Error and Attack Tolerance of Complex Networks

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Error and Attack Tolerance of Complex Networks

• Albert, Jeong, Barabási
• (presented by Walfredo)

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Networks

• If we abstract details away, networks are a set
  of nodes, connected by links
• Networks model many systems
• Internet
• Web
• Cell
• Society

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Network Types

• Homogeneous
• All nodes have (statistically) the same number of
  links
• P(k) follows a Poisson distribution (Poisson is a
  generalization of Binomial)
• Heterogeneous
• Most nodes have very few links
• A few nodes have many links
• P(k) follows a power-law P(k) ck-?

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Network Types
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Poisson (Average 10)
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Power-Law P(k) ? k-2
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Models

• Erdös-Rényi ? Homogeneous
• Each possible link exists with probability p
• Scale-free ? Heterogeneous
• The network grows a node at a time
• The probability ?i that the new node is connected
  to node i is proportional to know many links node
  i owns (preferential attachment)

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Attacks Failures ? Diameter
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Attacks Failures ? Fragmentation
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Attacks Failures ? Fragmentation
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Doubts/Criticism

• What about disconnection in the diameter
  analysis?
• It is assumed that the cost of attacking is the
  same for all nodes
• But more important nodes are better defended
• So, attacking a more important node should be
  more difficult ( cost more in the model)