The role of student interactions in learning situations is a foundation of sociocultural learning theory, and social network analysis can be used to quantify student relations. We discuss how self-reported student interactions can be viewed as processes of meaning making and use this to understand how quantitative measures that describe the position in a network, called centrality measures, can be understood in terms of interactions that happen in the context of a university physics course. We apply this discussion to an empirical data set of self-reported student interactions. In a weekly administered survey, first year university students enrolled in an introductory physics course at a Danish university indicated with whom they remembered having communicated within different interaction categories. For three categories pertaining to (1) communication about how to solve physics problems in the course (called the PS category), (2) communications about the nature of "physics concepts" (called the CD category), and (3) social interactions that are not strictly related to the content of the physics classes (called the ICS category) in the introductory mechanics course, we use the survey data to create networks of student interaction. For each of these networks, we calculate centrality measures for each student and correlate these measures with grades from the introductory course, grades from two subsequent courses, and the pretest Force Concept Inventory (FCI) scores. We find highly significant correlations (p less than 0.001) between network centrality measures and grades in all networks. We find the "highest" correlations between network centrality measures and "future" grades. In the network composed of interactions regarding problem solving (the PS network), the centrality measures hide and PageRank show the highest correlations ("r" = -0.32 and "r" = 0.33, respectively) with future grades. In the CD network, the network measure target entropy shows the highest correlation ("r" = 0.45) with future grades. In the network composed solely of noncontent related social interactions, these patterns of correlation are maintained in the sense that these network measures show the highest correlations and maintain their internal ranking. Using hierarchical linear regression, we find that a linear model that adds the network measures "hide" and "target entropy," calculated on the ICS network, significantly improves a base model that uses only the FCI pretest scores from the beginning of the semester. Though one should not infer causality from these results, they do point to how social interactions in class are intertwined with academic interactions. We interpret this as an integral part of learning, and suggest that physics is a robust example. (Contains 5 tables, 3 figures, and 5 footnotes.)