A real network is usually governed by the laws of growth and preferential attachment. The assumption of a network from Erdo and Renyi does not perfectly describe how real networks work. Their assumption describe a fixed number of nodes and all the nodes are equivalent so they are linked randomly to each other. If we only have a fixed number of nodes we'll end up wit a static network. In real network, it is dynamic because there is always growth. New nodes are added into the network from time to time. This step underscores the fact that networks are assembled one node at a time. When new nodes are added in, they do not just link to any other random nodes. The nodes will more likely connect to the one that has more connected node. It also brings up the issue of richer-get-richer phenomenon. The early nodes have more chances of getting links than the latecomers.
A real network is usually governed by the laws of growth and preferential attachment. The assumption of a network from Erdo and Renyi does not perfectly describe how real networks work. Their assumption describe a fixed number of nodes and all the nodes are equivalent so they are linked randomly to each other. If we only have a fixed number of nodes we'll end up wit a static network. In real network, it is dynamic because there is always growth. New nodes are added into the network from time to time. This step underscores the fact that networks are assembled one node at a time. When new nodes are added in, they do not just link to any other random nodes. The nodes will more likely connect to the one that has more connected node. It also brings up the issue of richer-get-richer phenomenon. The early nodes have more chances of getting links than the latecomers.
To understand the function of growth and preferential attachment in a scale-free network, we should look at the application of these laws in real life scale-free network. The most recognizable scale-free network would be the World Wide Web. There is new documents added online everyday that links to other pages. Either it's just an internal link or not, it is still linked to other documents. The network is growing so fast that it's hard to keep track of the growth. We can look at the preferential attachment in a way that the documents that have the highest visit rate would most likely be visited again. It is just the tendency of people looking for familiar pages (Like big news channels). Google probably sorts its listings by the most popular one as the most relevant search result because it is the page that most people click and see. (We don't usually think about the term relevancy as a popularity issue; however, it is just the rate of usage of the page that determines the relevancy.) Moreover, same article would more likely to be cited again. People find their sources all over the place on the World Wide Web. There are always more links pointing to the hub; therefore, people tend to go toward the hub. I think we can also think about this as a possibility rate. Since there are more links pointing to the hub, it is more likely for people to be directed to the hubs instead of other nodes. We can look at this in the sense of a real social network. By bringing the example of the cocktail party where people meet people in a random setting. (Which is under the assumption of random network.) If we apply the scale-free network model into the cocktail party random meeting pattern, it would actually explains real life better. People do not just go into different clusters and create weak links, but people also usually just talk to certain people. These certain people are usually more social/attractive/good-looking. They become the hub. If you are at a cocktail party and everyone is talking to a social butterfly that has charming charisma, it is more likely that you would choose to talk to this social butterfly more. For latecomers to the party, they would probably choose to talk that center-of-attention person more than other people. (There can be the argument that the person is just attractive so people want to talk to him/her; however, I do believe this is a preferential attachment law in action at some sense.)
