February 18, 2013
Any Two Pages on the Web Are Connected By 19 Clicks or Less
The Opte Project creates visualizations of the 14 billion pages that make up the network of the web. Image via Opte Project
Note: After publishing this article, it came to our attention that Barabási originally made this finding in 1999, and it was merely referenced in the recent publication. We regret the error.
No one knows for sure how many individual pages are on the web, but right now, it’s estimated that there are more than 14 billion. Recently, though, Hungarian physicist Albert-László discovered something surprising about this massive number: Like actors in Hollywood connected by Kevin Bacon, from every single one of these pages you can navigate to any other in 19 clicks or less.
Barabási’s findings, published noted yesterday in Philosophical Transactions of the Royal Society (Correction: initially made way back in 1999), involved a simulated model of the web that he created to better understand its structure. He discovered that of the roughly 1 trillion web documents in existence—the aforementioned 14 billion-plus pages, along with every image, video or other file hosted on every single one of them—the vast majority are poorly connected, linked to perhaps just a few other pages or documents.
Distributed across the entire web, though, are a minority of pages—search engines, indexes and aggregators—that are very highly connected and can be used to move from area of the web to another. These nodes serve as the “Kevin Bacons” of the web, allowing users to navigate from most areas to most others in less than 19 clicks.
Barabási credits this “small world” of the web to human nature—the fact that we tend to group into communities, whether in real life or the virtual world. The pages of the web aren’t linked randomly, he says: They’re organized in an interconnected hierarchy of organizational themes, including region, country and subject area.
Interestingly, this means that no matter how large the web grows, the same interconnectedness will rule. Barabási analyzed the network looking at a variety of levels—examining anywhere from a tiny slice to the full 1 trillion documents—and found that regardless of scale, the same 19-click-or-less rule applied.
This arrangement, though, reveals cybersecurity risks. Barabási writes that knocking out a relatively small number of the crucial nodes that connect the web could isolate various pages and make it impossible to move from one to another. Of course, these vital nodes are among the most robustly protected parts of the web, but the findings still underline the significance of a few key pages.
To get an idea of what this interconnected massive network actually looks like, head over to the Opte Project, an endeavor started by Barrett Lyon in 2003 to create publicly available visualizations of the web. In the map above, for example, red lines represent links between web pages in Asia, green for Europe, the Middle East and Africa, blue for North America, yellow for Latin America and white for unknown IP addresses. Although the most recent visualization is several years old, Lyon reports that he’s currently working on a new version of the project that will be released soon.
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This is actually not true. This may be an average at best but the absolute claim that you can arrive at any webpage from any other webpage by clicking 19 hyperlinks within the pages is false.
I call BS.
As long as you are not providing an error margin, even an example will de-construct the entire theory you have here.
I have 2:
http://leglesslegolegolas.com/ and http://zombo.com/
Please determine the number of clicks between these two.
Well, Bob, you can now click through to those two pages through this one.
You just connected them.
*fewer
How about pages that have no outgoing links? How can two of these such pages be connected by 19 clicks or less?
The statement was: “from every single one of these pages you can navigate to any other in 19 clicks or less.”
Since Leglesslegolegolas.com does not contain any links, it is impossible to go *from* the page to another page — let alone any specific page, purely by clicking links.
Same goes for zombo.com.
Links aren’t bidirectional. This page now links to both mentioned pages, but neither of those pages link to this one. So it doesn’t change things at all.
Even without their existence on this page now linking them, as Sholiz pointed out, both are already referenced on Facebook pages, so they would easily link there as well I’m sure.
http://www.facebook.com/pages/httpwwwzombocom/47659507386
and
http://www.facebook.com/PointlessWebsites/posts/482641875128408
Also noticed both pages referenced on Tumblr accounts as well.
Well, Nancy & Sholiz, this was not my point, unfortunately.
…and only 5 clicks from the word “bacon”. New twist on 5 steps to Kevin Bacon.
So what about a page on the web and a page on the deep web?
Carey, you’re misunderstanding.
Start at http://www.zombo.com
From there, navigate to http://leglesslegolegolas.com/ *by only clicking links*
You can’t.
