Fluctuation-driven dynamics of the Internet topology

We study the dynamics of the Internet topology based on empirical data on the level of the autonomous systems. It is found that the fluctuations occurring in the stochastic process of connecting and disconnecting edges are important features of the Internet dynamics. The network's overall growth can be described approximately by a single characteristic degree growth rate g(eff) approximate to 0.016 and the fluctuation strength sigma(eff) approximate to 0.14, together with the vertex growth rate alpha approximate to 0.029. A stochastic model which incorporates these values and an adaptation rule newly introduced reproduces several features of the real Internet topology such as the correlations between the degrees of different vertices.