Common to use caret icons for this -- and they wouldn't conflict with the edge arrow style icon. A simple way to add support would be for a tool item icon to be a caret or carets that toggle the sidebar.
It's probably best not to toggle the sidebar completely. The user would benefit from having the tool icons still visible even when the sidebar is hidden
Description of new feature
Make it possible to hide the side panel. Probably animate the panel so it slides in and out.
Motivation for new feature
Gives the user more screen real-estate to see their network.