- 页码：第22页 2018-12-10 23:49:01
P.21: The premise of random network model is deeply egalitarian: We place the links completely randomly; thus all nodes have the same chance of getting one.
If the network is large, despite the links' completely random placement, almost all nodes will have approximately the same number of links.
One way is to interview all guests as they leave the cocktail party, asking them how many acquaintances they made. When everybody leaves, we can draw a histogram by plotting how many of the guests have one, two or exactly k new acquaintances. For random network model of Erodos and Renyi the shape of the histogram was derived and proved exactly in 1982, one of Erodos's students, Bela Bolobas, professor of mathematics at the University of Memphis in the United States and Trinity College in the United Kingdomg. The result shows that the histogram follows a Poisson distribution. A poisson distribution has a prominent peak, indicating that the majority of nodes have the same number of linkes as the average node does.
It predicts that it is exponentially rare to find someone who deviateds from the average by having considerably more or fewer links than average. Therefore, we end up with an extremely democratic society.
ER's random universe is dominated by the average.
P.23 They never planned to provide a universal theory of network formation. They were far more intrigued by the mathematical beauty of random networks than by the model’s ability to faithfully capture the webs nature created around them.
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