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(7)
Autonomic System
Internet Application
Internet Topology
Laplacian Matrix
Network Protocol
Spectral Analysis
Power Law
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Analysis of Internet Topologies: A Historical View
Analysis of Internet Topologies: A Historical View,Mohamadreza Najiminaini,Laxmi Subedi,Ljiljana Trajkovic
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Analysis of Internet Topologies: A Historical View
(
Citations: 2
)
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Mohamadreza Najiminaini
,
Laxmi Subedi
,
Ljiljana Trajkovic
Discovering properties of the
Internet topology
is important for evaluating performance of various network protocols and applications. The discovery of powerlaws and the application of
spectral analysis
to the
Internet topology
data indicate a complex behavior of the underlying network infrastructure that carries a variety of the Internet applications. In this paper, we present analysis of datasets collected from the Route Views project. The analysis of collected data shows certain historical trends in the development of the Internet topology. While values of various powerlaws exponents have not substantially changed over the recent years, spectral analysis of the normalized
Laplacian matrix
of the associated graphs reveals notable changes in the clustering of Autonomous System (AS) nodes and their connectivity.
Conference:
IEEE International Symposium on Circuits and Systems  ISCAS
, 2009
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Citation Context
(2)
...In this paper, we extend our previous analysis of the Route Views data [
8
] to include RIPE [3] datasets...
...It has also been observed that the powerlaw exponents associated with Internet topology have not substantially changed over the years in spite of the Internet exponential growth [7], [
8
]...
...These powerlaws also exhibit historical invariance [
8
]...
...In our earlier studies [
8
], [9] we employed spectral analysis to analyze the Route Views and RIPE datasets in order to find distinct clustering features of the Internet AS nodes...
...By analyzing plots of node degree vs. node rank, node degree frequency vs. degree, and eigenvalues vs. the order index, various powerlaws have been associated with Internet graph properties [4]–[6], [
8
]...
...In a recent study of the Route Views datasets [
8
], we observed the presence of powerlaws when various properties of AS nodes such as node degree and frequency of node degree were analyzed...
...For example, the dependencies between the graph eigenvalues and the eigenvalue index shown in Fig. 1 and Fig. 2 are similar to the reported graphs of the Route Views datasets [
8
]...
...On both the Route Views datasets [
8
], The connectivity graphs for Route Views and RIPE datasets indicated visible changes in the clustering of AS nodes and the AS connectivity over the period of five years [8]...
...On both the Route Views datasets [8], The connectivity graphs for Route Views and RIPE datasets indicated visible changes in the clustering of AS nodes and the AS connectivity over the period of five years [
8
]...
Laxmi Subedi
,
et al.
Spectral analysis of Internet topology graphs
...It has been observed that the powerlaw exponents associated with Internet topology have not substantially changed over the years in spite of the Internet exponential growth [11], [
12
]...
...For example, the connectivity graphs of these datasets indicate visible changes in the clustering of AS nodes and the AS connectivity over the period of five years [15], [
12
]...
...It has also been observed that the powerlaw exponents associated with the Internet topology have not substantially changed over the years in spite of the Internet exponential growth [11], [
12
], [15]...
...These powerlaws also exhibit historical invariance [
12
]...
...In reported studies [6], [
12
], [15] spectral analysis was employed to analyze the Route Views and RIPE datasets in order to find distinct clustering features of the Internet AS nodes...
...By analyzing plots of node degree vs. node rank, node degree frequency vs. degree, and eigenvalues vs. the order index, number of nodes within a number of hops vs. number of hops, various powerlaws have been associated with Internet graph properties [5], [8], [14], [
12
], [15]...
...In recent studies of the Route Views and RIPE datasets [
12
], [15] the presence of powerlaws was observed when various properties of AS nodes such as node degree Figure 1. RIPE (a) 2003 and (b) 2008 datasets: The node degree powerlaw exponents R are 20.7636 and 20.8439 for 2003 and 2008 datasets, respectively...
...For example, the dependencies between the graph eigenvalues and the eigenvalue index shown in Fig. 3 and Fig. 4 are similar to the reported graphs of the Route Views datasets [
12
]...
...The connectivity graphs for Route Views and RIPE datasets indicated visible changes in the clustering of AS nodes and the AS connectivity over the period of five years [
12
], [15]...
Ljiljana Trajkovic
.
Analysis of Internet Topologies
References
(13)
On Powerlaw Relationships of the Internet Topology
(
Citations: 2008
)
Michalis Faloutsos
,
Petros Faloutsos
,
Christos Faloutsos
Journal:
Computer Communication Review  CCR
, vol. 29, no. 4, pp. 251262, 1999
On inferring autonomous system relationships in the internet
(
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Lixin Gao
Journal:
IEEE/ACM Transactions on Networking  TON
, vol. 9, no. 6, pp. 733745, 2001
The Origin of PowerLaws in Internet Topologies Revisited
(
Citations: 289
)
Qian Chen
,
Hyunseok Chang
,
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,
Sugih Jamin
,
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,
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Conference:
IEEE INFOCOM  INFOCOM
, vol. 2, pp. 608617 vol.2, 2002
Towards capturing representative ASlevel Internet topologies
(
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)
Hyunseok Chang
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,
Walter Willinger
Journal:
Sigmetrics Performance Evaluation Review  SIGMETRICS
, vol. 30, no. 1, pp. 280281, 2002
Power laws and the ASlevel internet topology
(
Citations: 153
)
Georgos Siganos
,
Michalis Faloutsos
,
Petros Faloutsos
,
Christos Faloutsos
Journal:
IEEE/ACM Transactions on Networking  TON
, vol. 11, no. 4, pp. 514524, 2003
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Citations
(2)
Spectral analysis of Internet topology graphs
(
Citations: 1
)
Laxmi Subedi
,
Ljiljana Trajkovic
Conference:
IEEE International Symposium on Circuits and Systems  ISCAS
, pp. 18031806, 2010
Analysis of Internet Topologies
Ljiljana Trajkovic
Journal:
IEEE Circuits and Systems Magazine  IEEE CIRCUITS SYST MAG
, vol. 10, no. 3, pp. 4854, 2010