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 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


25 Responses to “The Link Love Law”

  1. Geert Says:

    Hi Philippe, does that mean you could predict what the succes of the follow-up movie of the Break-up could be? Why don’t we give it a try using the formula you told me about ?

  2. Philippe Says:

    Yes, in theory we could. but it’s only a probability calculation. According to the power law, there are more probabilities to receive incoming links for the next action(s).

  3. David Armano Says:

    Here is my very non-mathematical yet visual way of describing the similar phenomena of influence across the social network pertaining to bloggers.

  4. Philippe Says:

    @ David. I discovered your influence ripples post earlier this week thanks to Gavin Heaton. It’s a much more poetic version (without the preferential attachment rule if I’m not wrong) but it shows that influence has an exponential growth. Even if it’s not mathematic, it’s very correct.

  5. links for 2007-06-05 « ‘Cross The Breeze Says:

    […] The Link Love Law « Bad idea, indeed 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. (tags: blogging blogosphere science model network complex structure measurement prediction) […]

  6. bluurb Says:

    Thanks for the example using David Armano & Bring the Love Back, very much brought it to life and the forces of blogging. Interesting stuff. Let us know how you & Geert go on the follow up

  7. Eerst bijsluiter lezen, dan boemboem « Pietr over … Says:

    […] dank aan Bad Idea, Indeed, waar je ook even het artikel over de Link Love Law moet lezen) – […]

  8. Phil Says:

    Saw this blog in my incoming traffic log. Hi there. My thoughts on long tails and power laws are here, here and, more recently, here

  9. Philippe Says:

    Hi Phil, the incoming traffic comes from my next post (still in my drafts)

    Your posts about long tail and power laws are really impressive and I like your statement: ” The popularity of the Long Tail image has a lot in common with the popularity of celebrity gossip magazines.” 🙂

  10. Bob Glaza Says:

    First off, Phillipe – thank you for stopping by One Reader and leaving comment on Dona Nobis Pacem. Secondly, thanks for writing this post. And thirdly thanks for connecting the math to Armano’s ripple post (or thank David anyway :). In my first month of blogging I saw his visual sphere of influence. It felt like math was involved (doesn’t everything 🙂 – but pictures work better with me. There is so much learning in this world. I’m adding BadIdea blog to my reader.

  11. Phil Says:

    Oh, it’s you, Philippe – didn’t make the connection. Thanks for the good words on my “it’s a geek Web” post – I’ll look forward to your next. When I wrote those Long Tail posts I was more dogmatic (and angry) about the subject than I am now – I’d concede now that the classic Long Tail image does capture *something*. I just wish that Clay and Chris had started with a graph with number-of-blogs on the Y axis and number-of-inbound-links on X – it would still have been an interesting shape, but it would have made the high-traffic blogs look like lonely outliers instead of big important landmarks.

  12. Philippe Says:

    Hi Bob, I do the same with “One reader” 🙂

    Phil, I do the same with Gaping silence.

  13. Wikipedia Mathematics « Bad idea, indeed Says:

    […] Wikipedia Mathematics I wrote a post last week about the power law in the blogosphere. […]

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