One often hears about the strength of the students enrolled in a department are a major contributor to a department’s strength. While I may understand that there is a little bit of truth in that, how much do the strength of the students actually contribute to the department’s?
It sort of feeds on itself. Having good graduate students means that research groups can be more productive. This certainly helps, however, strong departments also are more likely to attract the best students.
Is there a specific reason you are asking this question?
I agree with @xraymancs. It’s a bidirectional relationship. There are other factors that contribute to the strength of a department, but having strong students means you basically have stronger research assistants who are helping produce the work and the publications that come from the department. The classes are also stronger (because the students can handle higher-level work) and perhaps the faculty are more productive (because they spend less time hand-holding the students, although that’s a very indirect effect).