In-depth understanding of nature of science (NOS) moves beyond knowledge of discrete NOS aspects to consider connections among NOS aspects. This study presents three teacher cases pre to post a nature of science graduate course to explore the potential of an innovative analytic approach that focuses on the connections individual learners make among NOS aspects, using individual epistemic network analysis (iENA). Participants' pre- and post-course Views of Nature of Science (VNOS) responses were analyzed using both traditional ratings of individual aspects as naïve, transitional, or informed. Then, the responses were coded for NOS connections, which were then modeled using iENA. Compared to traditional VNOS ratings of separate NOS aspects, iENA-based network models added association levels and clustering of NOS aspects. This clarified differences among the participants. Participants' post-course models showed more and more highly associated NOS aspects and increased clustering of NOS aspects, indicating more in-depth and integrated understandings. Additional improvements were recognized beyond those identified through traditional VNOS analysis for one participant who began the course with mostly informed understandings. Consideration of connections may be crucial to guide more effective interventions.