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

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

Content Provider	ACM Digital Library
Author	Kempe, David Clauset, Aaron Achlioptas, Dimitris Moore, Cristopher
Abstract	Understanding the structure of the Internet graph is a crucial step for building accurate network models and designing efficient algorithms for Internet applications. Yet, obtaining its graph structure is a surprisingly difficult task, as edges cannot be explicitly queried. Instead, empirical studies rely on traceroutes to build what are essentially single-source, all-destinations, shortest-path trees. These trees only sample a fraction of the network's edges, and a recent paper by Lakhina et al. found empirically that the resuting sample is intrinsically biased. For instance, the observed degree distribution under traceroute sampling exhibits a power law even when the underlying degree distribution is Poisson.In this paper, we study the bias of traceroute sampling systematically, and, for a very general class of underlying degree distributions, calculate the likely observed distributions explicitly. To do this, we use a continuous-time realization of the process of exposing the BFS tree of a random graph with a given degree distribution, calculate the expected degree distribution of the tree, and show that it is sharply concentrated. As example applications of our machinery, we show how 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.
Starting Page	694
Ending Page	703
Page Count	10
File Format	PDF
ISBN	1581139608
DOI	10.1145/1060590.1060693
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2005-05-22
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Internet mapping Power laws Random graphs
Content Type	Text
Resource Type	Article

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