Can The Network View The Sites Visited If I'm Using Another Network?

If you have access to the same computer he used Try just clicking on the arrow down button at the end of the address bar, if this doesnt work try pressing ctrl and H.  This might bring the history up on the left hand side of the screen.  This should work if he hasn't deleted his visited sites after he used it.

What do you mean
1. You have two separate Internet providers or are using another person's network.      
In that case No the provider cannot see the web pages visited on the other network  unless                     it has direct access  to your computer

2. If you are at work and on an account on a network
Then EVERYTHING  you do is monitored so don't do anything illegal also schools' networks are monitored