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Despite significant efforts to obtain an accurate picture of the Internet's connectivity structure at the level of individual autonomous systems (ASes), much has remained unknown in terms of the quality of the inferred AS maps that have been widely used by the research community. In this paper, we assess the quality of the inferred Internet maps through case studies of a sample set of ASes. These case studies allow us to establish the ground truth of connectivity between this set of ASes and their directly connected neighbors. A direct comparison between the ground truth and inferred topology maps yield insights into questions such as which parts of the actual topology are adequately captured by the inferred maps, which parts are missing and why, and what is the percentage of missing links in these parts. This information is critical in assessing, for each class of real-world networking problems, whether the use of currently inferred AS maps or proposed AS topology models is, or is not, appropriate. More importantly, our newly gained insights also point to new directions towards building realistic and economically viable Internet topology maps.