The viability of using complexity science in physics education research (PER) is exemplified by (1) situating central tenets of student persistence research in complexity science and (2) drawing on the methods that become available from this to illustrate analyzing the structural aspects of students' networked interactions as an important dynamic in student persistence. By drawing on the most cited characterizations of student persistence, we theorize that university environments are made up of social and academic systems, which PER work on student persistence has largely ignored. These systems are interpreted as being constituted from rules of interaction that affect the structural aspects of students' social and academic network interactions from a complexity science perspective. To illustrate this empirically, an exploration of the nature of the social and academic networks of university-level physics students is undertaken. This is done by combining complexity science with social network analysis to characterize structural similarities and differences of the social and academic networks of students in two courses. It is posited that framing a social network analysis within a complexity science perspective offers a new and powerful applicability across a broad range of PER topics.