Topology connectivity analysis of internet infrastructure using graph spectra

Çetinkaya, Egemen K.; Alenazi, Mohammed J. F.; Rohrer, Justin P.; Sterbenz, James P. G.

doi:10.1109/icumt.2012.6459764

Cited by 25 publications

(26 citation statements)

References 28 publications

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“…We calculate the spectral radius of the normalised Laplacian matrix ρ(L) shown in column 6 of Table 5. We note that we previously studied spectral radii of Laplacian matrices ρ(L) and adjacency matrices ρ(A), but did not observe any pattern for ρ(L) and ρ(A) [19].…”

Section: Flow Robustness and Spectral Propertiesmentioning

confidence: 53%

“…First, we analyse the normalised Laplacian spectra of several commercial and research networks and find that fibre topologies are structurally similar to other critical infrastructures such as freeways. In our earlier work, we show this by examining only two commercial networks [19], in this study we expand this to six networks. Second, we show that physical level topologies can be modelled by Gabriel graphs [35], since both are grid-like structures.…”

Section: Introductionmentioning

confidence: 96%

“…Acknowledgements This is a significantly extended version and substantial revision of papers that appeared in the 4th IEEE/IFIP International Workshop on Reliable Networks Design and Modeling (RNDM) 2012 [19] …”

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confidence: 99%

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Multilevel resilience analysis of transportation and communication networks

et al. 2015

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For many years the research community has attempted to model the Internet in order to better understand its behaviour and improve its performance. Since much of the structural complexity of the Inter- net is due to its multilevel operation, the Internet's multilevel nature is an important and non-trivial feature that researchers must consider when developing appropriate models. In this paper, we compare the normalised Laplacian spectra of physical-and logical-level topologies of four commercial ISPs and two research networks against the US freeway topology, and show analytically that physical level communication networks are structurally similar to the US freeway topology. We also generate synthetic Gabriel graphs of physical topologies and show that while these synthetic topologies capture the grid-like structure of actual topologies, they are more expensive than the actual physical level topologies based on a network cost model. Moreover, we introduce a distinction between geographic graphs that include degree-2 nodes needed to capture the geographic paths along which physical links follow, and structural graphs that eliminate these degree-2 nodes and capture only the interconnection properties of the physical graph and its multilevel relationship to logical graph overlays. Furthermore, we develop a multilevel graph evaluation framework and analyse the resilience of single and multilevel graphs using the flow robustness metric. We then confirm that dynamic routing performed over the lower levels helps to improve the performance of a higher level service, and that adaptive challenges more severely impact the performance of the higher levels than non-adaptive challenges.

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Section: Flow Robustness and Spectral Propertiesmentioning

confidence: 53%

Section: Introductionmentioning

confidence: 96%

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Multilevel resilience analysis of transportation and communication networks

et al. 2015

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“…The largest eigenvalue, i.e., the spectral radius, of a graph is an important graph parameter [14]. Cetinkaya et al [15,16] correlated the graph diversity with the spectral radius of the normalized Laplacian spectrum (NLS). Additionally, comparing with the spectral radii of adjacency and Laplacian spectra, Cetinkaya et al [15,16] found that the spectral radius of the NLS is an ideal measure for comparing the connectivity of graphs with different sizes.…”

Section: Introductionmentioning

confidence: 99%

Accurately and quickly calculating the weighted spectral distribution

Nie

Shi

et al. 2015

Telecommun Syst

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The weighted spectral distribution (WSD) is a measure defined on the normalized Laplacian spectrum. It can be used for comparing complex networks with different sizes (number of nodes) and provides a sensitive discrimination of the structural robustness of complex networks. In this paper, we design an algorithm for the accurate calculation of the WSD in large-scale complex networks by utilizing characteristics of the graph structure. As an extension to Sylvester's Law of Inertia for the calculation of the WSD based on spectral characteristics, our algorithm exhibits a higher time efficiency when applied to large-scale complex networks.

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“…Logical topology includes collecting, measuring and analysis of parameters on IP level. Physical topology includes defining physical connection, which is one of the main research challenges [1].…”

Section: Introductionmentioning

confidence: 99%