As far as I know, facebook wasn't banned until the 2008 Tibet riot, when facebook was used to rally people to anti-government demonstrations.
As said in the summary, a facebook clone, Renren, is extremely popular in China with 150 million users, among other social networking sites such as dating-oriented ones. It has pretty much all the fancy features of facebook plus its own innovations, but it's NOT censored, because i) Most of its users are Chinese. What Chinese government really fears is the connection with foreigners in the case of Facebook and Twitter. Though it sounds paradoxical, most people calling for more democracy and freedom in China are foreigners and Chinese expatriates in western countries, rather than people within China who tend to be rather indifferent. ii) Renren is the product an indigenous company in China. Therefore the government naturally expects that the company is more cooperative and controllable.
LinkedIn is obviously also not banned, because its scope is limited to professional activities. It's not likely that people will use it to promote anti-government demonstrations.
In short, social networking is big business in China and censorship is very selective.