Resumen
The current international society has entered an era of large-scale power transfer. Government interests have gradually transferred from national strength to national influence. As such, how to quantitatively present the fuzzy geopolitical influence (i.e., geo-influence) has attracted greater attention from scholars. The proposed concept of geo-influence conforms to this trend of power structure change in international relations, and provides a reference for national sustainable development on the international stage. This study sets up an index system and a mathematical model of geopolitical influence, and explores the spatio-temporal changes of the geo-influence of China and the United States (US) in South Asia over the past decade. Three primary results are found as follows: (1) In general, the geo-influence of China and the US in South Asia increased between 2003 and 2012. In terms of growth rate, the geo-influence of China in South Asia grew much faster than that of the US; (2) The overall strength and geo-influence show non-linear relationships. Strong national overall strength does not necessarily mean that one country has the strongest geo-influence; (3) National geo-influence is inversely proportional to the friction of distance. The larger the friction of distance is, the smaller national geo-potential is, and vice versa.