Power Law and Blog links

First the definition of Power law to start with.

A power law relates two scalar quantities x and y where the relationship can be written as y = a(xk)

Does scale-free network theory hold for web/blog? It appears that the well connected blogs do appear to collect links faster than less connected pages/blogs. Researchers are figuring out how search engines like Google alter the statistics of web/blogs.When user enters the search query, most never explore beyond the first two. (I am exception to this rule though) If they provide link from their own site to one of the pages they find it will be one of the top pages. By listing the same top 10 or 20 pages when ever a given query is received, search engines elevates those pages to celebrity status and they gain links at an inflated rate. That disturbs the distribution of links and makes it difficult for new pages to crawl up the stack.The distribution makes for an interesting problem in the network theory. A power law can no longer fully describe the connectivity of the web/blog.

I have this graph made from top 100 blogs as on 16-August-2006. The shape of the curve is from power law. Power law is supposed to explain social, biological and computer network. From Power law it can be deduced that only few blogs have thousands of links and rest have just one or two and trend will continue in future and famous blogs will become more famous. The prediction is based on preferential attachments, the idea that in general well connected things tend to garner ever more connections. By Power law prediction this blog gets cannot get huge number of connections as it is in the fag end of the power curve.

Remember the usefulness is defined as the reciprocal of the rank in the case of blog. This blog’s usefulness is 2.8819108221515193433854382809978e-6 that is 1/346992

Power law and Blog links 

There is some unrest in application of power law in other fields like internet routing as it doesn’t predict the correct behavior.

“Power law doesn’t necessarily mean anything, There is tendency for people to see a power law structure and assume that this process is going on, this is like a logical fallacy. Like saying, Bears like honey, my wife likes honey therefore my wife is a bear” – Mark Newman

(Adapted from New Scientist article)

Advertisements

2 Responses to “Power Law and Blog links”


  1. 1 S.Karthikeyan August 21, 2006 at 1:53 pm

    Arun:

    Thanks for stopping by and expecting you more often!

    Power law is intended to describe naturally evolving system. It is assumed that bloggers do not do any thing sinister to garner the in bound links. It just explains that there can no saturation, only few blogs gather enourmous amount links and others need to be satisfied with either one or two.

    Arun, here we are talking about in bound links and not the out bound links. So the blogger cannot influence people to connect to his blog forcefully, but the search engines can help him do that.

  2. 2 Arunn August 18, 2006 at 10:40 pm

    Karthikeyan:

    (nice header image and title)

    interesting thought, this post…

    if blogs that are connected would become more connectum ad infinitum, then there is a saturation right? even if we account for the generation of new blogs, well connected blogs should saturate with their connections, unless the new blogs generation is also a power law generation….

    and, if a blog is located at a point in the power law curve, then, if it (the author) tries to “connect” it with more blogs by some means, would this not work at all? I don’t understand this part…


Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s




Pages

Thru Lens

Tweets

View Karthikeyan S's profile on LinkedIn
Alltop, confirmation that we kick ass

%d bloggers like this: