Here is the diameter of the world wide web.

They calculated the d as 18.59. Any website in their large sample was less than 19 clicks away from any other website on average. The Internet is a Small Worlds Network. Despite it’s immense size, an agent can navigate from one end to another within a few clicks.

This ranks websites based on links. The result looks like this.
internet.jpg

That is a perfect example of a scale-free network. This gives an approximation of the social shape of the internet. It’s useful information for those trying to build search engines.

Here’s some of the methodolgy

To determine the local connectivity of the www, we constructed a robot, that adds to its database all URLs found on a document and recursively follows these to retrieve the related documents and URLs. From the collected data we determined the probability P out(k) (P in(k)) that a document has k outgoing (incoming) links. As Figs. 1a and b illustrate, we find that both P out(k) and P in(k) follow a power-law over several orders of magnitude…

The power law tail indicates that the probability of finding documents with a large number of links is rather significant, the network connectivity being dominated by highly connected web pages. The same is true for the incoming links: the probability of finding very popular addresses, to which a large number of other documents point, is non-negligible, an indication of the flocking sociology of the www. Furthermore, while the owner of each web page has complete freedom in choosing the number of links on a document and the addresses to which they point, the overall system obeys scaling laws characteristic only of highly interactive self-organized systems and critical phenomena

Internet sociology follows normal social rules. The internet did not turn out to be a random graph where individual nodes were linked into a random matrix. Instead, it organized into an power-law hierarchy. There are “upper-class” websites that gather a disproportionate amount of links, and “lower-class” websites that are barely linked at all.

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