The mathematics of social networks: understanding the “six degrees of separation” theory


“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)