The above map of the world, drawn by Facebook data structuring intern Paul Butler using connections between 10 million Facebook friends , is interesting enough in itself until you realize that all of the country borders are entirely drawn using Facebook friend connections too. Even if the world was dark and totally unmapped, Facebook could produce a remarkably good approximation of most of its continents’ boundaries, and even the borders of some countries.
It still took some clever math. Butler explains how he did it:
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.
Later I replaced the lines with great circle arcs, which are the shortest routes between two points on the Earth. Because the Earth is a sphere, these are often not straight lines on the projection.
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 traveling, a family member abroad, or an old college friend pulled away by the various forces of life.