Temporal fractal structures: origin of power laws in the world-wide Web

Using numerical simulations and scaling theory we study the dynamics of the world-wide Web from the growth rules recently proposed in Tadić (Physica A 293 (2001) 273) with appropriate parameters. We demonstrate that the emergence of power-law behavior of the out- and in-degree distributions in the Web involves occurrence of temporal fractal structures that are manifested in the scale-free growth of the local connectivity and in first-return time statistics. We also show how the scale-free behavior occurs in the statistics of random walks on the Web, where the walkers use information on the local graph connectivity.