The Link Love Law

A while ago, I was in contact with Renaud, who is studying and modelizing the structures of complex networks. I was very interested by his work but couldn’t really figure out how usable this was for a better understanding of the web and the blogosphere. I called him to discuss this topic and I discovered new horizons.

I understood that the blogosphere was what we call a scale-free network: In scale-free networks, some nodes act as “highly connected hubs”, although most nodes are of low degree. The scientist Albert-Laszlo Barabasi is one of the leading researchers of the complex network study. He developped an algorithm called the BA model based on two important principles:

- Incremental growth: scale-free network expand continuously over time by the addition of new nodes.

- Preferential attachment: new network members prefer to make a connection to the more popular existing members.

The BA model shows that scaling and power laws emerge in random networks. This model hasn’t been built for the blogosphere. The web is only one out of many scale-free networks. Examples of scale-free networks can be found in biology (protein interactions), in terrorist organisations and even in… the distribution of sexual relations.

Basically, this is the scientific background of the long tail model and Chris Anderson figured that out long before me. We experienced this power law recently with Bring the love back. We noticed that many links on blog that were posting the video were mentioning David Armano (David is a “hub” in the blog scale-free network) as source of the information adding a lot of extra links to David Armano’s blog. David became the biggest traffic broker of bringtheloveback.com. This is of course due to his very important readership but also to the preferential attachment law: Bloggers who discovered the bring the love back-movie through a smaller node (a blog with a lower authority ranking) pointing to David Armano have much more probability to link directly to David Armano’s post and bypass the primary source of information which eventually was benefitial for the bring the love back success.

The fact that the long tail is not only a volume distribution law but also a power law is very new to me. This adds a predictability element. It doesn’t only describes the internet landscape but also allows to predict what the growth pattern will be (at least gives probabilities of growth knowing that critical events can change the evolution pattern of the network).

This discovery (it might sound trivial for most of you but it’s new to me) makes me think about Maximilian Cohen is the wonderful movie ‘Pi‘: “11.15: Restate my assumptions: One, Mathematics is the language of nature. Two, Everything around us can be represented and understood through numbers. Three: If you graph the numbers of any system, patterns emerge. Therefore, there are patterns everywhere in nature. Evidence: The cycling of disease epidemics;the wax and wane of caribou populations; sun spot cycles; the rise and fall of the Nile. So, what about the stock market? The universe of numbers that represents the global economy. Millions of hands at work, billions of minds. A vast network, screaming with life. An organism. A natural organism. My hypothesis: Within the stock market, there is a pattern as well… Right in front of me… hiding behind the numbers. Always has been“

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