Fluctuation-driven dynamics of the Internet topology

We study the dynamics of the Internet topology based on the empirical data on the level of the autonomous systems. It is found that the fluctuations occurring in the edge creation are important features of the dynamics of the Internet topology. The degree growth rates fluctuate in time with different characteristics for each vertex. Overall growth can be described approximately by a single growth rate $g_{0} \approx 0.016$ with standard deviation $\sigma_{0} \approx 0.14$. From this, the exponent $\gamma$ of the power-law in the degree distribution is determined to be $\gamma \approx 2.09$, close to the value $\gamma \approx 2.15$ directly measured.