—The topology of the Internet has been extensively studied in recent years, driving a need for increasingly complex measurement infrastructures. These measurements have produced detailed topologies with steadily increasing temporal resolution, but concerns exist about the ability of active measurement to measure the true Internet topology. Difficulties in ensuring the accuracy of every individual measurement when millions of measurements are made daily, and concerns about the bias that might result from measurement along the tree of routes from each vantage point to the wider reaches of the Internet must be addressed. However, early discussions of these concerns were based mostly on synthetic data, oversimplified models or data with limited or biased observer distributions. In this paper, we show the importance that extensive sampling from a broad distribution of vantage points has on the resulting topology and bias. We present two methods for designing and analyzing the topology c...