Scholars have posited that systems’ architectures drive their lifecycle properties. Often, these architectures are modeled using network representations of systems. Specifically, Moses’s theory of generic architectures represents these as networks of resource/information flows that are related to flexibility and controllability in systematic ways. However, measuring the architectures of real systems remains a challenge. In this paper, we propose a generalization of the theory of generic architectures, in which the structure of Moses’s four generic structures – Tree-structured Hierarchies, Layered Hierarchy, Grid Network, and Teams, can be characterized by their “laterality” and “verticality”. Using unsupervised machine learning techniques, we extract dimensions characterizing the major sources of variance in 67 different real-world networks collected from different sources. We find that the dimensions capturing the most variance correspond to systems’ verticality and laterality, suggesting a set of metrics that may be used to measure the concordance of real-world systems with the four structures posited by generic architecture theory. These results generalize across multiple methodologies.