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

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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

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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)

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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)

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Outline

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

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Background Complex Networks
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Background Terminology
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Background Random-regular Network (RR)
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• Background Erdos-Rényi Network (ER)

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Background Scale-free Network (SF)
?
R. Cohen and S. Havlin, Complex networks
structure, robustness and function
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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)?

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Robustness of networks under attacks

• Type of the attack random attack, targeted
  attack, localized attack (a new type of attack)

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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

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Outline

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

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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

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

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Percolation of localized attack RR and ER
 
 
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Percolation of localized attack SF
 
 
 
 
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Real-world Networks
Internet
Airline Network
http//openflights.org/data.html http//informatio
ntechnologypramod.blogspot.com/2010/10/p2p.html
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Real-world Networks
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Outline

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

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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

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Structure of the network Clustering
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Interdependent Networks
q
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Interdependent Networks with clustering
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Outline

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

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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.

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Thank you !