LH Private BuddyPress is a simple, single mission plugin with no settings to change, you install and activate it and it immediately turns your BuddyPress site into a private network in so much as once it is active then any attempt by a non logged in user to access any of the BuddyPress pages will be redirected to the login page.
BuddyPress Members Only is a BuddyPress plugin that will redirect any attempt to access your sites pages from none logged in users to the register page thus enforcing a completely private network.
BP Registration Options is a simple plugin designed to do two things: It enables moderation of new BuddyPress users, and it turns a BuddyPress site into a private network.
Simple BuddyPress Profile Privacy is a plugin that allows site members to choose who can see all aspects on their profile as well as giving them an option to hide themselves from the members directory.
BP Simple Private is a Plugin that allows site admins to create fully private networks within their BuddyPress site.