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

Saturday, March 3, 2012

The small world of this blog

In August 2010, I published in this blog an article titled Network of Feedbacks on eBay.

In that article, I explained that a small-world network is a network in which some large nodes (called "hubs") with a lot of links reduce the average number of links you need to go through in order to connect all nodes with each other. I also said that the relationship between the N number of nodes with a given L number of links follows a power law of the form

N = A x Lg

where A is a constant.

I showed that the network formed by a sample of people giving and receiving feedback on eBay is a small-world network with g = -1.526.

On Christmas day last year, I decided that the time had come to check whether the visitors to my blog (i.e., You) formed a small-world network.

To do so, I considered each country as a node, and grouped the 122 countries from which I had received visits according to the number of unique visitors (at the time, a total of 5790). To compensate for the fact that there were many countries with few visitors and few countries with lots of visitors ( the hubs), I chose intervals that had a doubling upper value: 1 to 10, 11 to 20, 21 to 40, 41 to 80, 81 to 160, 161 to 320, 321 to 640, 641 to 1280, and 1281 to 2560. Then, to plot the intervals, I chose an abscissa that was in the middle of each interval on a logarithmic scale: L = exp((ln(Xmax) + ln(Xmin))/2).

This resulted in the following table of values:

L 3.16 14.83 28.98 57.27 113.84 226.98 453.25 905.80 1810.90

and the following plot:

As you can see, the coefficient of determination R2 is quite close to 1. This means that the number of countries vs. their number of visitors of this blog well approximates a power law, which in turns indicates that my visitors belong to a small world.

When I sampled the data, the countries with at least 100 visitors were: the USA (the most WWW-active country in the English speaking world), Australia (my home country), India (1 Gpeople and English speaking), the UK (large English-speaking country), Germany, Canada (largish English-speaking country), Italy, France, and Spain.

The high number of visitors from Germany, Italy, and France can perhaps at least in part be explained by the fact that I lived in those countries and actually grew up in Italy. Therefore, I have several contacts in each one of them.

I have no explanation of why more than 100 Spaniards, a comparatively small nation and non-English speaking, visited my blog.

But the reasons why those countries are hubs of people interested in my blog are immaterial. They exists and the size of the nodes follows a power-law distribution. The fact that the sample for the largest hubs is statistically poor, will probably cause changes in the slope as more visitors discover my blog, But that doesn't change the basic result.

Therefore, to all new visitors who are reading this article, I would like to say:

Welcome to my small world!

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