The most common functionality for a network without a router is to be self-contained and have no point in or out. This is a secure network as it has no connection to the Internet and is good for keeping two or three computers linked up for sharing financial documents or a QuickBooks database.
We can connect two computers directly with a cross-over cable and have a LAN without a router. Computer 1 can access computer 2’s resources, printers and file shares. Computer 2 can access computer 1’s resources as well but this setup limits you to having only two computers connected.