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.
It’s interesting to note that Russia and China (all of Central Asia, really) are almost nonexistent. As is the west coast of Australia, which is slightly more shocking. You can see a larger version of the image here.