exploiting the robustness on power-law networks yilin shen , nam p. nguyen, my t. thai
DESCRIPTION
Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai Presented by : Yilin Shen Dept. Computer Information Science and Engineering University of Florida. Outline. Motivation: Power-law Networks Models , Measurement and Threat Taxonomy - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai](https://reader035.vdocument.in/reader035/viewer/2022062813/56816675550346895dda0e24/html5/thumbnails/1.jpg)
Exploiting the Robustness on Power-Law Networks
Yilin Shen, Nam P. Nguyen, My T. Thai
Presented by :Yilin ShenDept. Computer Information Science and Engineering University of Florida
![Page 2: Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai](https://reader035.vdocument.in/reader035/viewer/2022062813/56816675550346895dda0e24/html5/thumbnails/2.jpg)
2
Outline
Motivation: Power-law Networks Models, Measurement and Threat Taxonomy
Power-Law Random Graph Model Vulnerability Measurement Threat Taxonomy
Preliminaries Uniform Random Failures Preferential Attacks Degree-Centrality Attacks
![Page 3: Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai](https://reader035.vdocument.in/reader035/viewer/2022062813/56816675550346895dda0e24/html5/thumbnails/3.jpg)
3
Outline
Motivation: Power-law Networks Models, Measurement and Threat Taxonomy
Power-Law Random Graph Model Vulnerability Measurement Threat Taxonomy
Preliminaries Uniform Random Failures Preferential Attacks Degree-Centrality Attacks
![Page 4: Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai](https://reader035.vdocument.in/reader035/viewer/2022062813/56816675550346895dda0e24/html5/thumbnails/4.jpg)
Motivation: Power-Law Networks
4
Main Property:The number of nodes having kconnections is proportional to
k-β
β is a parameter whose value is typically in the range 1 < β < 4
4
Internet in December 1998 http://cs.stanford.edu/people/jure/pubs/powergrowth-kdd05.ppt
Few High Degree NodesMany Low Degree Nodes
![Page 5: Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai](https://reader035.vdocument.in/reader035/viewer/2022062813/56816675550346895dda0e24/html5/thumbnails/5.jpg)
5
More Real Network Examples
Many large-scale real-world networks appear to exhibit a power-law graph
Internet: β = 2.1 World Wide Web: β = 2.1 Social Networks: β = 2.3 Protein-protein interaction networks: β = 2.5
![Page 6: Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai](https://reader035.vdocument.in/reader035/viewer/2022062813/56816675550346895dda0e24/html5/thumbnails/6.jpg)
6
Outline
Motivation: Power-law Networks Models, Measurement and Threat Taxonomy
Power-Law Random Graph Model Vulnerability Measurement Threat Taxonomy
Preliminaries Uniform Random Failures Preferential Attacks Degree-Centrality Attacks
![Page 7: Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai](https://reader035.vdocument.in/reader035/viewer/2022062813/56816675550346895dda0e24/html5/thumbnails/7.jpg)
7
() Power-law Graph
Definition (() Graph G()):
![Page 8: Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai](https://reader035.vdocument.in/reader035/viewer/2022062813/56816675550346895dda0e24/html5/thumbnails/8.jpg)
8
Power-Law Random Graph Model
Form a set L containing dv disjoint copy of vertex v (mini-vertices);
Choose a random matching of the elements of L; For two vertices u and v, there is an edge between them if
and only if at least one edge of the random perfect matching was connecting copies of u to copies of v.
![Page 9: Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai](https://reader035.vdocument.in/reader035/viewer/2022062813/56816675550346895dda0e24/html5/thumbnails/9.jpg)
9
Outline
Motivation: Power-law Networks Models, Measurement and Threat Taxonomy
Power-Law Random Graph Model Vulnerability Measurement Threat Taxonomy
Preliminaries Uniform Random Failures Preferential Attacks Degree-Centrality Attacks
![Page 10: Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai](https://reader035.vdocument.in/reader035/viewer/2022062813/56816675550346895dda0e24/html5/thumbnails/10.jpg)
10
Vulnerability Measurement
Total Pairwise Connectivity P(in residual power-law networks after the failures and attacks)
Why is Total Pairwise Connectivity an effective measurement?
It can control the balance among disconnected components while ensuring the nonexistence of giant components.
