Based on the data released by UNESCO on international student mobility in tertiary education from 2001 to 2015, this paper draws on network science to construct a multidimensional weighted directed network heterogeneity model. This model combines the GIS spatial analysis method and the negative binomial regression model to study spatiotemporal evolution and factors influencing international student mobility networks. The results are as follows. First, in terms of the evolutionary characteristics of time series, the linkages of international student mobility networks have increased from 4921 to 9137, and its average weighted degree centrality has rapidly increased from 8004 to 20,834, which indicates that both the number of international students and the choices of overseas routines are mounting. Second, in terms of the topological structure, it has evolved from a single core comprising the United States into dual cores comprising the United States and China. Gradually, Asian countries have become the main body of international student mobility networks, while the centrality of European countries has reduced. Thirdly, in terms of spatial structure, the international student mobility network has a significant core-periphery structure and hierarchical characteristics. The countries in the core, strong semi-periphery and semi-periphery alternate with countries from other tiers. The spatial patterns of the international student mobility network "from east to west, and from south to north" are changing. China and Australia have become the new regional centers of international student mobility networks, meaning that regionalization has become an important trend. Finally, regression analysis shows that the flow of international students correlates positively with the quality of higher education in destination countries, the number of students in colleges and universities, the per capita GDP, the historical links connection between the destination country and the country of origin, and the level of globalization. Geographical distance and linguistic proximity have a significant negative correlation with the flow of international students, indicating that the impediment of language is rapidly weakening, while geographical distance still hinders student mobility.