“Six degrees of separation is the theory that everyone and everything is six or fewer steps away, by way of introduction, from any other person in the world, so that a chain of “a friend of a friend” statements can be made to connect any two people in a maximum of six steps“
I’ve been intrigued by that theory and curious to investigate its mathematical basis.
A first step I took was to try to better understand the possible mathematical models aimed to reproduce the basic mechanisms about how the connections between people (or other abstract items ) can build up and develop.
Good sources for this quest were the following books:
- Duncan J. Watts – Small Worlds: The Dynamics of Networks between Order and Randomness – 
- Steven Strogatz – Sync – 
Here is a first personal investigation (made with Mathematica and exported as CDF) about Watts’ α-model:
Go to the demonstration’s page (in english)
Go to the demonstration’s page (in italian)