We suggest a method that conceptualizes a company’s IS architecture—its set of information systems (IS) and integrations—as a weighted and directed graph. Going beyond an undifferentiated treatment of integration qualities, we present a scoring model to assign integration weights to integration links. Thereupon, we introduce weighted centrality measures from network analysis to identify important systems in the architecture with respect to their architectural embeddedness. Drawing on the case of a production company, we demonstrate our approach by concentrating on selected systems and integrations, such as the close and complex integration of an ERP and a product lifecycle management (PLM) system. Focusing on the technical challenges of enterprise transformations, our work contributes to enterprise architects’ toolbox as it enables a more fine-grained understanding of critical systems with high change complexity.