Here's rule of thumb no. 999,999: Since I'm guessing you don't have a ton of extra income as a grad student and you are looking at a period of potential unemployment you should save up as much as you can. Even if your new employer gives a relo bonus, you'll still need extra cash for first, last, deposit, a new futon, all that stuff.
Once you get a job, your emergency fund should to go approximately zero and just start investing. The reason why everyone says you should have XX months in cash is because the market could drop, and that money wouldn't be available to you in an emergency. And that's true enough. But actual emergencies are rare by definition (moving is a planned expense that should be saved up for in cash equivalents). And significant stock market drops are rare as well, and when they do happen the market doesn't go to zero, it just goes down a certain percentage. It would suck if they both happened at the same time, but it wouldn't knock you out.
If you are at a state university, you are technically a state employee, so very likely you could open a line of credit at a state employees credit union and that could be tapped in an emergency. When you live the university the line of credit will remain open.