What could be an electronic way to verify that someone is from a specific university department or university? How could I verify that a person is a student/faculty/researcher at a specific department of any university in world?  I could ask the user to verify the official email address provided by that university to him but not all universities in world provide a email address to their people. A considerably large percentage of universities do not provide.

What could be other ways to collect only verified people in some group for a university department ?
There is no good fully automated way of doing this, because there is no central clearing-house are too many ways the humans maintain imprecise machine-readable records.  

If you are willing to have a human process, you can deal with a lot of the problem cases with a combination of Google and phone calls.  That still won't ensure that an institution that you personally aren't familiar with is real, given all of the diploma mills in the world, but it will at least reduce the likelihood of giving access to a legitimate institution to the wrong person.