The Laplacian spectrum of a graph
SIAM Journal on Matrix Analysis and Applications
On power-law relationships of the Internet topology
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
Proceedings of the 2001 conference on Applications, technologies, architectures, and protocols for computer communications
On the origin of power laws in Internet topologies
ACM SIGCOMM Computer Communication Review
IEEE Communications Magazine
Investigation and application of Laplace spectra of orgraphs with the ring structure
Automation and Remote Control
Spectral geometry for simultaneously clustering and ranking query search results
Proceedings of the 31st annual international ACM SIGIR conference on Research and development in information retrieval
Spectral Properties of Adjacency and Distance Matrices for Various Networks
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part II
The observable part of a network
IEEE/ACM Transactions on Networking (TON)
Connectivity Measures for Internet Topologies on the Level of Autonomous Systems
Operations Research
A weighted spectrum metric for comparison of internet topologies
ACM SIGMETRICS Performance Evaluation Review
Weighted spectral distribution for internet topology analysis: theory and applications
IEEE/ACM Transactions on Networking (TON)
Ring structure digraphs: Spectrum of adjacency matrix and application
Automation and Remote Control
Analysis of internet topologies
IEEE Circuits and Systems Magazine - Special issue on complex networks applications in circuits and systems
Scalable Uniform Graph Sampling by Local Computation
SIAM Journal on Scientific Computing
Computer Science Review
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In this paper we study properties of the Internet topology on the autonomous system (AS) level. We find that the normalized Laplacian spectrum (nls) of a graphpro vides a concise fingerprint of the corresponding network topology. The nls of AS graphs remains stable over time in spite of the explosive growth of the Internet, but the nls of synthetic graphs obtained using the state-of-the-art topology generator Inet-2.1 is significantly different, in particular concerning the multiplicity of eigenvalue 1. We relate this multiplicity to the sizes of certain subgraphs and thus obtain a new structural classification of the nodes in the AS graphs, which is also plausible in networking terms. These findings as well as new power-law relationships discovered in the interconnection structure of the subgraphs may lead to a new generator that creates more realistic topologies by combining structural and power-law properties.