Using Gnome Shell, how do I get rid of the Network icon from the top right in the panel?
I would suggest using the Evil Status Icon Forever extension. Install it by clicking the On toggle switch HERE and open and edit the extension.js once installed:
You then change the section below by uncommenting what you'd like to hide, in your case "network" so it would look like so:
Ctrl+s to save.
Or you could
l300lvl's answer is so much better