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This paper reports some observations on the relationships between three measures of the size of the Internet over more than ten years. The size of the BGP4 routing table, the number of active BGP4 Autonomous Systems, and a lower bound on the total size of the Internet, appear to have fairly simple relationships despite the Internet's growth by two orders of magnitude. In particular, it is observed that the size of the BGP4 system appears to have grown approximately in proportion to the square root of the lower-bound size of the globally addressable Internet. A simple model that partially explains this square law is described.
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