1. Open a single-tabbed web browser.
2. Go to leglesslegolas.com.
3. Clear your browser cache.
4. Now, starting by clicking one of the hyperlinks within the leglesslegolas page, navigate to zombo.com in less than 19 clicks.
5. Can’t do it, can you? leglesslegolas.com has no outgoing hyperlinks.
19 clicks or FEWER.
Journalistic standards, please.
UPDATE:
It still can’t beat the Six Degrees of Kevin Bacon so I believe the world to be safe!
The lamb of reading comprehension has be handily slaughtered on the altar of literalism in the scribblings above. I long for the days when comments are posted by educated folk capable of discovering and understanding the implied rather than those who have yet to move beyond the surface.
Internet Smart Guys: “It says, ‘Any two pages.’ That’s so stupid! What if pages don’t have links? Huh? Ever thought of that, wise guy?”
It’s clear neither Barabasi nor Stromberg understood or used “connected” to mean “linked.” /sarcasm
I mean, really, at what point does reading comprehension fail so mightily that one is not capable of inferring even shallowest layer in implied meaning?
To Bob with his example of
http://leglesslegolegolas.com/ and http://zombo.com/
By posting those two hyperlinks, the pages are now linked through this webpage. Furthermore, you could easily reach both of these pages by navigating through the 4Chan Boards.
@Mark: Blimey, you complain about poor reading comprehension, yet you clearly failed to read this blog post properly. How exactly should I interpret this following paragraph?
“Distributed across the entire web, though, are a minority of pages—search engines, indexes and aggregators—that are very highly connected and can be used to move from area of the web to another. These nodes serve as the “Kevin Bacons” of the web, allowing users to navigate from most areas to most others in less than 19 clicks.”
The only reasonable interpretation I see is that the study is actually about clicking links to get from one page to another. Since the actual paper isn’t published in an open-access journal and therefore is pay-walled I can only guess as to what Barabási meant.
try connect my email page to your email page with 19 clicks.
Jon,
The “minority of pages” are “crucial nodes.” That is, they are “very highly connected” like Kevin Bacon happens to be. Bacon has been in enough films that it is possible to connect him with almost every actor with no more than six “links.” The “links” referred to in Bacon’s case are actors who have appeared in a film together. So, suppose Actor A has never been in a film with Bacon. However, Actor B has been in a film with Bacon. Then, somewhere along the line Actor A and Actor B were in a movie together. That means Actor A is “linked” to Bacon through Actor B. Of course, the chain can stretch out to include more actors, but it is claimed that at most one needs six such links to connect any actor in Hollywood to Bacon. That’s what Barabasi is talking about. These “crucial nodes” are the Bacon’s of the Web which allow us to navigate from Point A to Point J.
If you’d really like to know more about what Barabasi is talking about, you can read a limited amount from his book Linked through Amazon. Chapter 12 in particular addresses the Web. While it doesn’t include the material covered in the study above, it does cover some of the basic connections between network science/theory and the Web and how it behaves as a “network.”
Jon,
Or, alternatively, you can read about scale-free networks. If you go to the Wikipedia article about scale-free networks, there is an included image which gives a visual representation of such a network which can help you and others understand the idea better.
Barabasi’s 19 degrees of separation result was published in 1999 in a Nature Magazine article titled “Internet: Diameter of the World-Wide Web.” The Philosophical Transactions article merely cited the result. But after this Smithsonian article, it got picked up all over the web and treated as “news.”
The cool thing, though, is that the mistake caused a spike in media activity surrounding Barabasi’s research, a function of the network on which the spike is taking place. I blogged about this weird meta-phenomenon yesterday, take a look: bit.ly/WbxdUW
Angela, thanks for pointing out the error. We’ve corrected the article.
No problem, I really think it’s an amazing example of how the internet works. Humanity’s burstiness causes bursts in the artifacts we leave behind, like article clicks!
By: http://leglesslegolegolas.com/ and http://zombo.com/
Navigate to http://leglesslegolegolas.com , one click on url input, type http://zombo.com , press enter and I’m there with just one click. :trollface: