This application allows you to create gdf files (a simple text format that specifies an undirected graph) from the friendship relations of either your personal network or the groups you are a member of. These files can then be analyzed and visualized using graph visualization software such as GUESS or the powerful and very easy to use gephi platform.
Elgg is an open source social platform
Comparison of projects - The protocols of these projects are generally open and free. The software of the projects is generally free and open source.
ostatus based social network, just for some testing
Idno is a social networking platform designed to be as easy to use from your phone or tablet as from your laptop or desktop workstation.
onesocialweb is to enable free, open, and decentralized social applications on the web. Its protocol can be used to turn any XMPP server into a full fledged social network, participating in the onesocialweb federation. The suite of extensions covers all the usual social networking use cases such as user profiles, relationships, activity streams and third party applications. In addition, it provides support for fine grained access control, realtime notification and collaboration.