Hello Donatella,
Thank you for the comment.
I think you are saying that because you are thinking of online social networks. In that case, what you said is true. We have many online social networks. But that is an artifact of the technology and business competition out there. From a sociology and social anthropology point of view, we really have only one social network in real life.
You wouldn't say your high school friends belong to your social network, and colleagues are not part of your social network, woud you? Just because the data of our professional network sits in a different social netwroking service from our friendship network, it doesn't mean they are not part of the network. In real life, they are all interconnected.
However, people can have different social graphs of your single network. I highly recommend you take a quick read on Social Network Analysis 101. I think it will address the confusion between social network and social graph. And I believe it will be clear that we only have one social network, but many social graphs.
OK, hope I addressed your question. Thanks for stopping by and commenting.