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 power-law relationships of the Internet topology
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
Computer
BRITE: A Flexible Generator of Internet Topologies
BRITE: A Flexible Generator of Internet Topologies
On the bias of traceroute sampling: or, power-law degree distributions in regular graphs
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Evolution and Structure of the Internet: A Statistical Physics Approach
Evolution and Structure of the Internet: A Statistical Physics Approach
Evolution of Networks: From Biological Nets to the Internet and WWW (Physics)
Evolution of Networks: From Biological Nets to the Internet and WWW (Physics)
The internet AS-level topology: three data sources and one definitive metric
ACM SIGCOMM Computer Communication Review
AS relationships: inference and validation
ACM SIGCOMM Computer Communication Review
The workshop on internet topology (wit) report
ACM SIGCOMM Computer Communication Review
Orbis: rescaling degree correlations to generate annotated internet topologies
Proceedings of the 2007 conference on Applications, technologies, architectures, and protocols for computer communications
A quicker way to discover nearby peers
CoNEXT '07 Proceedings of the 2007 ACM CoNEXT conference
On the bias of traceroute sampling: Or, power-law degree distributions in regular graphs
Journal of the ACM (JACM)
Graph annotations in modeling complex network topologies
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Mobile IPv6 deployments: Graph-based analysis and practical guidelines
Computer Communications
A logic distance-based method for deploying probing sources in the topology discovery
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
Time-based sampling of social network activity graphs
Proceedings of the Eighth Workshop on Mining and Learning with Graphs
Evaluation of a new method for measuring the internet degree distribution: Simulation results
Computer Communications
Scalable Uniform Graph Sampling by Local Computation
SIAM Journal on Scientific Computing
Network verification via routing table queries
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
Network discovery and verification with distance queries
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
Review: A critical look at power law modelling of the Internet
Computer Communications
Computer Science Review
Approximate discovery of random graphs
SAGA'07 Proceedings of the 4th international conference on Stochastic Algorithms: foundations and applications
k-Dense communities in the Internet AS-level topology graph
Computer Networks: The International Journal of Computer and Telecommunications Networking
Graph reconstruction via distance oracles
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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Mapping the Internet generally consists in sampling the network from a limited set of sources by using traceroute-like probes. This methodology, akin to the merging of different spanning trees to a set of destination, has been argued to introduce uncontrolled sampling biases that might produce statistical properties of the sampled graph which sharply differ from the original ones. In this paper, we explore these biases and provide a statistical analysis of their origin. We derive an analytical approximation for the probability of edge and vertex detection that exploits the role of the number of sources and targets and allows us to relate the global topological properties of the underlying network with the statistical accuracy of the sampled graph. In particular, we find that the edge and vertex detection probability depends on the betweenness centrality of each element. This allows us to show that shortest path routed sampling provides a better characterization of underlying graphs with broad distributions of connectivity. We complement the analytical discussion with a throughout numerical investigation of simulated mapping strategies in network models with different topologies. We show that sampled graphs provide a fair qualitative characterization of the statistical properties of the original networks in a fair range of different strategies and exploration parameters. Moreover, we characterize the level of redundancy and completeness of the exploration process as a function of the topological properties of the network. Finally, we study numerically how the fraction of vertices and edges discovered in the sampled graph depends on the particular deployements of probing sources. The results might hint the steps toward more efficient mapping strategies.