A map of friendships

By T.S. and G.D.

PAUL BUTLER, an intern at Facebook, has created a striking map that shows the volume of friendships between particular parts of the world. As he explains on the company's website:

I defined weights for each pair of cities as a function of the Euclidean distance between them and the number of friends between them. Then I plotted lines between the pairs by weight, so that pairs of cities with the most friendships between them were drawn on top of the others. I used a color ramp from black to blue to white, with each line's color depending on its weight. I also transformed some of the lines to wrap around the image, rather than spanning more than halfway around the world.

After a few minutes of rendering, the new plot appeared, and I was a bit taken aback by what I saw. The blob had turned into a surprisingly detailed map of the world. Not only were continents visible, certain international borders were apparent as well. What really struck me, though, was knowing that the lines didn't represent coasts or rivers or political borders, but real human relationships. Each line might represent a friendship made while travelling, a family member abroad, or an old college friend pulled away by the various forces of life.

The map is indeed surprisingly detailed, at least in the parts of the world where Facebook is widely used. A detail showing South Asia is shown above; Indonesia, which recently overtook Britain to become Facebook's second-largest market, is prominently illuminated. The parts of the world where there are few people remain in darkness, as do countries where Facebook is not the dominant social network (Brazil) or is blocked (China). For a full explanation of how the map was created, check out Mr Butler's note. His map is, of course, reminiscent of the NASA image from 2000 showing the Earth at night, in which populated areas are brightly lit. But it was derived in a completely different way.