During the COVID-19 crisis, European Union (EU) health policy has become high politics. Key parts of EU health cooperation have, however, long developed more discretely in European administrative networks (EANs) and become core building blocks in the institutional architecture of an EU health policy. In these networks, health experts interact regularly and, by doing so, pool key resources and develop common standards. However, are some network members more influential than others in defining the way forward, and if so, why? In this paper, we examine the structure of networked health cooperation in the case of health technology assessment (HTA), by means of unique survey data and social network analysis, employing exponential random graph models (ERGMs) for different types of interaction. A horizontal structure of interaction fosters cooperation by and for all, whereas a hierarchical structure allows certain members to set agendas and place themselves in a powerful position. We find that the network structure is indeed hierarchical, with some members constituting the core of the network based on their national HTA experience as well as external contact relations.