Linked is the title of a groundbreaking book by Prof. Barabasi on the structure of networks (see this previous post). A network is a broader concept than communication networks. A network is defined by links between actors, such as social relations (the famous ” just 6 handshakes away from everyone in the world” ), the way diseases (or ideas) are disseminated, or links between websites on the Internet.
The most interesting fact is the way links are distributed. If we would state that most people have a few relationships (links) and some people have many links, everybody would agree.
As soon as you start to define this distribution more in detail the fun starts. We tend to assume a so-called normal or Gaussian distribution (a bell-curve) . In the graph below a normal distribution is drawn.
The X-axis is the number of links a person has, the Y-axis is the percentage of persons that has this number of links.
It turns out that in reality many networks follow a different curve, a so-called power law.
The difference is visible : in a normal distribution there virtually no “nodes” with a large number of links, in a power law distribution there are.
The implication is that in most networks a significant number of supernodes exist with an incredible amount of links (if you assume a normal distribution they do NOT exist). These supernodes turn out to be extremely important for the distribution of information within and the stability of the network. They are responsible for the fact that indeed you are no more than 6 handshakes away from everybody else, usually no more than 3.
This concept explains for instance the fact that Amsterdam is considered to be an international hub (metropolis) although the city has less than 10 % of the inhabitants of a midsized Chinese city. Count the links, it is a supernode.
(more to follow)
