While some scholars, such as Stone Sweet and Ryan, describe Europe's multi-level system of courts as an emerging 'cosmopolitan legal order', few have attempted to study the case citations representing the defining features of the order, namely the interdependence of courts at each level, and the embeddedness of international law in national court decisions. We construct an original database of case citations based on judgments of the European Court of Human Rights (ECtHR), the Court of Justice of the European Union (CJEU), and high national courts made available by CODICES, and apply network analysis and text-as-data methods to assess the dynamic interactions among these courts. Our work makes several empirical contributions to the literature on the Europeanization of law and courts: that Europe's 'cosmopolitan legal order' operates more as an interconnected, heterarchical network and less like a hierarchical legal system; that the ECtHR's status today as the 'ultimate supranational arbiter of human rights in Europe' in the words of Kelemen is assured by the propensity of national courts to cite its case law; and that high national courts use their case citations strategically to signal to domestic and international audiences their commitment to the values of the 'cosmopolitan legal order'. After identifying the forces that give the network its unique shape, we discuss the implications of the governance architecture for the effective promotion of the values that inspired the legal order.