Guido Caldarelli

Universita' di Roma I

 

The fractal properties of Internet

Networks and web 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, 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 optimize the number of points connected with respect to the length of the web and with respect to the amount of material or information transferred. In this paper we provide a measure of the Internet web, by using the theoretical framework introduced for the statistical mechanics of the river networks. The connections between users and providers that link all the world web are studied and modeled as branches of a world spanning tree. Here we show that the Internet web, from a user's perspective, manifests robust scaling properties of the type$ P(n) \propto n^{-t}$ where n is the size of the basin connected to a given point, P represents the density of probability of finding n points uphill and $t\simeq 1.9$ is a characteristic universal exponent.

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