![Page 11: Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai](https://reader035.vdocument.in/reader035/viewer/2022062813/56816675550346895dda0e24/html5/thumbnails/11.jpg)
11
Outline
Motivation: Power-law Networks Models, Measurement and Threat Taxonomy
Power-Law Random Graph Model Vulnerability Measurement Threat Taxonomy
Preliminaries Uniform Random Failures Preferential Attacks Degree-Centrality Attacks
![Page 12: Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai](https://reader035.vdocument.in/reader035/viewer/2022062813/56816675550346895dda0e24/html5/thumbnails/12.jpg)
12
Threat Taxonomy
Uniform Random Failure Each node in G() fails randomly with the same probability p
Preferential Attack Each node in G() is attacked with higher probability if it has a larger
degree Degree-Centrality Attack
The adversary only attacks the set of centrality nodes with maximum degrees in G()
![Page 13: Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai](https://reader035.vdocument.in/reader035/viewer/2022062813/56816675550346895dda0e24/html5/thumbnails/13.jpg)
13
Outline
Motivation: Power-law Networks Models, Measurement and Threat Taxonomy
Power-Law Random Graph Model Vulnerability Measurement Threat Taxonomy
Preliminaries Uniform Random Failures Preferential Attacks Degree-Centrality Attacks
![Page 14: Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai](https://reader035.vdocument.in/reader035/viewer/2022062813/56816675550346895dda0e24/html5/thumbnails/14.jpg)
14
Two Lemmas in Literature
M. Molloy and B. Reed (1995)
![Page 15: Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai](https://reader035.vdocument.in/reader035/viewer/2022062813/56816675550346895dda0e24/html5/thumbnails/15.jpg)
15
Two Lemmas in Literature (Cont.)
F. Chung et al. (2002)
![Page 16: Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai](https://reader035.vdocument.in/reader035/viewer/2022062813/56816675550346895dda0e24/html5/thumbnails/16.jpg)
16
Some Fundamental Results
Relations between largest connected component and total pairwise connectivity
Robustness of power-law networks
![Page 17: Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai](https://reader035.vdocument.in/reader035/viewer/2022062813/56816675550346895dda0e24/html5/thumbnails/17.jpg)
17
Outline
Motivation: Power-law Networks Models, Measurement and Threat Taxonomy
Power-Law Random Graph Model Vulnerability Measurement Threat Taxonomy
Preliminaries Uniform Random Failures Preferential Attacks Degree-Centrality Attacks
![Page 18: Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai](https://reader035.vdocument.in/reader035/viewer/2022062813/56816675550346895dda0e24/html5/thumbnails/18.jpg)
18
Uniform Random Failures
![Page 19: Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai](https://reader035.vdocument.in/reader035/viewer/2022062813/56816675550346895dda0e24/html5/thumbnails/19.jpg)
19
The Idea of Proof
Compute the expected degree distribution of graph Gr
Use M. Molloy and B. Reed (1995) to find a threshold β0
When β β0, we use the branching process method
![Page 20: Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai](https://reader035.vdocument.in/reader035/viewer/2022062813/56816675550346895dda0e24/html5/thumbnails/20.jpg)
20
Visualization
The power-law networks are extremely robust even when the failure probability is unrealistically large
Even though PLN is affected, the number of node-pairs after failure is close to original PLN
Smaller β is better
![Page 21: Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai](https://reader035.vdocument.in/reader035/viewer/2022062813/56816675550346895dda0e24/html5/thumbnails/21.jpg)
21
Outline
Motivation: Power-law Networks Models, Measurement and Threat Taxonomy
Power-Law Random Graph Model Vulnerability Measurement Threat Taxonomy
Preliminaries Uniform Random Failures Preferential Attacks Degree-Centrality Attacks
![Page 22: Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai](https://reader035.vdocument.in/reader035/viewer/2022062813/56816675550346895dda0e24/html5/thumbnails/22.jpg)
22
Interactive Preferential Attacks
By choosing a different parameter β′, a node of degree i in G(α, ) has probability
to be attacked Main Theorem.
![Page 23: Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai](https://reader035.vdocument.in/reader035/viewer/2022062813/56816675550346895dda0e24/html5/thumbnails/23.jpg)
23
Expected Preferential Attacks
To attack the expected c nodes A node of degree i is attacked with probability
Main Theorem.
![Page 24: Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai](https://reader035.vdocument.in/reader035/viewer/2022062813/56816675550346895dda0e24/html5/thumbnails/24.jpg)
24
Visualization
Power-Law Networks will not be affected only when under around expected 13% of nodes are attacked
Smaller β is better
![Page 25: Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai](https://reader035.vdocument.in/reader035/viewer/2022062813/56816675550346895dda0e24/html5/thumbnails/25.jpg)
25
Outline
Motivation: Power-law Networks Models, Measurement and Threat Taxonomy
Power-Law Random Graph Model Vulnerability Measurement Threat Taxonomy
Preliminaries Uniform Random Failures Preferential Attacks Degree-Centrality Attacks
![Page 26: Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai](https://reader035.vdocument.in/reader035/viewer/2022062813/56816675550346895dda0e24/html5/thumbnails/26.jpg)
26
Degree-Centrality Attacks
The intruders intentionally attack the “hubs”, that is, the set of nodes with highest degrees (larger than x0)
Main Theorem.
![Page 27: Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai](https://reader035.vdocument.in/reader035/viewer/2022062813/56816675550346895dda0e24/html5/thumbnails/27.jpg)
27
Visualization
Power-Law Networks will not be affected only when under 5% of degree-centrality nodes are attacked
Smaller β is better
![Page 28: Exploiting the Robustness on Power-Law Networks Yilin Shen , Nam P. Nguyen, My T. Thai](https://reader035.vdocument.in/reader035/viewer/2022062813/56816675550346895dda0e24/html5/thumbnails/28.jpg)
28
Thank you for listening!