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Statistical theory of Internet exploration.
Luca Dall'asta1, Ignacio Alvarez-Hamelin, Alain Barrat
1Laboratoire de Physique Théorique, Bâtiment 210, Université de Paris-Sud, 91405 ORSAY Cedex, France.
Summary
Internet mapping uses data packets to create network graphs. This study reveals map accuracy depends on network topology, with heterogeneous networks being better represented.
Area of Science:
- Computer Science
- Network Science
- Graph Theory
Background:
- Internet mapping often uses Internet tomography, merging discovered paths to represent network topology.
- The statistical reliability of these empirical network maps is a critical, yet often overlooked, issue.
Purpose of the Study:
- To analyze the statistical reliability and potential sampling biases in Internet mapping techniques.
- To understand how network topology influences the accuracy of empirical Internet maps.
Main Methods:
- Modeling the network sampling process on synthetic graphs.
- Employing a mean-field approximation to derive probabilities of edge and vertex detection.
- Conducting numerical investigations of simulated mapping strategies on diverse network models.
Main Results:
- Derived expressions for edge and vertex detection probabilities, clarifying sampling bias origins.
- Established a direct relationship between map accuracy and network topological properties, specifically betweenness centrality.
- Demonstrated that statistically heterogeneous network topologies are more accurately captured than homogeneous ones.
Conclusions:
- The statistical accuracy of Internet maps is fundamentally linked to the underlying network's topology.
- Understanding topological influences is crucial for improving the reliability of Internet mapping techniques and mitigating sampling biases.