1. Error and Attack Tolerance of Complex Networks Albert, Jeong, Barabási (presented by Walfredo)

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

3. 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 - 

4. Network Types

5. Poisson (Average = 10)

6. Power-Law P(k)  k -2

7. 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)

8. Attacks + Failures  Diameter

9. Attacks + Failures  Fragmentation

11. 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)