Revealing the fractal and self-similarity of realistic collective human mobility

Revealing the fractal scaling laws of collective human mobility is benefit to understand the complexity of collective human mobility behaviours and has broad application prospects, such as infectious disease prevention, because fractal networks are potentially more robust against targeted attacks than non-fractal networks. Although many statistical indicators of individual human mobility had been observed in power-law distributions, there is still no evidence so far to verify the fractal or self-similarity of collective human mobility behaviours. This study uncovered the fractal and self-similarity properties on realistic weighted human mobility networks at world-, nation-, and city-wide scales. After observing the necessary conditions of network fractal, i.e., the evident power-law probability distributions of weight-related metrics, the fractal dimensions of weighted human mobility networks were measured to be about 0.67 similar to 0.88. Furthermore, experimental results demonstrated their distinct statistical self-similarity and approximately structural self-similarity. These exciting findings can enhance the fire-new understandings of collective human mobility behaviours, and provide novel solutions for many real-world applications.