From: http://en.wikipedia.org/wiki/Six_degrees_of_separation

*“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*– [1999] - Steven Strogatz –
*Sync*– [2003]

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)