Many universities are working to improve their graduation rates. The factors that correlate to student success and hence graduation rates are many, varying from pre-institutional factors, including high school GPA and admissions scores, to institutional factors, including student support services and the quality of faculty. An essential institutional factor that is often overlooked is the structure of the curriculum. In this paper we consider the degree to which the underlying curriculum that a student must traverse in order to earn a degree impacts progress. Using data mining methods, complex network analysis and graph theory, this paper proposes a framework for analyzing university course enrollment networks at the program level. The analyses we provide are based on quantifying the importance of course enrollment sequences on a student's final GPA, a metric that is highly correlated to graduation rates. In particular, we investigate the orderings of courses enrollment sequences that best contribute to student performance and achievement. Experimental results, using data from the University of New Mexico, show that Electrical Engineering students who graduated with "high GPA" values tend to follow a common course enrollment sequence that is quite different than that of students who graduated with relatively "low GPA" values. This work may be useful to both students and decision makers at universities as it presents a robust framework for analyzing the ease of flow of students through curricula, which may lead to improvements that facilitate improved student success.