Open AccessDOI
A Spectral Analysis of the Internet Topology
TLDR
The nor- malized Laplacian spectrum of AS graphs is unique in spite of the explosive growth of the Internet and distinctive in setting AS graphs apart from synthetic ones, suggesting it is an excellent candidate as a concise finger print of Internet-like graphs.Abstract:
In this paper we investigate properties of the Internet topology on the AS (autonomous system) level. Among techniques in spectral graph theory, we find the nor- malized Laplacian spectrum ( ) of AS graphs 1) unique in spite of the explosive growth of the Internet and 2) distinctive in setting AS graphs apart from synthetic ones. These prop- erties suggest that is an excellent candidate as a concise finger print of Internet-like graphs. Further analysis into the theory of leads us to a new structural classification of AS graphs with plausible inter- pretations in networking terms. Extensive analysis by AS- level data supports this claim. More importantly, along the way, new power-law relationships are unveiled, giving rise to a hybrid model encompassing both structural and power- law properties. We think that these new insights may have a profound impact on future protocol evaluation and design.read more
Citations
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Proceedings ArticleDOI
Network topology generators: degree-based vs. structural
TL;DR: It is found that network generators based on the degree distribution more accurately capture the large-scale structure of measured topologies, and an explanation is sought by examining the nature of hierarchy in the Internet more closely.
Inet-3.0: Internet Topology Generator
Jared Winick,Sugih Jamin +1 more
TL;DR: In this article, the authors present version 3.0 of Inet, an Autonomous system (AS) level Internet topology generator, which improves upon Inet-2.2 by creating topologies with more accurate degree distributions and minimum vertex covers.
Journal ArticleDOI
The internet AS-level topology: three data sources and one definitive metric
Priya Mahadevan,Dmitri Krioukov,Marina Fomenkov,Xenofontas Dimitropoulos,kc claffy,Amin Vahdat +5 more
TL;DR: An extensive set of characteristics for Internet AS topologies extracted from the three data sources most frequently used by the research community: traceroutes, BGP, and WHOIS is calculated.
Proceedings ArticleDOI
Spectral analysis of Internet topologies
TL;DR: Spectral analysis of the Internet topology at the autonomous system (AS) level is performed by adapting the standard spectral filtering method of examining the eigenvectors corresponding to the largest eigenvalues of matrices related to the adjacency matrix of the topology to suggest clusters of ASs with natural semantic proximity.
Journal ArticleDOI
Topological properties of high-voltage electrical transmission networks
TL;DR: In this paper, the topological properties of high-voltage electrical power transmission networks in several UE countries (the Italian 380 kV, the French 400 kV and the Spanish 400kV networks) have been studied from available data.
References
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Book
Spectral Graph Theory
TL;DR: Eigenvalues and the Laplacian of a graph Isoperimetric problems Diameters and eigenvalues Paths, flows, and routing Eigen values and quasi-randomness
Proceedings ArticleDOI
On power-law relationships of the Internet topology
TL;DR: These power-laws hold for three snapshots of the Internet, between November 1997 and December 1998, despite a 45% growth of its size during that period, and can be used to generate and select realistic topologies for simulation purposes.
Journal ArticleDOI
Routing of multipoint connections
TL;DR: In this article, a weighted greedy algorithm is proposed for a version of the dynamic Steiner tree problem, which allows endpoints to come and go during the life of a connection.
Journal ArticleDOI
Modeling Internet topology
TL;DR: This article discusses how graph-based models can be used to represent the topology of large networks, particularly aspects of locality and hierarchy present in the Internet.
Journal ArticleDOI
The Laplacian spectrum of a graph
TL;DR: In this paper, the Laplacian matrix of a graph G = D(G) - A(G), where G is a graph and A is the adjacency matrix of vertices, is investigated.