PreferentialAttachment

A mechanism proposed by Barabasi et al to explain the PowerLaw distribution in the connectedness of web sites.

From the paper:

"Similarly, a newly created Web page will be more likely to include links to well-known popular documents with already-high connectivity, and a new manuscript is more likely to cite a well-known and thus much-cited paper than its less-cited and consequently less-known peer. These examples indicate that the probability with which a new vertex connects to the existing vertices is not uniform; there is a higher probability that it will be linked to a vertex that already has a large number of connections."

Another way of putting this: as the network of interconnected nodes grows new nodes connect to the existing network or new connections are made (or are remade) between those already in the network. Lots of different information might drive how those connections get made. For example new connections could be made at random by drawing a random node; or new connections could be made by mimicing an existing connection. If the new connections model the existing connections you will get a PowerLaw outcome.

PreferentialAttachment may also be the mechanism generating PowerLaw phenomena in other domains. For example,

References

A.-L. Barabási, and R. Albert, Emergence of scaling in random networks, Science, 286, 509-512 (1999).

Translations / traductions


CategoryCommunityScience?

Discussion

So, I grok why lots of bloggers only link to superstar bloggers or to well-known media and commercial sites. I just wonder if there's anything even remotely related to community in that.

If I link to a Boing Boing bit, does that put me and Cory Doctorow into some kind of group effort? What is our CommonCause? I think the weakness of the so-called "blogging community" makes this kind of a moot point w/r/t community.

I also think it doesn't really translate into other kinds of communities. WorldWideWeb links are special in that they're one-way. I can link to BoingBoing without anyone there acknowledging it whatsoever. Most other kinds of links are two-way. If I have a relationship with someone in a club, town, or IRC channel, they know it, and they accede to it.

My instinctual feeling is that in other kinds of communities, approaching the central members of the community for a relationship is kind of daunting. I think new or peripheral members will approach other peripheral members, since they're more accessible.

It is, however, interesting in terms of content. It'd be interesting to see the distribution of links to pages on your average wiki. Actually, I can generate that info myself… I'll try it out on WikiTravel and see what I can come up with. --EvanProdromou 2004-06-07 15:34 UTC

I'm trying to find some cheesy way to link this page to SpokeVsCircleCommunications, which overlaps what you just said a lot. :)

The preferential attachment scenario drives most open systems into a power-law distribution. For examples english words, last names, city sizes, code execution frequency…. Wiki's will have power-law and preferential attachment in the absence of intervention (such as a strong organizing hand).

This relates to community because if you look at communication patterns between members of a community, or for example posting frequency to a mailing list, these almost always power-law distributed. The impression that communities have elite members who form the core of that community is, looked at another way, just the naming of the power law elite in that community along some metric.

The feeling I get from your comment, though, is that "blogs and wikis are no different." "Powerlaw distribution here, powerlaw distribution there. What's the fuss?"

But it seems dramatically different to me.

For instance, in blogging community, it is really hard to get the attention of a group of people.

In a wiki, it's easy. You just post.

I think the effects of this are dramatic.

Also, in a wiki, website style makes much less of a difference than it does in blogs. After all, everyone on the wiki has the same website style. This could be viewed as "uniforms" for everyone.

And then there's shared easy to use LinkLanguage. There's probably more.

I think the conversation has become really abstract, though. What do we care about? What are we looking for? Why are we talking about preferential attachment and the power law?

This suggests to me that we should be talking on another page. PreferentialAttachment is just a particular phenomenon.

Are we talking about fairness in communication? Are we talking about elites? Are we talking about the way we should communicate? Are we talking about the output of our mediums? Are we talking about blogs vs. wiki? Are we talking about the way communities work?

What are we talking about?

My early morning feeling ? …. After saying that i "love" what's going on here … and that the question i feel urged to ask would rather be What the hell are "we" doing here? .. ??
To me, what "you guys" seem to be talking about is a huge lot of meta … and … almost no communication
Meta is fine … it's great to see it going … but without a demo of the communication it is supposed to be applying to … it sounds difficult to me to say what it's use is
Can you buy this?
Wish you could.

Luigi: If we're at the you guys stage, I think we're already off course.

But I don't understand what's wrong about the "meta" part. If I was going to write a (new) CW mission statement, I'd say:

:CommunityWiki is for exploring issues in community. We want to help people start, maintain, and enjoy the communities they participate in, both on- and off-line (but admittedly more on- than off-). We do this by identifying and describing problems, trends, and characteristics of communities that use any kind of technology, and sharing "best practices" or new ideas for fixing or dealing with those problems.

So, I think that the meta is part of what we do here. That said, we only manage to talk about community by participating in community, and it's bad if you think we're not doing it right.

Anyways: explain to me so I get this. I want to buy what you're selling. B-)

Evan: i didn't say meta is wrong .. i "tried" to say meta is great but it seems to be unbalancedto me
maybe i'm pretending to behave as an end user here … some kind of so called devil's advocate …
If you come and see me with your CW mission statement my likely prospective end user reaction would be the classical so what?
Maybe it only takes adding a note like as per example shown …. ?? …
i dont think you are wrong … you probably got me wrong … i believe i'm participating in what's going on here … i'm waiting to enable myself to start a demo that could make one of the possible examples for your CW mission statement .. am i not ?

:-) I assume that when LionKimbro enquires "What are we talking about?" he's means "here" where "here" means this node and not this wiki. Interesting question.

These PreferentialAttachement? and PowerLaw nodes sort of hang out in mid air; but it is the air of wiki about communities so I'd assume that were talking about that the PowerLaw distribution and the process that gives rise to it as it relates to communities.

Play the two way card: We could tackle that by getting a generic feel for the process that gives rise to it. One the other hand we could look for examples of the pattern in communities and then puzzle back toward the general principles.

I think there is a bit of both going on here. For example I'm fascinated that if you look at email traffic in all the email lists at source forge (pdf) you discover that the posters are power-law distributed. That's certainly a fact about the engagement of members in their communities that I would not have expected. But I know accept it as a given and I've come to think that much of what we call the community core, or elite, or cabal is just a side effect of some generic process that leads to this outcome.

So what I'm trying to talk about is power-law distributions, the processes that generate them, and how that relates to various aspects of communities and group forming.

Meanwhile, I:

needto
learn
moretypography skills

I still don't get it; I'm thinking: "What?"

I mean, I can parse the phrases "the processes that generate them," "how that relates to various aspects of communities and group forming."

But, that's pretty vague.

I'm just trying to get at the heart of this. I'm thinking: "What does this mean in terms of people? What does this mean in terms of what we do? If we understand these things, what can or will we do differently, than we did before? Can we write our software differently, understanding something here?"

I'm not saying there's no such thing; I'm just wondering what it is.

It's good some times to think about things, when there's no clear goal or end or meaning in mind. But, I'm wondering right now what it is. :)

If most of the statistics you can extract about patterns in communities are power-law, then the process that gives rise to that seems pretty worthy of study. For example the severity of the resulting inequality might be something you could engineer your software to temper.

I think this is a cool phenomenon to discuss and understand. It is so pervasive and interesting that I'm sure it'll have some bearing somewhere.

re: This relates to community because if you look at communication patterns between members of a community, or for example posting frequency to a mailing list, these almost always power-law distributed. The impression that communities have elite members who form the core of that community is, looked at another way, just the naming of the power law elite in that community along some metric.

so do you think that PreferentialAttachment figures in there? Or is that an example of just PowerLaw, without a PreferentialAttachment mechanism?

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