Interactions and Influence of World Painters From the Reduced Google Matrix of Wikipedia Networks

This paper concentrates on extracting painting art history knowledge from the network structure of Wikipedia. Therefore, we construct theoretical networks of webpages representing the hyper-linked structure of articles of seven Wikipedia language editions. These seven networks are analyzed to extract the most influential painters in each edition using Google matrix theory. Importance of webpages of over 3000 painters is measured using the PageRank algorithm. The most influential painters are enlisted and their ties are studied with the reduced Google matrix analysis. The reduced Google matrix is a powerful method that captures both direct and hidden interactions between a subset of selected nodes taking into account the indirect links between these nodes via the remaining part of large global network. This method originates from the scattering theory of nuclear and mesoscopic physics and field of quantum chaos. In this paper, we show that it is possible to extract from the components of the reduced Google matrix meaningful information on the ties between these painters. For instance, our analysis groups together painters that belong to the same painting movement and shows meaningful ties between painters of different movements. We also determine the influence of painters on world countries using link sensitivity between Wikipedia articles of painters and countries. The reduced Google matrix approach allows to obtain a balanced view of various cultural opinions of Wikipedia language editions. The world countries with the largest number of top painters of selected seven Wikipedia editions are found to be Italy, France, and Russia. We argue that this approach gives meaningful information about art and that it could be a part of extensive network analysis on human knowledge and cultures.