Collaborative learning environments in undergraduate introductory physics courses, such as those promoted by Modeling Instruction (MI), influence both student performance and student social interactions. Because collaborative learning is inherently a social activity, we applied Network Analysis methods to examine student social interactions within the classroom using a survey administered periodically in class. We then calculated centrality, which is a family of measures that quantify how connected or "central" a particular student is within the classroom social network. In order to understand what centrality means in this context, we investigated the relationships among centrality, student demographics, and student outcomes in a large-scale MI classroom with 70 students and 6 instructors. We addressed two research questions: "Is centrality predicted by sex, ethnicity, incoming GPA, or Force-Motion Concept Evaluation (FMCE) pre-score?" and "Does centrality predict FMCE gain or final grade in course?" A series of linear regressions showed that centrality can be predicted by sex and incoming GPA, and is a predictor of FMCE gain.