On the bias of traceroute sampling: Or, power-law degree distributions in regular graphs

Abstract

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 <i>traceroute</i> 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 that the degree distribution under traceroute sampling exhibits a power law even when the underlying degree distribution is Poisson. 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 &#916;-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.

DOI: 10.1145/1538902.1538905

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@article{Achlioptas2005OnTB, title={On the bias of traceroute sampling: Or, power-law degree distributions in regular graphs}, author={Dimitris Achlioptas and Aaron Clauset and David Kempe and Cristopher Moore}, journal={J. ACM}, year={2005}, volume={56}, pages={21:1-21:28} }