I'm missing a bit of inbetween-math, and having some trouble understanding this, but:
I want to generate a set of data that follows a power law. Let's say I have 10,000,000 people who like a power-law-distribution of 1,000,000 items, sorted into groups by popularity. Could someone give me an example of/explain to me:
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How many people like the 25 most-popular items? How many like the next 50 most-popular items? How many like the next 100? Etc. In simplest-terms/math possible, how do I calculate the number of liked-items for person-N?
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Could you break this down for me a bit? Is there a more specific description of what kind of power law this graph follows?
I apologize for my lack of background-knowledge here–I'm coming from a non-mathematical background. Thanks!
Best Answer
Power law is a ranked distribution. Let us assume that we have the twitter personalities on the x-axis and the number of followers they have on the y-axis. The distribution is plotted in such a way that the personality with the highest number of followers is introduced on the first position of the x-axis, the personality with the second highest number of followers is introduced on the second position of the x-axis, so on and so forth, and the last personality on the x-axis has the least number of followers.
The plot can be modeled as y = C(x^-a) Apply log on both sides : log(y) = log(C) - a.log(x) -a is the slope the line and C is some control parameter. substitute the ranked numerical user id (for twitter personality) at 'x', and set the C and -a values. This results in mapped 'y' (number of twitter followers) value.
Ref: http://www.hpl.hp.com/research/idl/papers/ranking/ranking.html#ap1