Discussion forums provide a channel for students to engage with peers and course material outside of class, accessible even to commuter and nontraditional populations. Forums can build classroom community and aid learning, but students do not always take up these tools. We use network analysis to compare three semesters of forum logs from an introductory calculus-based physics course. The networks show dense structures of collaboration that differ significantly between semesters, even though aggregate participation statistics remain steady. After characterizing network structure for each semester, we correlate students' centrality--a numeric measure of network position--with final course grade. Finally, we use a backbone extraction procedure to clean up "noise" in the network and clarify centrality-grade correlations. We find that more central network positions are positively linked with course success in the two semesters with denser forum networks. Centrality is a more reliable indicator of grade than non-network measures such as postcount. Backbone extraction destroys these correlations, suggesting that the noise is in fact signal and further analysis of the discussion transcripts is required.