We compute nodal centrality measures on the collaboration networks of students enrolled in three upper-division physics courses, usually taken sequentially, at the Colorado School of Mines. These are complex networks in which links between students indicate assistance with homework. The courses included in the study are intermediate classical mechanics, introductory quantum mechanics, and intermediate electromagnetism. By correlating these nodal centrality measures with students' scores on homework and exams, we find four centrality measures that correlate significantly with students' homework scores in all three courses: in-strength, out-strength, closeness centrality, and harmonic centrality. These correlations suggest that students who not only collaborate often, but also collaborate significantly with many different people tend to achieve higher grades. Centrality measures between simultaneous collaboration networks (analytical versus numerical homework collaboration) composed of the same students also correlate with each other, suggesting that students' collaboration strategies remain relatively stable when presented with homework assignments targeting different skills. Additionally, we correlate centrality measures between collaboration networks from different courses and find that the four centrality measures with the strongest relationship to students' homework scores are also the most stable measures across networks involving different courses. Correlations of centrality measures with exam scores were generally smaller than the correlations with homework scores, though this finding varied across courses.