Internet not working and unplugged the power cord = Unknown Homegroup

The internet wasn't working, so I tried to figure out what was wrong. The Control Panel said to restart the modem and router. Then I had to unplug the power cord and wait 10 sec before plugging it back in, which I did. Now when I look at the wi-fi, I'm connected to 'Network 2', a Homegroup, and not our normal wi-fi (as in it's a different name). Is there something that I should be worried about? 'Cause I looked at the network map, and it said that we're connected to 'Unknown', and not the wi-fi with the name that we usually use.

If the "Unknown" or "Network 2" network is not the same as what you usually connect to then the chances are it is not password protected, so when you unplugged your modem and router your computer saw this other network and connected to it automatically.

However in order for your computer to have connected to this other network you will at some point have told your computer to connect to it.

Either way you should disconnect from this "Network 2" and reconnect to the WiFi you normally use, and it would be advisable to remove this "Network 2" from the list of connections by using this tutorial from Microsoft: Delete a network connection in Windows 7 and Windows Server 2008 R2