## Friday, June 19, 2009

### Distance matters: Facebook contacts have a scale-invariant spectrum

The physics arXiv blog has brought our attention to a paper that seems pretty interesting to me:
Goldenberg, Levy: Distance Is Not Dead: Social Interaction and Geographical Distance in the Internet Era
We often like to say that the Internet has made our blue planet smaller by simplifying the geographically distant relationships. We live in a global village, and so on.

However, what is often neglected in these popular clichés is that the Internet has also simplified the local relationships. And in fact, the computers have also simplified our ability to distinguish the nearby contacts from the distant ones. We have good reasons to prefer the local ones in many contexts because they can be coupled to physical interactions and the same interests in local events.

As a result, our focus actually became relatively more local and less global, since the first moments when the communication over arbitrary distances became acceptably doable and cheap.

The figure above summarizes the best power law fit for the number of Facebook contacts, written as a distribution "f(r)dr" with respect to the distance "r" in miles. You can see that the distribution goes essentially as "1/r": their exponent is "-1.03" which is very close to minus one.

This is an interesting exponent because "dr/r" is the same thing as "d ln(r)". It means that the number of contacts is the same for every "decade".

One has N contacts between 1 and 10 miles, N contacts between 10 and 100 miles, N contacts between 100 and 1,000 miles, and perhaps N contacts between 1,000 and 10,000 miles. In this sense, the map of the contacts is statistically self-similar, at least if you neglect far infrared effects such as the finiteness of the Earth that fails to be flat. ;-)

We are thinking hierarchically and we tend to be equally interested in every level of the hierarchy that we belong to. If you wish, a part of my interest goes to Pilsen, an equally large part to the rest of Western Bohemia, another part to the rest of Bohemia, another part to Central Europe, another part to Europe, and so on.

(No, I haven't yet created a Facebook account. With Twitter, I would like be a canonical example of their reactionary "traitor" users, for reasons that look very sensible to me.)