The diameter of a cycle plus a random matching
SIAM Journal on Discrete Mathematics
Generating functionology
Hypergeometric functions and their applications
Hypergeometric functions and their applications
Randomized algorithms
A critical point for random graphs with a given degree sequence
Random Graphs 93 Proceedings of the sixth international seminar on Random graphs and probabilistic methods in combinatorics and computer science
On routes and multicast trees in the Internet
ACM SIGCOMM Computer Communication Review
On power-law relationships of the Internet topology
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
On the marginal utility of network topology measurements
IMW '01 Proceedings of the 1st ACM SIGCOMM Workshop on Internet Measurement
Heuristically Optimized Trade-Offs: A New Paradigm for Power Laws in the Internet
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
The Size of the Giant Component of a Random Graph with a Given Degree Sequence
Combinatorics, Probability and Computing
Measuring ISP topologies with rocketfuel
IEEE/ACM Transactions on Networking (TON)
DIMES: let the internet measure itself
ACM SIGCOMM Computer Communication Review
Understanding internet topology: principles, models, and validation
IEEE/ACM Transactions on Networking (TON)
Exploring networks with traceroute-like probes: theory and simulations
Theoretical Computer Science - Complex networks
Relevance of massively distributed explorations of the internet topology: qualitative results
Computer Networks: The International Journal of Computer and Telecommunications Networking
Describing and simulating internet routes
Computer Networks: The International Journal of Computer and Telecommunications Networking
The web as a graph: measurements, models, and methods
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Bias reduction in traceroute sampling - towards a more accurate map of the internet
WAW'07 Proceedings of the 5th international conference on Algorithms and models for the web-graph
Estimating and sampling graphs with multidimensional random walks
IMC '10 Proceedings of the 10th ACM SIGCOMM conference on Internet measurement
Correcting for missing data in information cascades
Proceedings of the fourth ACM international conference on Web search and data mining
Evaluation of a new method for measuring the internet degree distribution: Simulation results
Computer Communications
Impact of sources and destinations on the observed properties of the internet topology
Computer Communications
Walking on a graph with a magnifying glass: stratified sampling via weighted random walks
Proceedings of the ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
Topology discovery of sparse random graphs with few participants
Proceedings of the ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
Walking on a graph with a magnifying glass: stratified sampling via weighted random walks
ACM SIGMETRICS Performance Evaluation Review - Performance evaluation review
Topology discovery of sparse random graphs with few participants
ACM SIGMETRICS Performance Evaluation Review - Performance evaluation review
A fast algorithm to find all high degree vertices in power law graphs
Proceedings of the 21st international conference companion on World Wide Web
A fast algorithm to find all high degree vertices in graphs with a power law degree sequence
WAW'12 Proceedings of the 9th international conference on Algorithms and Models for the Web Graph
A compact routing scheme and approximate distance oracle for power-law graphs
ACM Transactions on Algorithms (TALG)
Characterizing branching processes from sampled data
Proceedings of the 22nd international conference on World Wide Web companion
Shortest-path queries in static networks
ACM Computing Surveys (CSUR)
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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 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 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.