During the first year of graduate studies, students are mainly focused on taking classes, preparing for the written qualifying exam and adjusting to graduate student life at Rutgers.
During the second year students are focused on identifying potential research areas and advisors, and preparing for the oral qualifying exam.
The graduate program mentoring committee consists of faculty members who are each assigned a group of entering students. The assignment of mentors to students is not based on research interests. Rather the mentor is available to the student to discuss concerns that arise during the first years, and to help the student make contacts with potential research advisors. The graduate program director also serves a general advising role for all students.
The assignment of mentors to students is arbitrary, and students are encouraged to establish their own informal mentoring relationships with faculty. You may find useful information in the handbook How to get the mentoring you want, published by the graduate school of the University of Michigan.