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Robustness%20and%20Structure%20of%20Complex%20Networks

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PhD Thesis Defense Robustness and Structure of Complex Networks Shuai Shao Boston University, Physics Department Advisor: Prof. Gene Stanley Co-advisor: Prof. Shlomo ... – PowerPoint PPT presentation

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Title: Robustness%20and%20Structure%20of%20Complex%20Networks


1
Robustness and Structure of Complex Networks
PhD Thesis Defense
  • Shuai Shao
  • Boston University, Physics Department
  • Advisor Prof. Gene Stanley
  • Co-advisor Prof. Shlomo Havlin
  • Collaborators Xuqing Huang, Xin Yuan, Prof.
    Xin Zhang,
  • Prof. Sergey Buldyrev, Prof. Huijuan
    Wang

2
Overview Projects and Publications
  • Percolation of localized attack on complex
    networks
  • Percolation of localized attack on complex
    networks (NJP 17(2), 023409)
  • The influence of the broadness of the degree
    distribution on networks robustness comparing
    localized attack and random attack (arXiv
    1504.06900)
  • Networks with clustering structure
  • The robustness of interdependent clustered
    networks (EPL 101(1), 18002)
  • Robustness of a partially interdependent network
    formed of clustered networks (PRE 89(3), 032812)
  • Network of interdependent networks overview of
    theory and applications
  • (Networks of Networks The Last Frontier of
    Complexity, 3-36)
  • Empirical study of real-world networks
  • Dynamic motifs in socio-economic networks (EPL
    108(5), 58001)

3
Overview Projects and Publications
  • Percolation of localized attack on complex
    networks
  • Percolation of localized attack on complex
    networks (NJP 17(2), 023409)
  • The influence of the broadness of the degree
    distribution on networks robustness comparing
    localized attack and random attack (arXiv
    1504.06900)
  • Networks with clustering structure
  • The robustness of interdependent clustered
    networks (EPL 101(1), 18002)
  • Robustness of a partially interdependent network
    formed of clustered networks (PRE 89(3), 032812)
  • Network of interdependent networks overview of
    theory and applications
  • (Networks of Networks The Last Frontier of
    Complexity, 3-36)
  • Empirical study of real-world networks
  • Dynamic motifs in socio-economic networks (EPL
    108(5), 58001)

4
Outline
  • Background
  • Part I Robustness of complex networks under
    localized attack
  • Part II Robustness of interdependent networks
    with clustering
  • Summary

5
Background Complex Networks
6
Background Terminology
7
Background Random-regular Network (RR)
8
  • Background Erdos-Rényi Network (ER)

9
Background Scale-free Network (SF)
?
R. Cohen and S. Havlin, Complex networks
structure, robustness and function
10
Robustness of networks under attacks
  • If some nodes in the network are attacked and
    disabled, will the network keep functional (P8)?
  • How many nodes should be attacked in order to
    collapse the entire network (pc)?

11
Robustness of networks under attacks
  • Type of the attack random attack, targeted
    attack, localized attack (a new type of attack)

12
Robustness of networks under attacks
  • Type of the attack random attack, targeted
    attack, localized attack (a new type of attack)
  • Structure of the network RR networks, ER
    networks, SF networks, clustered networks

13
Outline
  • Background
  • Part I Robustness of complex networks under
    localized attack
  • Part II Robustness of interdependent networks
    with clustering
  • Summary

14
Robustness of networks under attacks
  • Type of the attack random attack, targeted
    attack, localized attack (a new type of attack)
  • Structure of the network RR networks, ER
    networks, SF networks, clustered networks

15
Localized Attack a new type of attack
Localized attack Attacking nodes by shell
structure. Reflecting localized damages computer
viruses, earthquakes, floods
16
Localized Attack a new type of attack
17
Can percolation properties of localized attack be
solved?
Lattice(Square) RR ER SF
Random attack
A new type of attack Localized attack
18
Theoretical framework generating function method

19
Percolation of localized attack RR and ER
 
 
20
Percolation of localized attack SF
 
 
 
 
21
Real-world Networks
Internet
Airline Network
http//openflights.org/data.html http//informatio
ntechnologypramod.blogspot.com/2010/10/p2p.html
22
Real-world Networks
23
Outline
  • Background
  • Part I Robustness of complex networks under
    localized attack
  • Part II Robustness of interdependent networks
    with clustering
  • Summary

24
Robustness of networks under attacks
  • Type of the attack random attack, targeted
    attack, localized attack (a new type of attack)
  • Structure of the network RR networks, ER
    networks, SF networks, networks with clustering

25
Structure of the network Clustering
26
Interdependent Networks
q
27
Interdependent Networks with clustering
28
Outline
  • Background / Motivation
  • Part I Robustness of complex networks under
    localized attack
  • Part II Robustness of interdependent networks
    with clustering
  • Summary

29
Summary
  • Proposed the theoretical framework for the
    robustness of complex networks under localized
    attack and solved the percolation properties
  • Compared localized attack and random attack on
    ER, RR and SF networks
  • ER networks are equivalently robust under two
    types of attack
  • RR networks are more robust under localized
    attack
  • Robustness of SF networks depends crucially on
    the scale parameter ?
  • 3. Real-world networks are much more fragile
    to localized attack than to random attack
  • 4. Clustering structure in interdependent
    networks makes the system less robust under
    attack.

30
Thank you !
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