Scale-free human migration and the geography of social networks

The "gravitational law of social interaction", by which the probability of a social link decreases inversely with the square of the geographic distance, has been recently documented. The source of this spatial property of social networks, however, is yet unknown. The formation of social links is related to human dynamics both on the day-to-day, typically small scale, level of mobility, and on larger scale migration (or reallocation) movements. In this study we analyze human migration patterns by investigating the migration of 46.8 million individuals across the US during 19952000. We find that the probability of migration decreases as a power law of the distance, with exponent -1. We show that this finding offers an explanation for the gravitational law of social interaction. Possible explanations and implications of the scale-free migration pattern are discussed.