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 Internet Protocol (IP) addresses typically rely on indirect methods like traceroute 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 Lakhina et al. [2003] found empirically that the resulting sample is intrinsically biased. Further, in simulations, they observed A preliminary version of this article appeared in In this article, we study the bias of traceroute sampling mathematically and, for a very general class of underlying degree distributions, explicitly calculate the distribution that will be observed. As example applications of our machinery, we prove that traceroute sampling finds power-law degree distributions in both δ-regular and Poisson-distributed random graphs. Thus, our work puts the observations of Lakhina et al. on a rigorous footing, and extends them to nearly arbitrary degree distributions.
Achlioptas et al. used this powerful idea in REF to study the bias of traceroute sampling in random graphs with a given degree distribution.
On the bias of traceroute sampling: Or, power-law degree distributions in regular graphs
JACM
Physics Computer Science Mathematics