The fractal properties of Internet

PACS. 05.10.-a – Computational methods in statistical physics and nonlinear dynamics. PACS. 92.40.Fb – Rivers, runoff, and streamflow. Abstract. – In this paper we show that the Internet web, from a user’s perspective, manifests robust scaling properties of the type P (n) ∝ n −τ,wheren is the size of the basin connected to a given point, P represents the density of probability of finding n points downhill and τ =1.9 ± 0.1 s a characteristic universal exponent. This scale-free structure is a result of the spontaneous growth of the web, but is not necessarily the optimal one for efficient transport. We introduce an appropriate figure of merit and suggest that a planning of few big links, acting as information highways, may noticeably increase the efficiency of the net without affecting its robustness. Networks are present in many aspects of everyday life, from the watershed where the rivers water is collected, to the veins and lymphatic channels that distribute blood and nutrition in animals and plants 1, 2, to the telephone or electricity or internet webs that transport in our houses the services we need. In all these cases, the network properties should be such to optimise some cost function, as, for example, the number of points connected with respect