They are especially important for online encyclopedias such as Wikipedia: an article can often only be understood in the context of related articles, and hyperlinks make it easy to explore this context. But important links are often missing, and several methods have been proposed to alleviate this problem by learning a linking model based on the structure of the existing links. Here we propose a novel approach to identifying missing links in Wikipedia. We build on the fact that the ultimate purpose of Wikipedia links is to aid navigation. Rather than merely suggesting new links that are in tune with the structure of existing links, our method finds missing links that would immediately enhance Wikipedia's navigability. We leverage data sets of navigation paths collected through a Wikipedia-based human-computation game in which users must find a short path from a start to a target article by only clicking links encountered along the way. We harness human navigational traces to identify a set of candidates for missing links and then rank these candidates. Experiments show that our procedure identifies missing links of high quality

Interactions of cultures and top people of Wikipedia from ranking of 24 language editions

Wikipedia is a huge global repository of human knowledge, that can be leveraged to investigate interwinements between cultures. With this aim, we apply methods of Markov chains and Google matrix, for the analysis of the hyperlink networks of 24 Wikipedia language editions, and rank all their articles by PageRank, 2DRank and CheiRank algorithms. Using automatic extraction of people names, we obtain the top 100 historical figures, for each edition and for each algorithm. We investigate their spatial, temporal, and gender distributions in dependence of their cultural origins. Our study demonstrates not only the existence of skewness with local figures, mainly recognized only in their own cultures, but also the existence of global historical figures appearing in a large number of editions. By determining the birth time and place of these persons, we perform an analysis of the evolution of such figures through 35 centuries of human history for each language, thus recovering interactions and entanglement of cultures over time. We also obtain the distributions of historical figures over world countries, highlighting geographical aspects of cross-cultural links. Considering historical figures who appear in multiple editions as interactions between cultures, we construct a network of cultures and identify the most influential cultures according to this network.Comment: 32 pages. 10 figures. Submitted for publication. Supporting information is available on http://www.quantware.ups-tlse.fr/QWLIB/topwikipeople