Ok, let’s get the basics down when it comes to networks most of the knowledge starts with Leonard Euler and a mathematical problem called the Konigsberg Bridge Problem back in 1736. There is a great historical description of Euler’s work and then the two guys Erdos and Renyi who came along in the 1950’s in a book by three legends in networks The title is Structure and Dynamics of Networks ( http://www.amazon.com/Structure-Dynamics-Networks-Princeton-Complexity/dp/0691113572 ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1216137076&sr=1-1 ) by Mark Newman Laszlo Barabasi and Ducan Watts. Be prepared to do a little math to get through this one but it is worth it. If you want a less mathematical book to start with I highly reccomend Linked by Laszlo Barabasi.
These guys set the stage for what may be to key to the web and what really motivates google (by the way search is secondary) . Back to networks at first most of the work was around directed graphs by that I mean a bunch of point or nodes that are connected by lines or edges. Now when it comes to the web direction is very important. If you think of each of these nodes as a web site and each of the lines or edges as a link then the direction of the link is very very important.
So at first everyone was interested in random graphs, and that is a graph where the likelihood that a edge hits or terminates at your node is about equal to that hitting any other node. Not alot of difference from one node, point or web site than anyone elses. Not very interesting for the average web person is it? If you answered yes then keep on reading if you think that this idea of a random graph (that is what it is called ) is very interesting then there is a lot of reading out there on random graphs(http://tinyurl.com/8lmx9) and what makes them special. Now don’t get me wrong I like a random graph as much as the next guy, I just really like something call a Free-Scale Graph much more.
The most outastnding feature of random graphs is that if a node is taken out the effect on the network is minimal. This is not the case with Free Scale Networks. Free Scale networks are exactly that a network that is free of scale. I know you are thinking what the heck does that mean, well I will tell you. In a randow network the number of connections any one node has is roughly the same in fact if you were to graph them you would get a normal distribution. An example from the book Linked is if you were to graph the hieght of human beings the graph would be on the one end heights of 4 feet to the other end of the graph somewhere around 7 feet with a mean around 6 feet. If this was a free of scale network you may have a person at 40 feet and another at 1 foot, there would not be a uniform distribution. What this means for the internet is that some web sites (remember nodes) will have only one link to the site and another like Facebook or Myspace a hundred million links to the site.
Now if you read the papers in the Structure and Dynamics of Networks book you will find that a free scale network obeys what is called a power law, more on this later.
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