June-2-2017
Chapter 8-1: The fitness model
The fitness model proposed that Nodes still acquire links following a power law ~
t^β , But the dynamic exponent, β, which measures how fast a node grabs new links, is different for each node. It is proportional to the node's fitness, such that a node that is twice as fit as any other node will acquire links faster because its dynamic exponent is twice as large. The speed at which node acquire links is no longer a matter of seniority. Independent of when a node joins the network, a fit node will soon leave behind all nodes with smaller fitness, e.g., Google over other old search engines and Apple devices over other devices.
Every network has its won fitness distribution, which demonstrates how similar or different the nodes in the networks are. In networks where most of the nodes have comparable fitness, the distribution follows a narrowly peaked bell curve. In other networks, the range of fitness is very wide such that a few nodes are much more fit than most others. Google, is a thousand times more interesting to all web surfers than any personal web page.
Fitness-get-rich behavior means the fittest node in networks will inevitably grow to become the biggest hubs.
Network with Winner-takes-all behavior is not scale-free, there is only one hub and many tiny nodes, e.g., Microsoft Windows.
Nodes always compete for connections because links represent survival in an interconnected world.
Chapter 8-2: Comparisons among random model, scale-free model, and fitness model.
Random model: network is regarded as static graphs.
Scale-free model: Networks are dynamic, but it changes constantly through the addition of new nodes and links.
Fitness model: describe networks as competitive systems in which nodes fight fiercely for links.
