Here’s the basic plan(let’s call it Cryptbook) that I came up with. Users access the network using a separate client (much like an IM/twitter client). The Cryptbook server holds all the data and serves it in an encrypted form. The client is responsible for encrypting the data (using public key cryptography) before sending it to the server and decrypting the data that is requested. Additionally, it is responsible for presenting the data in the format requested by the user (profile page, news feed etc.) The basic idea is that the users own their data and share it precisely with who they want to and the owner of the networking server has no access.
What are the potential flaws with such a social network? Also, how many of you would be willing to pay to use a social network?