The dataset contains friendship connections of Spanish users and their city of residence. After some preprocessing of the data done by David in Phyton they obtained a network of cities with weights encoding the number of friendships between cities.
Then all that was left to do was to obtain the geo-coordinates of these cities (which you found here), choose a colormap and draw a line between every pair of cities with more than 50 inter-city connections (the choice of 50 is arbitrary but a good compromise between computation time and visual effects).
If one draws the edges by decreasing distance as described by Paul Butler in this blog entry and encode the euclidean distance between the nodes in the colour of the edges, Matlab does the rest. No magic needed.
