On distinguishing between Internet power law topology generators

Recent work has shown that the node degree in the WWW induced graph and the autonomous system (AS) level Internet topology exhibit power laws. Since then, several algorithms have been proposed to generate such power law graphs. We evaluate the effectiveness of these generators to generate representative AS-level topologies. Our conclusions are mixed. Although they (mostly) do a reasonable job at capturing the power law exponent, they do less well in capturing the clustering phenomena exhibited by the Internet topology. Based on these results, we propose a variation of the recent incremental topology generator of R. Albert and A. Barabasi (see Phys. Rev. Letters, vol.85, p.5234-7, 2000) that is more successful at matching the power law exponent and the clustering behavior of the Internet. Last, we comment on the small world behavior of the Internet topology.