Command used to test the connection to other computer in the network?

I believe the command you are looking for is "Ping".

For example, if your computer has an IP address of 192.168.0.2, and the other computer has an IP address of 192.168.0.3, then you would type

ping 192.168.0.3

... from the .2 computer. You should see response times.

The etymology is from ping-pong. You send a ping from one computer to another, it sends a pong back.