Barabási, Albert-László. “Rich Get Richer”
The random model of Erdos and Renyi rests on tro simple and often disregarded assumptions.
The web is always growing, and therefore cannot be assumed to be static when analysing its structure.
Most networks share this essential feature of growth.
Model A. nodes link randomly to one another. The longer a node is in the web, the more time it has to gain links.
However, links aren’t (always) random, as computer users select the nodes/pages that they want to visit. For example, you have a choice of which website to visit in a Google search, or you may be taken to a random page in the search results. I tend to agree with Barabasi here when he says he doesn’t think anyone ever uses this option.
The better known a website is, the more links it acquires and it can therefore be referred to as a hub. Users prefer to link to the better connected hub – while our individual choices are highly unpredictable, as a group we follow strict patterns.
Real networks are governed by two laws:
growth – for each given period of time we add a new node to the network. This step underscores the fact that the networks are assembled one node at a time.
preferential attachment – We assume that each new node connects to the existing nodes with two links. It is twice as likely that a newer node will connect to the more connected node when given a choice.
Each network starts from a small nucleus and expands with the addition of new nodes.