LinkedIn (Plaxo, MySpace Friends, etc...) is a platform in which you can employ graph theory to test the Six Degrees of Separation meme. Each member is a node in a graph. Each member's Contacts (Friends) list is a list of edges to other nodes in the graph.

For each node in the graph, traverse the graph to every other node in the graph. This is an order-N-squared problem -- LinkedIn does it as part of the per-member contacts list update process. LinkedIn stores connection paths. Is the shortest path from one node to every other node always <= 6 -- or is it another number? More importantly, The Six Degrees of Separation meme has implicit in it some notion of Gain-through-connectivity. What gain can be extracted from the network, when we have full access to it?