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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
The web as a graph: measurements, models, and methods
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Community-oriented network measurement infrastructure (CONMI) workshop report
ACM SIGCOMM Computer Communication Review
Theoretical Computer Science - Complex networks
Exploring networks with traceroute-like probes: theory and simulations
Theoretical Computer Science - Complex networks
On unbiased sampling for unstructured peer-to-peer networks
Proceedings of the 6th ACM SIGCOMM conference on Internet measurement
Observed structure of addresses in IP traffic
IEEE/ACM Transactions on Networking (TON)
Relevance of massively distributed explorations of the internet topology: qualitative results
Computer Networks: The International Journal of Computer and Telecommunications Networking
Probabilistic heuristics for disseminating information in networks
IEEE/ACM Transactions on Networking (TON)
Recovering the Long-Range Links in Augmented Graphs
SIROCCO '08 Proceedings of the 15th international colloquium on Structural Information and Communication Complexity
A Θ( logn)-approximation for the set cover problem with set ownership
Information Processing Letters
The degree distribution of random k-trees
Theoretical Computer Science
The observable part of a network
IEEE/ACM Transactions on Networking (TON)
On unbiased sampling for unstructured peer-to-peer networks
IEEE/ACM Transactions on Networking (TON)
Lord of the links: a framework for discovering missing links in the internet topology
IEEE/ACM Transactions on Networking (TON)
Efficient measurement of complex networks using link queries
INFOCOM'09 Proceedings of the 28th IEEE international conference on Computer Communications Workshops
Recovering the long-range links in augmented graphs
Theoretical Computer Science
Sampling networks by the union of m shortest path trees
Computer Networks: The International Journal of Computer and Telecommunications Networking
Criticality analysis of Internet infrastructure
Computer Networks: The International Journal of Computer and Telecommunications Networking
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
Random dot product graph models for social networks
WAW'07 Proceedings of the 5th international conference on Algorithms and models for the web-graph
Incentive-compatible interdomain routing with linear utilities
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Time-based sampling of social network activity graphs
Proceedings of the Eighth Workshop on Mining and Learning with Graphs
TraceNET: an internet topology data collector
IMC '10 Proceedings of the 10th ACM SIGCOMM conference on Internet measurement
The impact of IXPs on the AS-level topology structure of the Internet
Computer Communications
Network science: a new paradigm shift
IEEE Network: The Magazine of Global Internetworking
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Computer Communications
Scalable Uniform Graph Sampling by Local Computation
SIAM Journal on Scientific Computing
A systematic framework for unearthing the missing links: measurements and impact
NSDI'07 Proceedings of the 4th USENIX conference on Networked systems design & implementation
Rules of thumb for information acquisition from large and redundant data
ECIR'11 Proceedings of the 33rd European conference on Advances in information retrieval
Benefits of bias: towards better characterization of network sampling
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
Network discovery and verification with distance queries
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
Computer Science Review
Estimating network layer subnet characteristics via statistical sampling
IFIP'12 Proceedings of the 11th international IFIP TC 6 conference on Networking - Volume Part I
Approximate discovery of random graphs
SAGA'07 Proceedings of the 4th international conference on Stochastic Algorithms: foundations and applications
On the incompleteness of the AS-level graph: a novel methodology for BGP route collector placement
Proceedings of the 2012 ACM conference on Internet measurement conference
k-Dense communities in the Internet AS-level topology graph
Computer Networks: The International Journal of Computer and Telecommunications Networking
Potential networks, contagious communities, and understanding social network structure
Proceedings of the 22nd international conference on World Wide Web
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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.