Developing a sense of community among students is one of the three pillars of an overall reform effort to increase participation in physics, and the sciences more broadly, at Florida International University. The emergence of a research and learning community, embedded within a course reform effort, has contributed to increased recruitment and retention of physics majors. We utilize social network analysis to quantify interactions in Florida International University's Physics Learning Center (PLC) that support the development of academic and social integration. The tools of social network analysis allow us to visualize and quantify student interactions and characterize the roles of students within a social network. After providing a brief introduction to social network analysis, we use sequential multiple regression modeling to evaluate factors that contribute to participation in the learning community. Results of the sequential multiple regression indicate that the PLC learning community is an equitable environment as we find that gender and ethnicity are not significant predictors of participation in the PLC. We find that providing students space for collaboration provides a vital element in the formation of a supportive learning community.