I'm working on a web project where I need to let users authenticate using their Gmail accounts. Everything looks fine like the user can sign up and I can create a User object out of his information gathered from Google on the server side and make a new user in the database. I have a password field for the user creation process. Basically, we have no value for the password field when the user signs up using his Gmail account. Since the password field is empty, the user can't log in using his email and password. He has to log in via his Gmail account. (Using the Google's overlay interface)
The concern is should the user be able to set a password for his account and make himself able to log in using his email address and password? If so, what happens to his account linked to Google? I've tried several services and once I set a new password for my account, it unlinks my account to Google and I need to reconnect my account to Google on my own.
Thanks.