A quantitative comparison of graph-based models for Internet topology
IEEE/ACM Transactions on Networking (TON)
Structural Graph Matching Using the EM Algorithm and Singular Value Decomposition
IEEE Transactions on Pattern Analysis and Machine Intelligence - Graph Algorithms and Computer Vision
On the Spectrum and Structure of Internet Topology Graphs
IICS '02 Proceedings of the Second International Workshop on Innovative Internet Computing Systems
On the Approximability of the Maximum Common Subgraph Problem
STACS '92 Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science
The internet AS-level topology: three data sources and one definitive metric
ACM SIGCOMM Computer Communication Review
Observing the evolution of internet as topology
Proceedings of the 2007 conference on Applications, technologies, architectures, and protocols for computer communications
Testing the reachability of (new) address space
Proceedings of the 2007 SIGCOMM workshop on Internet network management
Tuning Topology Generators Using Spectral Distributions
SIPEW '08 Proceedings of the SPEC international workshop on Performance Evaluation: Metrics, Models and Benchmarks
The flattening internet topology: natural evolution, unsightly barnacles or contrived collapse?
PAM'08 Proceedings of the 9th international conference on Passive and active network measurement
Discriminating graphs through spectral projections
Computer Networks: The International Journal of Computer and Telecommunications Networking
Mixing biases: structural changes in the AS topology evolution
TMA'10 Proceedings of the Second international conference on Traffic Monitoring and Analysis
Diversity dynamics in online networks
Proceedings of the 23rd ACM conference on Hypertext and social media
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Comparing graphs to determine the level of underlying structural similarity between them is a widely encountered problem in computer science. It is particularly relevant to the study of Internet topologies, such as the generation of synthetic topologies to represent the Internet's AS topology. We derive a new metric that enables exactly such a structural comparison: the weighted spectral distribution. We then apply this metric to three aspects of the study of the Internet's AS topology. i) We use it to quantify the effect of changing the mixing properties of a simple synthetic network generator. ii) We use this quantitative understanding to examine the evolution of the Internet's AS topology over approximately seven years, finding that the distinction between the Internet core and periphery has blurred over time. iii) We use the metric to derive optimal parameterizations of several widely used AS topology generators with respect to a large-scale measurement of the real AS topology.