What criteria are used to rank graduate programs?
What criteria are used to rank graduate programs?

Before enrolling in a PhD program, you should identify your personal goals and needs, and evaluate graduate programs yourself according to your own criteria.  When doing so, consider life both during and after your graduate studies.  Mathematical formulas for ranging graduate programs do exist, but they are inaccurate and measure something different from your personal needs.  An applicant to a graduate program should be sophisticated enough to perform their own evaluation based on a range of data sources.
In short:  Don't rank graduate programs in same way universities are ranked.
Further, your supervisor is usually more important than your program.

Also, will the quality of one's graduate education or future academic career opportunities be affected by the rank of the program?

This is a duplicate.  University rank/stature - How much does it affect one&#39;s career post-Ph.D?