Liked the article of John Udell last year about scale-free networks? Want to know why on average, every page on the WWW is only 17 clicks away from any other one (compare: Six Degrees of freedom from Milgram).
In the May edition of Scientific American (p60-p68) Albert-László Barabási and Eric Bonabeau have an interesting article on that very same topic. It's copyrighted and cannot be posted here, but the public summary of the article comes on their website:
Networks are everywhere. The brain is a network of nerve cells connected by axons, and cells themselves are networks of molecules connected by biochemical reactions. Societies, too, are networks of people linked by friendships, familial relationships and professional ties. On a larger scale, food webs and ecosystems can be represented as networks of species. And networks pervade technology: the Internet, power grids and transportation systems are but a few examples. Even the language we are using to convey these thoughts to you is a network, made up of words connected by syntactic relationships.
Yet despite the importance and pervasiveness of networks, scientists have had little understanding of their structure and properties. How do the interactions of several malfunctioning nodes in a complex genetic network result in cancer? How does diffusion occur so rapidly in certain social and communications systems, leading to epidemics of diseases and computer viruses? How do some networks continue to function even after the vast majority of their nodes have failed?...
[The Internet as a scale-free network visualization; image by KC Claffy]
The mathematical background of the publication comes apparently from a whitepaper that they wrote last year for the University of Notre Dame - and which is publicly available in PDF here. If you're not into the maths of networks, skip this one - if you are, it'll help you replicate the examples mentioned in Scientific American about Cellular Metabolism (2001), the Internet (1999-), protein networks and sexual relationships.
The various articles show that in a scale free network, such as social networks and the Internet, the distribution of nodes linkage follows the power law in which most nodes have just a few connections and some nodes have a great number of those.
Consider that Google became a much more powerful node in the search-engine network than AltaVista, but any of the competitors with strong linkage (through innovative features) can take over Google's #1 ranking anytime.
Also see: Albert-László Barabási's website http://www.nd.edu/~alb/
[Blogged from 35,000 feet]
This happened at 6:37:14 AM or
|
Weblog
