Own or control? The difference is just money, and if all you care about is the control part, the Chinese state controls all the Chinese social networks. You can see what state control does to a social network: Say what you want as long as it's not about politics (or a few non-political but sensitive areas such as porn), and say what WE want if it relates to anything political.
Yes, actually I'd like to better understand what China does do with their state control of social media.
Clearly you can explicitly suppress certain political views. But I think there's probably a lot more you could do. For example, down rank content that while not banned, is seen as undesirable.
Beyond that, I'm sure there are many other forms of social manipulation which a state which wishes to control their population could apply.
The way North Korea uses watermarking to track the progress of file distribution is kind of interesting. But nothing compared to the psychological manipulation you could do with a social network.