Graph Theory: Six Degrees of Separation Problem

This famous statement — the six degrees of separation — claims that there is at most 6 degrees of separation between you and anyone else on Earth. Here we feature a simple algorithm that simulates how we are connected, and indeed confirms the claim. We also explain how it applies to web crawlers: Any web page is connected to any other web page by a path of 6 links at most.

The algorithm below is rudimentary and can be used for simulation purposes by any programmer: It does not even use tree or graph structures. Applied to a population of 2,000,000 people, each having 20 friends, we show that there is a path involving 6 levels or intermediaries between you and anyone else. Note that the shortest path typically involves fewer levels, as some people have far more than 20 connections.

Starting with you, at level one, you have twenty friends or connections. These connections in turn have 20 friends, so at level two, you are connected to 400 people. At level three, you are connected to 7,985 people, which is a little less than 20 x 400, since some level-3 connections were already level-2 or level-1. And so on.

To read the full article with simulator, application to web crawling, some maths, and source code, click here.