# How the webbed get webbier, part II

## by phil on Friday Sep 26, 2003 11:55 AM systems, networks

Here is a quick section-by-section summary of chapter 8, "Einstein's Legacy" in Linked. (for chapter 7 click here). Final summary is at the end.

8.0 - In 2000, I discovered Google.

8.1 - Given the "scale-free" model discussed in chapter 7, how could the latecomer Google dethrone Inktomi? We need to factor in the unique characteristics of each node, and not just their unique set of links (duh).

8.2-3 - fitness connectivity product - So, add to the scale-free model the fitness connectivity product: multiply the number of links you have by the relative attractiveness your node has to determine the probability that someone will link you. Specifically if you have k links, and n fitness the probability that you will be linked is (kn/(sum-over-whole-net(kn)). In

the case of Google, it's fitness could have been 10x compared to Inktomi, and thus helped accelerate its dominance. In math terms, the connectivity of a node is t^b where b is proportional to the fitness.

In other words, if your site is two times as useful as another site, then you can expect a lot more than double advantage in terms of growth.

8.4-8.5 - The author discovered a crisp connection between the condensation of subatomic particles in a huge quantum gas. Hence network theory could govern physics and vice-versa.

8.6 - So there are two categories of complex networks: 1) the scale-free model is preserved in the case of the Internet, and there are many hubs changing positions in a hiearchy (this is called, the fit-get-ric) 2) winner-takes-all, where one hub dominates and becomes a star.

8.7 - Windows is an example of a star.

8.8 - go go go, we have much to learn

Summary: in competitive networks where individual nodes have varying fitness, precedence and relative fitness have an accelerating impact on the speed with which nodes aquire links.

You know those posters that show graphs of the connections on the Internet, it would be nice to see that graph animated over time... I'd imagine they'd look like little spiders, competing to spin webs at really fast paces, with some dying off and others dominating over time.