Error and Attack Tolerance of Complex Networks

Albert, Jeong, Barabási

(presented by Walfredo)

Networks

• If we abstract details away, networks are a set of nodes, connected by links

• Networks model many systems– Internet– Web– Cell– Society

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-

Network Types

Poisson (Average = 10)

0

0,02

0,04

0,06

0,08

0,1

0,12

0,14

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

Power-Law P(k) k-2

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

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)

Attacks + Failures Diameter

Attacks + Failures Fragmentation

Attacks + Failures Fragmentation

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)