Curricular analytics (CA) is a quantitative method that analyzes the sequence of courses (curriculum) that students in an undergraduate academic program must complete to fulfill the requirements of the program. The main hypothesis of CA is that the less complex a curriculum is, the more likely it is that students complete the program. This study compares the curricular complexity of undergraduate physics programs at 60 institutions in the United States. The institutions were divided into three tiers based on national rankings of the physics graduate program, and the means of each tier were compared. No significant difference between the means of each tier was found, indicating that there is not a relationship between program curricular complexity and program ranking. Further analysis focused on the physics, chemistry, and mathematics courses, defined as the core courses of the curriculum. Significant differences in the number of required core courses and the complexity per core course were measured between the tiers; both were measured as large effects. Programs with the highest rankings required fewer core courses while having a higher complexity per core course. These institutions have more strict prerequisite requirements than lower ranking programs. This study also showed complexity was quantitatively related to curricular flexibility operationalized as the number of available eight-semester degree plans. The number of available degree plans exponentially decreased with increasing core complexity per course. Modifications to a curriculum at one institution were analyzed; a similar relationship between the number of available degree plans and increasing complexity per core course was found.