Do i file as a dependent or independent? I am 24 (have been since April of last year), am in graduate school, live with my parents, and do not pay rent/bills.

You were over 24 at the end of 2017?  Did you earn over $4050 in 2017?

I was still 24 by the end of 2017. I turned 24 in april that year. I made around $5200 in 2017

If you were 24 at the end of 2017 and made over $4050, your parents cannot claim you, despite your continuing education. Once you are 24, the full-time student status does not over ride the $4050 income limit.

WHO CAN I CLAIM AS A DEPENDENT?
You can claim a child, relative, friend, fiance (etc.) as a dependent on your 2017 taxes as long as they meet the following requirements:
Qualifying child
• They are related to you.
• They aren't claimed as a dependent by someone else.
• They are a U.S. citizen, resident alien, national, or a Canadian or Mexican resident.
• They aren’t filing a joint return with their spouse.
• They are under the age of 19 (or 24 for full-time students).
? No age limit for permanently and totally disabled children.
• They live with you for more than half the year (exceptions apply).
Qualifying relative
• They don't have to be related to you (despite the name).
• They aren't claimed as a dependent by someone else.
• They are a U.S. citizen, resident alien, national, or a Canadian or Mexican resident.
• They aren’t filing a joint return with their spouse.
• They lived with you the entire year.
• They made less than $4,050 in 2017.
• You provided more than half of their financial support. More info
When you add someone as a dependent, we'll ask a series of questions to make sure you can claim them.

If you were over 24 by December 31, 2017, you parents can only claim you as a Dependent on their return, if you meet the income limits and other qualifications. 

In order for your parents to claim you, you would have to have earned less than $4,050 for 2017.

Here's more info:

https://ttlc.intuit.com/replies/5187060

Edited 2/4/18 11:32 AM

Does her status as a graduate student change the answer?

No, except she would not be eligible for the American Opportunity Credit (max $2500) but only for the Lifetime Learning Credit (max $2000).

@TurboTaxMarilynG   I think you may have accidentally missed OP's age in her question.

Thank you!

You are welcome!