  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 vs. 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.
