Would transferring to a better school in the middle of a graduate program irreparably hurt my professional connections and academic reputation? I did not get accepted into any good graduate programs.  For various reasons, I feel I could do much better if I reapplied next year.  This question isn't about the feasibility of doing so, but of the affect on my professional reputation and network.

It is an investment for the university to give me funding, so it would be a jerk move to transfer simply for the increase in prestige.  But how much of a jerk move would it be?  Would it burn my colleagues and advisors so hard that I would scar my reputation for the rest of my career?  Would I simply lose these people as connections, but have no lasting affect other than that?  Or would everyone be understanding that this is a professional choice, that I am looking out for my future?  (If so, could I request recommendations from professors in the program?)


  If I transfer to a better school either at the end of my first or second year as a graduate student, how much will this piss people off?


To be clear, I am talking about transferring from a mid-ranked state school to somewhere good, at least top 20 hopefully top 10.  And since I am sure this matters, the discipline is mathematics.
This is fine. Don't feel guilty at all. I say this as a math professor at a mid-ranked state school, who has written rec letters for students who, for various reasons, wanted to transfer out.

Be sure not to speak ill of the place you're leaving, but you owe it to yourself to seek out the best opportunities available. Good luck!