The ERASMUS program is the most extensive cooperation network of European higher education institutions. The network involves 90% of European universities and hundreds of thousands of students. The allocated money and number of travelers in the program are growing yearly. By considering the interconnection of institutions, the study asks how the program’s budget performs, whether the program can achieve its expected goals, and how the program contributes to the development of a European identity, interactions among young people from different countries and learning among cultures. Our goal was to review and explore the elements of network structures that can be used to understand the complexity of the whole ERASMUS student mobility network at the institutional level. The results suggest some socioeconomic and individual behavioral factors underpinning the emergence of the network. While the nodes are spatially distributed, geographical distance does not play a role in the network’s structure, although parallel travelling strategies exist, i.e., in terms of preference of short- and long-distance. The European regions of home and host countries also affect the network. One of the most considerable driving forces of edge formation between institutions are the subject areas represented by participating institutions. The study finds that faculties of institutions are connected rather than institutions, and multilayer network model suggested to explore the mechanisms of those connections. The results indicate that the information uncovered by the study is helpful to scholars and policymakers.