This article presents topological genealogy (TG) as a methodology to research transnational digital governance, and particularly how digital infrastructures are implicated in enacting such forms of governance. Inspired by the field of social topology, TG is centrally interested in investigating the conjoined production of digital infrastructures and present-day education policymaking as governance; as well as how both produce, and are produced by, processes of flows and change. Notably, the TG methodology helps to disentangle digital governance in, through and as change. Through a worked example of the European Commission's eTwinning platform, the article shows TG in action, and complements the topological analysis with methodological foregroundings. These show how the methodology impacts as much the fabrication of research data and its subsequent analysis as it impacts the doings of the researcher.