If in a dream you see yourself as a graduate student, in real life you will have to study and work hard. After all you will be happy with the results of put efforts, but before that you need to go a long and thorny path.
A conversation with a graduate student on topics which are interesting to you indicates your need to increase and develop your professional skills. The time of relaxation has passed, and now you need to think of own future and of position which you will have in society. You should recognize the opportunity and lucky chance to change your life for better.
A dream, in which you teach graduate students, means that you have quite high self-esteem.
For a young lady, to date with a graduate student, means that in nearest future she will face perfidy of a close girlfriend.
In a dream you are accepted to a graduate school for postgraduate studies, this dream warns you about danger to get into unpleasant situation. And only your hard mental work will help you to manage it.
If you were immatriculated to postgraduate school but because of some reasons you refused to go there, it means that very soon you will know some information about your enemies. This information will help you to move on career ladder.