This article analyzes how infrastructures take part in constituting Europe as a material collectivity. To that end, it modifies Bruno Latour’s sociology of associations in two respects: In order to theorize the relation between connectivity and collectivity, we consider the political rationalities that infrastructures embody and the political spatiality that they configure. This theoretical perspective is put to a test in exploring the “infrastructuralism” that lies at the core of the European project. After tracing both the operative and imaginary significance of infrastructure policy historically, the analysis concentrates on the most recent initiative to build trans-European energy networks. We demonstrate that the neoliberal configuration of infrastructural collectivity manifests itself in a specific spatial configuration of the market. Europe’s infrastructuralism defines the common as a topological space of corridors and high-voltage lines, which align territorial cohesion with fragmentation.