Using intra-European interregional trade data, we analyze the topology of the E.U. regional trade network. A triad census analysis confirms the intuition that the interregional trade network (and, thus, the European economic integration) is far from being complete. The majority of the E.U. interregional trade patterns are characterized by simple, at best bilateral, configurations. Moreover, we analyze the effect of trade costs in shaping the topological structure of the network. It emerges that the relative presence of simple trade configurations increases with distance, while the relative presence of more complex trade configurations decreases with distance. Finally, we discuss the theoretical underpinnings of these empirical facts through a simple new economic geography model with three regions. In this model, we analyze how trade costs shape the pattern of the trade network. On the whole we find a correspondence between theoretic and empirical results. However, details differ and they suggest directions for further research.