Abstract: With the size of Internet growing fast, the topology model of Internet is becoming an appealing point in research community. People make try to put deep insight into the nature of Internet topology, by constructing more models from initial Waxman random model to I3A，GLP, and PFP. A number of topology metrics were proposed, including node degree, cluster, and betweeness, to describe the topology characters. Non-extensive entropy, which is employed extensively in statistical physics,was introduced for a new Internet topology metric in this paper. It is used to depict the purity of node degree distribution. In order to evaluate the non-extensive entropy as topology metric, we analycd the consistency of BA, Waxman and real topology generated from CAIDA，by their non-extensive entropies. Finally, we argued that I3A is more in accordance with real Internet topology by comparing their non-extensive entropy, which confirms that non-extensive is fit for topology metric.

Key words: Internet,Topology model,Non-extensive entropy