c11_netw_resilience - Topological perturbation of complex...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Topological perturbation of complex etworks networks Perturbations in complex systems can deactivate some of the edges or nodes. dge loss: the edge is deleted ffects on the global topology: Edge loss: the edge is deleted Node loss: the node and all its edges are deleted Effects on the global topology: • increase of path lengths, • separation into isolated clusters. More connected network - less effect of an edge removal But bridges are definite points of vulnerability! The effect of a node removal depends on the number and p characteristics of its edges.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Resilience to perturbations Topological resilience studied in the literature: the remaining nodes are still connected. the average distance does not increase. x Propose other measures of resilience Ex. Propose other measures of resilience. Testing resilience to incremental damage: remove edges/nodes one by one, and look at the size of the giant connected component the average distance between nodes in the giant connected gg component x What factors affect the topological resilience of a network? Ex. What factors affect the topological resilience of a network?
Background image of page 2
Review: components in a random graph Erd ő s-Rényi (uniform) random graph: •If the graph contains only isolated trees. 0 lim = pN N • If the graph has isolated trees and cycles. •At a giant connected component appears. 1 c cN p 1 < = with 1 c cN p 1 = = with • The size of the giant connected component approaches N rapidly as c increases. he graph is connected if The graph is connected if Random graph with degree distribution P(k): N / N ln p > gp g ( ) • A giant connected component exists if 2 2 k k Ex. How is this related to topological resilience?
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Edge removal in random graphs Start with a connected ER random graph with conn. prob. p. Remove a random fraction f of the edges. N / N ln p > Expected result: an ER graph with conn. prob. p(1-f) Connected if or a broad class of starting graphs there exists a threshold edge N / N ln ) f 1 ( p > For a broad class of starting graphs, there exists a threshold edge removal probability such that if a smaller fraction of edges is removed the graph is still connected. B. Bollobas, Random Graphs, 1985
Background image of page 4
Node removal emoving a node deactivates all its edges Removing a node deactivates all its edges. We can expect that the effect of the node removal will depend n the number of edges it had. on the number of edges it had. The size of the connected component will decrease at least by one. Assume we have two networks with the same number of nodes and edges, and remove a randomly chosen fraction f of the nodes. Can the two networks’ resilience be different?
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Breakdown transition in general random graphs Consider a random graph with arbitrary P(k 0 ) A giant cluster exists if each node is connected to at least two other nodes.
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

This document was uploaded on 03/01/2011.

Page1 / 28

c11_netw_resilience - Topological perturbation of complex...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online