Facebook Visualizer is a tool to graphically explore your facebook social network. You can use it to see how all your contacts are connected to each other, and in the process disclose unknown common friends.
The tool allows filtering your network by Gender and Relationship Status (single, engaged, etc). You can also choose to see the inner connections of your facebook network and play with the distance between nodes (friends).
Touchgraph, allows users to see how their Facebook friends are connected, and who has the most photos together. Users can also explore their own personal networks by graphing photos from anyone's album, or view the connections between members of a group. The interactive tags feature seems also quite interesting. Make sure you have the latest version of java and a Facebook account to take advantage of this tool.