This article applies a method of multidimensional scaling (visualization of multi-dimensional structures) to studying different dimensions of power competition between the great states. On the basis of analysis of the Neo-Realist, Neo-Liberal, and World-systems theory literature on global hegemony, 8 criteria of global leadership were defined: GDP per capita (PPP), military expenditure (% of GDP), amount of currency reserves (including gold), export of goods and services, direct foreign investments, population size in urban agglomerations with more than one million people (% of total population), articles in peer-reviewed scholarly journals, and patent applications. A group of 19 states of the G-20 (excluding the EU) was selected for comparative analysis. Four models visualizing positions of 19 countries according to 8 dimensions were created: for 2004, 2009, 2013, and 2016. These results were compared to the results of calculation including 14 countries: Argentine, Brazil, China, Germany, Spain, France, Great Britain, India, Italy, Japan, Mexico, Russia, Turkey, and the USA. Using mathematical methods of analysis, as traditionally applied in IR literature, turns the making of such models into a very complicated task. Therefore, the mathematical method of the visualization of multi-dimensional structures developed by Russian scholars was applied to this task. The models demonstrate that China’s positions sharply increased in 2009 and since that time China has started to slowly replace USA as an absolute leader. However, if we analyze leadership within specific categories included into our model, the USA still hold leading (or close to leading) positions according to the majority of parameters, while China has a strictly defined profile of leadership connected to its accelerated economic and technical development. However, China is still far from leadership, from the point of view of the development of social structures and even regarding the military dimension.