I read this paper from cmu about powerlaw graph generation. But I was unable to understand the equation given in section 3.3 for Expected number of nodes with degree k. Can someone please explain the equation in detail.
Will be thankful if you can point to resource to read about binomial cascading.
http://repository.cmu.edu/cgi/viewcontent.cgi?article=1541&context=compsci
My best idea on how to help you get some sense of what they are doing is referring you to my work in S-convexity, since it has to do with percentages. You will notice that we have (1-x) and x, basically. That is what you have there. We also have an exponent there. It is just that it is between 0 and 1, so that the effects would be the opposite to what you get there. Notice that a fraction between 0 and 1 will increase if raised to a fraction between 0 and 1, so say 1/4 becomes 1/2 if raised to 1/2. A normal number, however, above 1, will decrease with the fractional exponent and increase with a normal one, which is what you have. It seems to me that they must have played with a basic expression and the data they had to get to this formula, so that it is not really something you can translate easily into an explanation. Have you asked the own authors? That would be my first intuition: That you should ask them this question. Researchers could be like myself and be willing, at that moment of their earthly existence, to give you all attention on earth. You may be lucky. Never know.
Thank you Lago Augusto Carvalho and Marcia Ricci Pinheiro for your response. It helped.
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