analysis and visualization of large scale networks using...
TRANSCRIPT
![Page 1: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/1.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
Analysis and visualization of large scalenetworks using the k -core decomposition
J. Ignacio Alvarez-Hamelin∗
Luca Dall’Asta∗
Alain Barrat∗
Alessandro Vespignani†∗
∗Laboratoire de Physique Théorique, Université Paris-Sud XI
†School of Informatics and Department of Physics, Indiana University
European Conference on Complex SystemsECCS’05 :: Paris :: 14-18 November 2005
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 2: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/2.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
Plan
1 k -core decomposition
2 A k -core analysis of AS and IR Internet graphs
3 Network fingerprints
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 3: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/3.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
Plan
1 k -core decomposition
2 A k -core analysis of AS and IR Internet graphs
3 Network fingerprints
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 4: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/4.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
k -core decompositionIntroduction
Motivation : Analysis of complex networks,in particular their hierarchy.
The hierarchy is related to the role that vertices play, i.e. thecentrality and connectivity patterns. The connectivity is mainlyrelated to :
robustnessfaults,attacks
routing (to find a path between two vertices)QoS,efficiency (of a determined parameter).
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 5: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/5.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
k -core decompositionIntroduction
Motivation : Analysis of complex networks,in particular their hierarchy.
The hierarchy is related to the role that vertices play, i.e. thecentrality and connectivity patterns. The connectivity is mainlyrelated to :
robustnessfaults,attacks
routing (to find a path between two vertices)QoS,efficiency (of a determined parameter).
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 6: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/6.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
k -core decompositionIntroduction
Motivation : Analysis of complex networks,in particular their hierarchy.
The hierarchy is related to the role that vertices play, i.e. thecentrality and connectivity patterns. The connectivity is mainlyrelated to :
robustnessfaults,attacks
routing (to find a path between two vertices)QoS,efficiency (of a determined parameter).
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 7: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/7.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
k -core decompositionDefinition
Given G = {V , E} a undirected graph, where V is the verticesset and E is the edges set.
Definition [Batagelj and Zaversnik, 2002] :
A subgraph H = (C, E |C) induced by the set C ⊆ V is a k -coreor a core of order k iff ∀v ∈ C : degree H(v) ≥ k , and H is themaximum subgraph with this property.
Then, a minimal degree k is imposed to the core of order k .
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 8: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/8.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
k -core decompositionDefinition
Given G = {V , E} a undirected graph, where V is the verticesset and E is the edges set.
Definition [Batagelj and Zaversnik, 2002] :
A subgraph H = (C, E |C) induced by the set C ⊆ V is a k -coreor a core of order k iff ∀v ∈ C : degree H(v) ≥ k , and H is themaximum subgraph with this property.
Then, a minimal degree k is imposed to the core of order k .
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 9: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/9.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
k -core decompositionDefinition
Given G = {V , E} a undirected graph, where V is the verticesset and E is the edges set.
Definition [Batagelj and Zaversnik, 2002] :
A subgraph H = (C, E |C) induced by the set C ⊆ V is a k -coreor a core of order k iff ∀v ∈ C : degree H(v) ≥ k , and H is themaximum subgraph with this property.
Then, a minimal degree k is imposed to the core of order k .
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 10: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/10.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
k -core decompositionExamples
tree : 1-core
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 11: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/11.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
k -core decompositionExamples
tree : 2-core ?
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 12: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/12.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
k -core decompositionExamples
tree : ����XXXX2-core ?
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 13: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/13.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
k -core decompositionExamples
tree : 1-core cycle : 2-core
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 14: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/14.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
k -core decompositionExamples
tree : 1-core cycle : 2-core clique n : (n − 1)-core
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 15: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/15.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
k -core decompositionExamples
A graph :
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 16: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/16.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
k -core decompositionExamples
A graph :
3−core
2−core
1−core
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 17: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/17.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
k -core decompositionExamples
A graph :
3−core
2−core
1−core
Definition
A vertex i has coreness c, or its shell index is c, if it belongs tothe c-core but not to (c + 1)-core.
