In four simple steps:
Go to http://www.whatismyip.com on each computer
Compare the IP addresses on each computer with one another. So if on one computer the ip address is 127.0.0.1, and on the other computer it is 10.0.0.3, then they are on different networks, and your brother/roommate/sister/dog can make their own nation, just be sure to never login from one another's computer. If they are the same, then they can't. PERIOD
....
Profit!