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The Internet AS level topology, upon which BGP4 runs, plays a vital role in the analysis and study of the global routing behavior. However, the study of the topology itself is not as comprehensive and extensive as the protocol. In this paper, the inherent local connectivity preference nature of the Internet AS level topology is studied from several perspectives. The presence of strong local connectivity preference in the AS graph is quantitatively verified along with the demonstration of the weakness for PFP model-which is regarded as the most accurate Internet AS level topology generator to date-to capture it. A locality-driven PFP(LDPFP) model is proposed to capture the local connectivity preference feature of the AS graph.