All web pages connected by 19 clicks or less, physicist finds

This image, courtesy of The Opte Project, shows a visual representation of the Web's interconnectedness.

The estimated one-trillion documents and billions of pages on the web are all connected by an average of just 19 clicks, according to new research from a Hungarian physicist who found cyberspace parallels to Hollywood’s 'Six Degrees of Kevin Bacon' theory.

Albert-Laszlo Barabasi's work was published this week in the journal Philosophical Transactions of the Royal Society, as part of a discussion on web science.

The Kevin Bacon theory states that every actor in Hollywood is connected to the "Footloose" star by six degrees or less. For example, Kevin Bacon and Charlie Chaplin are two degrees apart because Chaplin appeared in "The Gentleman Tramp" with Walter Matthau, and Matthau and Bacon appeared together in "JFK."

Barabasi says everything on the web is similarly connected through small "nodes," such as specialized web pages, and large, highly-connected nodes such as Facebook and Google, which serve as the hubs that hold the entire network together.

That means that wherever you are in the world, and whatever obscure site or random page you happen to be looking at, you could navigate to any other possible location in about 19 clicks.

In his discussion paper, Barabasi calls it the "small world property" -- a rule which states that two nodes in a network, even one as large as the web, "are likely to be connected by a relatively short path of nodes -- in the case of the web, the path length is about 19."

Barabasi also says the web is a "scale-free" network as opposed to a random network. That means that instead of all nodes having roughly the same level of connectedness, "we should expect a few nodes to be very highly connected, and the vast majority to have smaller degree than the average."

And the connectedness of the network remains constant regardless of how large it grows.

Barabasi, who teaches at Northeastern and Harvard University and is the author of "Bursts: The Hidden Pattern Behind Everything We Do," has made a career of studying complex networks.

He says humans tend to group into communities of like-minded individuals with similar interests and geographic location, both in the real world and online -- a trend that is present whether the network is small or massive.

There's a certain hierarchy that is often present on the web as well, Barabasi found.

Nodes that appeared earlier in the network are more likely to become hubs because the older a page or site is, the longer it has had an opportunity to create outgoing links and to collect incoming links, which serve as the currency of connectivity on the web.

However, the age of a node, in relation to its connectedness, is more of a guiding principal than a hard and fast rule. Facebook and Twitter, for example, are relative newcomers to the web that have quickly shot to the top in terms of their connected status.