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 18: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/18.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
k -core decompositionComplexity of the k -core decomposition
G is represented by its vertex list, where each one has aneighbors list.
1 Make an ordered array of lists, where each list iscomposed by the vertices with the same degree :O(n), where n is the number of vertices.
2 Compute each k -core starting by the minimum degreekmin, until any vertex remains in the graph :O(e), where e is the number of edges.
In general, the complexity is O(n + e)⇒ it is very useful for large networks .
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 19: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/19.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
k -core decompositionComplexity of the k -core decomposition
G is represented by its vertex list, where each one has aneighbors list.
1 Make an ordered array of lists, where each list iscomposed by the vertices with the same degree :O(n), where n is the number of vertices.
2 Compute each k -core starting by the minimum degreekmin, until any vertex remains in the graph :O(e), where e is the number of edges.
In general, the complexity is O(n + e)⇒ it is very useful for large networks .
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 20: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/20.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
k -core decompositionComplexity of the k -core decomposition
G is represented by its vertex list, where each one has aneighbors list.
1 Make an ordered array of lists, where each list iscomposed by the vertices with the same degree :O(n), where n is the number of vertices.
2 Compute each k -core starting by the minimum degreekmin, until any vertex remains in the graph :O(e), where e is the number of edges.
In general, the complexity is O(n + e)⇒ it is very useful for large networks .
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 21: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/21.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
k -core decompositionComplexity of the k -core decomposition
G is represented by its vertex list, where each one has aneighbors list.
1 Make an ordered array of lists, where each list iscomposed by the vertices with the same degree :O(n), where n is the number of vertices.
2 Compute each k -core starting by the minimum degreekmin, until any vertex remains in the graph :O(e), where e is the number of edges.
In general, the complexity is O(n + e)⇒ it is very useful for large networks .
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 22: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/22.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
k -core decompositionComplexity of the k -core decomposition
G is represented by its vertex list, where each one has aneighbors list.
1 Make an ordered array of lists, where each list iscomposed by the vertices with the same degree :O(n), where n is the number of vertices.
2 Compute each k -core starting by the minimum degreekmin, until any vertex remains in the graph :O(e), where e is the number of edges.
In general, the complexity is O(n + e)⇒ it is very useful for large networks .
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 23: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/23.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
Plan
1 k -core decomposition
2 A k -core analysis of AS and IR Internet graphs
3 Network fingerprints
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 24: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/24.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
Applying k -core decompositionto Internet graphs
We computed the k -cores of AS and IR Internet maps,then, we computed for each k -core :
their size as function of k
the cumulative degree distribution
the average clustering as a function of the degree
the average neighbors degree as a funtion of the degree
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 25: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/25.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
Applying k -core decompositionto Internet graphs
We computed the k -cores of AS and IR Internet maps,then, we computed for each k -core :
their size as function of k
the cumulative degree distribution
the average clustering as a function of the degree
the average neighbors degree as a funtion of the degree
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 26: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/26.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
Applying k -core to Internet graphs
1 10 100k
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RV 04/2005CAIDA 04/2005DIMES 05/2005INET-3.0
k -core size as function of k
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 27: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/27.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
Applying k -core to Internet graphs
10-3
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Cumulative degree distribution
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 28: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/28.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
Applying k -core to Internet graphs
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Average clustering distribution as degree function
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 29: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/29.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
Applying k -core to Internet graphs
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Average neighbors degree distribution as degree function
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 30: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/30.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
Plan
1 k -core decomposition
2 A k -core analysis of AS and IR Internet graphs
3 Network fingerprints
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 31: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/31.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
Network fingerprintAS_CAIDA [5] 04/2005, 23 symmetrical sources
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 32: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/32.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
Network fingerprintIR_CAIDA [5] 2003, 23 symmetrical sources
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 33: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/33.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
Network fingerprintComparation between IR and AS of CAIDA
Autonomous System graph
Router graph
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 34: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/34.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
Summary
k -core decomposition
Due to low complexity, it can be applied to analysis andvisualization of large scale networks, e.g. Internet.
