If you don't see certain friends (or any at all) who definitely play Supercity at the bottom of the game screen, or the "Invite Friends" list is empty, you need to reinstall the app with proper permissions. Don't worry, you will not lose your city.
Please follow these instructions to delete the game and install it again:
Find Supercity and click the Settings
Click "Remove App"
at the bottom of the window:
If asked for confirmation, click "Remove"
The game will start loading, and a confirmation window will appear in the center of the screen. Click "Edit this"
to set the app permissions:
Make sure that the "Friend list"
option is turned on, then click "Continue"