Influence of petroleum and gas trade of Russia on EU economies from the Google matrix analysis of UN COMTRADE data

Using the United Nations COMTRADE database [1] we apply the reduced Google matrix (REGOMAX) algorithm to analyze the multiproduct world trade in years 2004-2016. Our approach allows to determine the trade balance sensitivity of a group of countries to a specific product price increase from a specific exporting country taking into account all direct and indirect trade pathways via all world countries exchanging 61 UN COMTRADE identified trade products. On the basis of this approach we present the influence of trade in petroleum and gas products from Russia, USA, Saudi Arabia and Norway determining the sensitivity of each EU country. We show that the REGOMAX approach provides a new and more detailed analysis of trade influence propagation comparing to the usual approach based on export and import flows. The crisis contagtion on this world multiproduct trade network, induced by increase of petroleum price, is also analyzed. PACS. XX.XX. XX No PACS code given The statistical data of UN COMTRADE and the World Trade Organization (WTO) Statistical Review 2018 demonstrate the vital importance of the international trade between world countries for their development and progress. Also the whole world economy deeply depends on the world trade. At present the UN COMTRADE database contains data for 294 UN countries and former countries with more than 10 trade products. Thus the whole matrix of trade monetary flows reaches a large size ∼ 10. In fact for each year the commercial exchange between countries represents the directed network with transactions of various commodities (products) expressed in their US dollar (USD) values of the given year. It is clear that the recent research developments in the field of complex networks should find useful applications for analysis of this multiproduct World Trade Network (WTN). In [2,3] it was proposed to use the methods of the Google matrix G, PageRank and CheiRank algorithms for analysis of the WTN. The PageRank algorithm had been invented by Brin and Page [4] for the ranking of nodes of the World Wide Web (WWW) being at the foundation grounds of the Google search engine [4]. The applications of these methods to a variety of real directed networks are described in [6]. In contrast to the usual economy approach based on bilateral import and export flows, the Google matrix analysis treats all world countries on equal grounds (since all columns with outgoing country flows of G are normalized to unity so that rich and poor countries have equal consideration) and also the PageRank and CheiRank algorithms take into account the whole chain of transactions incorporating the importance of specific network nodes. This is drastically different from the simple bilateral transactions of import and export. Usually in directed networks, like WWW or Wikipedia, the PageRank vector of the Google matrix plays the dominant role since its components are on average proportional to the number of ingoing links. For the WTN the ingoing flows are related to import. However, the outgoing flows, related to export, are also important for trade. Thus we also use the Google matrix G∗, constructed from the inverted transaction flows, with its PageRank eigenvector, called CheiRank vector. The components of this vector are on average proportional to the number of outgoing links in the original WTN. The construction rules of G and G∗ for the case of multiproduct WTN are described in detail. In many cases it is important to know the effective interactions of trade transactions for a specific region (i.e., for selected nodes of the global network) on which one wants to focus the analysis. This requires to know not only direct links between nodes but also the indirect (or hidden) links which connect the selected nodes via the remaining part of the global network. Recently the reduced Google matrix (REGOMAX) algorithm has been invented in and tested with various directed networks. This algorithm originates from the scattering theory of nuclear and mesoscopic physics and the field of quantum chaos. In this 2 C. Coquidé et al.: Influence of petroleum and gas trade on EU economies work, using the COMTRADE data, we apply the REGOMAX algorithm to analyze the influence on European Union (EU) countries of petroleum and gas trade from Russia (RU), USA (US), Saudi Arabia (SA) and Norway (NO). With this approach we are able to measure the sensitivity of EU countries to the supply of petroleum and gas from one of these four countries taking into account the global WTN, i.e., taking into account all direct and indirect transactions of 61 major products with the rest of the world. We collected the multiproduct (multicommodities) trade data from UN COMTRADE database for Nc = 227 countries, Np = 61 products given by 2 digits from the Standard International Trade Classification (SITC) Rev. 1, and for years 2004, 2008, 2012, 2016. These 61 products represent all smaller subdivided specific products which number goes up to ∼ 10. This approach was used in [3]. However, in this way there we had the effect of global price change of petroleum or gas for all countries. Here, we want to determine the sensitivity of country balance to a flow of petroleum from a specific country (e.g. RU, US, or SA). -2 -1 0 1 2 3 dB /dδ x 10 c 0 4 nu mb er o f