Self-similarity of k -cores on the distributions (cumulativedegree, average neighbors degree and clustering)
Visualization using k -cores yields fingerprints useful tovalidate models and to compare different maps.
Public visualization tool :http ://xavier.informatics.indiana.edu/lanet-vi/
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 35: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/35.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
Summary
k -core decomposition
Due to low complexity, it can be applied to analysis andvisualization of large scale networks, e.g. Internet.
Self-similarity of k -cores on the distributions (cumulativedegree, average neighbors degree and clustering)
Visualization using k -cores yields fingerprints useful tovalidate models and to compare different maps.
Public visualization tool :http ://xavier.informatics.indiana.edu/lanet-vi/
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 36: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/36.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
Summary
k -core decomposition
Due to low complexity, it can be applied to analysis andvisualization of large scale networks, e.g. Internet.
Self-similarity of k -cores on the distributions (cumulativedegree, average neighbors degree and clustering)
Visualization using k -cores yields fingerprints useful tovalidate models and to compare different maps.
Public visualization tool :http ://xavier.informatics.indiana.edu/lanet-vi/
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 37: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/37.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
Summary
k -core decomposition
Due to low complexity, it can be applied to analysis andvisualization of large scale networks, e.g. Internet.
Self-similarity of k -cores on the distributions (cumulativedegree, average neighbors degree and clustering)
Visualization using k -cores yields fingerprints useful tovalidate models and to compare different maps.
Public visualization tool :http ://xavier.informatics.indiana.edu/lanet-vi/
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 38: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/38.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
Summary
k -core decomposition
Due to low complexity, it can be applied to analysis andvisualization of large scale networks, e.g. Internet.
Self-similarity of k -cores on the distributions (cumulativedegree, average neighbors degree and clustering)
Visualization using k -cores yields fingerprints useful tovalidate models and to compare different maps.
Public visualization tool :http ://xavier.informatics.indiana.edu/lanet-vi/
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores
![Page 39: Analysis and visualization of large scale networks using ...cnet.fi.uba.ar/ignacio.alvarez-hamelin/eccs/ECCS05_alvarez-hamelin.pdf · k-core decomposition A k-core analysis of AS](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a7122377f8b9a9d538c9d2d/html5/thumbnails/39.jpg)
k -core decompositionA k -core analysis of AS and IR Internet graphs
Network fingerprints
V. Batagelj and M. Zaversnik.
Generalized Cores.CoRR, cs.DS/0202039, 2002.
M. Baur, U. Brandes, M. Gaertler, and D. Wagner.
Drawing the AS Graph in 2.5 Dimensions.In "12th International Symposium on Graph Drawing, Springer-Verlag editor", pages 43–48, 2004.
J. I. Alvarez-Hamelin, L. Dall’Asta, A. Barrat, and A. Vespignani.
k -core decomposition : a tool for the visualization of large scale networks.arxiv.org, cs.NI/0504107, 2005.
LArge NETwork VIsualization tool.http ://xavier.informatics.indiana.edu/lanet-vi/ .
Router-Level Topology Measurements" "Cooperative Association for Internet Data Analysis.http ://www.caida.org/tools/measurement/skitter/ router_topology/ .
University of Oregon Route Views Project.http ://www.routeviews.org/ .
"Distributed Internet MEasurements and Simulations".http ://www.netdimes.org .
Jared Winick and Sugih Jamin.
Inet-3.0 : Internet topology generator.Technical Report UM-CSE-TR-456-02, Department of EECS, University of Michigan, 2002.
J.I.Alvarez-Hamelin :: ECCS’05 Analysis and visualization using k -cores