Understanding the graph structure of the Internet is a crucial step for building accurate network models and designing efficient algorithms for Internet applications.Yet,obtaining this graph structure can be a surprisingly difficult task,as edges cannot be explicitly queried.For instance, empirical studies of the network of InternetProtocol (IP) addresses typically rely on indirect methods like trace route to build what are approximately single-source,all-destinations,shortest-path trees. These trees only sample a fraction of the network’s edges,and a paper by Lakhinaetal.[2003]found empirically that there sulting sample is intrinsically biased.Further,in simulations,they observed that the degree distribution under trace route sampling exhibits a power law even when the underlying degree distribution is Poisson.