ordered/random network.
From the reading of Barabasi, the goal of graph theory can be considered as an aim to discover and catalogue the properties of the various graphs. I would like to see the formation of random graphs as a process of finding simple solution to a complex system.
It is suggested that when the nodes are randomly placed and connected, each node will have approximately same amount of links. This is considered to be a random network. However, of course, it is necessary for each node to be at least connecting to one link to begin the clustering emergence. On the other hand, a random network would act different. The theory behind random network is that the average number of links per node increases beyond the critical one, the number nodes left out of the giant cluster decreases exponentially. The more nodes that exist in the network, the least likely it is for us to find an isolated node. From the example of the cocktail party where clusters of strangers move around and have interaction with other clusters to create a weak link that connects each cluster. Maybe the density of connection is not as important; however, each cluster is connected to one another in a way. Our society is democratic because everyone’s link average out and deviate the norm in order for the society to happen.
Talking about the Weak ties in the cocktail party, it raises the point of small world networks in a sense that people are connected more so by the weak ties instead of the familiar first degree connections. Most of the people find jobs and find their “connection” in society through those weak ties. The weak ties are considered the people that belong to another cluster. This may sound like a weird idea that people actually get useful and helpful information not from the closest connection. This is because the people in the same cluster would have the same source for information. There would be no point getting help from them because you know everything they do. Our society is a collection of complete graphs. Different fields/groups are connected to one another by something.
From the entry The small worlds of They Rule posted by Laura in the Connectives, the website They Rule excellently illustrate the idea of the random network and how different groups of cluster connects to one another. We can see how each company is connected to another in a glance.
