Mathemagenic

Valdis Krebs in From Social Networking in Academia - The Erdos collaboration network:

Experts have long argued about the optimal structure of a person's professional network. Some say that a dense, cohesive network brings more social capital, while others argue that a sparse, radial network, one that provides opportunities for innovation and entrepreneurial activity, equates to greater social capital. Erdõs's network shows both patterns -- a densely connected core along with loosely coupled radial branches reaching out from the core. According to Ron Burt -- a leading expert on social capital -- this structure may be the optimal pattern for success. According to Burt, radial ties reach diverse information and knowledge to create value, while the dense, trusted ties deliver value in discovered opportunities. For a complete analysis read Burt's seminal work -- The Network Structure of Social Capital[PDF].