I am 21/M, and I am about to start my PhD at a R-1 university in the US in two weeks (if it matters, it's a southeastern state.) A month ago, I started talking to a 19/F on an online chat platform - she is also joining the same university this year, as an undergrad freshman. We have become pretty good friends over the past month, and we plan to hangout in person & keep in touch in the future. To clarify, I am not a TA for any of her classes, and there is no power dynamic involved. Since I am an international student, I do not know much about the culture associated with social interactions in the US, especially in a university setting. I have been stressed about whether it is "okay" to continue and maintain such a friendship over the next few years of graduate school.
How are grad-undergrad friendships & relationships viewed by other students (grad or undergrad) at the university? Are they common, or not so much? I understand that there are no legal and ethical issues in my case.
Are there any problems that I could potentially run into, and things that I should keep in mind? I fear that I am worrying too much, and I don't want to push a good friend away.
I know that there have been a few similar posts on this site before - but I'm trying to seek US-specific advice for my particular situation (i.e., small age gap, but different phases of life in academia). Thank you!
Edit: The subject areas are different - I am a Math PhD and she intends to pursue Civil Engineering.