D. Zinoviev, "Topology and Geometry of Online Social networks," Proc. of The 12th World Multi-Conference on Systemics, Cybernetics and Informatics, Orlando, FL, July 2008, vol. VI, pp. 138-143 

Abstract:

In this paper, we study certain geometric and topological properties of online social networks using the concept of density and geometric vector spaces. "Moi Krug" ("My Circle"), a Russian social network that promotes the principle of the "six degrees of separation" and is positioning itself as a vehicle for professionals and recruiters seeking each others' services, is used as a test vehicle.

arXiv entry:

http://arxiv.org/abs/0807.3996