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In this paper, the authors investigate the evolution of the IPv4 and IPv6 Internet topologies at the Autonomous System (AS) level over a long period of time. They provide abundant empirical evidence that there is a phase transition in the growth trend of the two networks. For the IPv4 network, the phase change occurred in 2001. Before then the network's size grew exponentially, and thereafter it followed a linear growth. Changes are also observed around the same time for the maximum node degree, the average node degree and the average shortest path length.
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