...If an employee is using these social-media sites in his or her professional capacity, does the employer have the right to take the contacts away once the employee leaves?
The correct answer is: shut up.
Minnesota Headhunter pointed at a couple discussions of whether making connections via LinkedIn can lead to violations of non-compete agreement--- or even be viewed as leaking your company's customer list! Although I can't speak to the legal issues here, this seems like yet another example of how social networks are not well-represented within social apps. People have different sorts of connections--- friend, gaming buddy, ex-coworker, vendor, etc. Although the distinctions may not always be clear-cut, there does seem to be a need to distinguish and categorize various types of links.