Non-Gaussian behavior of the internet topological fluctuations

The traditional Gibrat's hypotheses were once used to model the topological fluctuations of Internet. Although it seems to reproduce the scaling relation of Internet's degree distribution, the detailed micro-dynamics have never been empirically validated. Here, we analyze the distribution of degree growth rates of the Internet for various time scales. We find that in contrast to the traditional Gibrat's assumptions, none of the degree growth rates are normally distributed, but behaves as an exponential decrease on its body and a power-law decay on its tail. Moreover, the observed growth rate distribution turns out independent of the initial degree when the time interval enlarges to a year. Our observations do not consist with the traditional Gibrat law model and suggest a more complex fluctuation mechanism underlying the evolution of Internet.