While some just reference commercial(paid) well know social networking cloned scripts, let me add some lines to it, and tell you that there are free scripts available to download by everyone. i.e There are some Digg clones, like pligg, PHPDug.
Here is a list of them, which you can try and setup your own social network at no cost:
This is a good option if you don’t have money to start your own project. the deployment of this scripts are generally easy, and almost no code knowledge is need.