I use this blog as a soap box to preach (ahem... to talk :-) about subjects that interest me.

Thursday, March 8, 2012

More on visitors to this blog

My second-last article showed that the countries of people who visit this blog form a small-world network. To prove it, I plotted the number of countries versus their number of unique visitors and showed that it resulted in a power-law dependency.

But what if you simply rank the countries on the basis of their number of visitors and then plot the number of visitors per country against the country ranks?

I didn't really know what to expect. I knew in advance that the points would run from top left to bottom right, because the highest ranks (1, 2, ...) are for countries with large numbers of visitors, while the lowest ranks are for countries with small numbers of visitors. That was a direct consequence of how I had defined the ranking. I also knew that I would have many more points for the lower ranks. But why should there be a relationship between the number of visitors of a country and its rank? A rank seems such an ad-hock number...

If the points aligned along a curve, it would imply the presence of some sort of correlation among the countries, which seems preposterous.

Guess what? the plot turns out to be a power law:

N(R) = 1524.4 * R-1.1685

With R = number-of-visitors rank and N = number of visitors.

If you choose any pair of countries R1 and R2, you obtain:

N1/N2 = (R1/R2) -1.1685

If the exponent where -1, you would have straight inverse proportionality: double the rank and you half the number of visitors. As it is, The number of visitors decreases a bit more rapidly: when you double the rank, you get a bit less than half the number of visitors (~0.445). And this happens in the same way for, say, ranks 3 and 6 as for ranks 10 and 20 or 50 and 100.

What is the meaning of this? Some deeper understanding is required...

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