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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
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
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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
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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
Motivation: Power-Law Networks
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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
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Internet in December 1998 http://cs.stanford.edu/people/jure/pubs/powergrowth-kdd05.ppt
Few High Degree NodesMany Low Degree Nodes
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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
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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
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() Power-law Graph
Definition (() Graph G()):
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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.
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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
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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.
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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
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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()
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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
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Two Lemmas in Literature
M. Molloy and B. Reed (1995)
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Two Lemmas in Literature (Cont.)
F. Chung et al. (2002)
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Some Fundamental Results
Relations between largest connected component and total pairwise connectivity
Robustness of power-law networks
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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
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Uniform Random Failures
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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
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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
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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
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Interactive Preferential Attacks
By choosing a different parameter β′, a node of degree i in G(α, ) has probability
to be attacked Main Theorem.
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Expected Preferential Attacks
To attack the expected c nodes A node of degree i is attacked with probability
Main Theorem.
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Visualization
Power-Law Networks will not be affected only when under around expected 13% of nodes are attacked
Smaller β is better
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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
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Degree-Centrality Attacks
The intruders intentionally attack the “hubs”, that is, the set of nodes with highest degrees (larger than x0)
Main Theorem.
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Visualization
Power-Law Networks will not be affected only when under 5% of degree-centrality nodes are attacked
Smaller β is better
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Thank you for listening!
