Network Resilience - Complex Networks - Lecture Slides, Slides of Data Communication Systems and Computer Networks

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Lecture 20

Network resilience

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Outline

 network resilience

 effects of node and edge removal

 example: power grid

 example: biological networks

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Bond percolation in Networks

 Edge removal

 bond percolation : each edge is removed with probability (1-p)

 corresponds to random failure of links

 targeted attack : causing the most damage to the network with

the removal of the fewest edges

 strategies: remove edges that are most likely to break apart the network or lengthen the average shortest path  e.g. usually edges with high betweenness

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Edge percolation

50 nodes, 116 edges, average degree 4. after 25 % edge removal - > 76 edges, average degree 3. still well above percolation threshold

How many edges would you have to remove to break up an Erdos Renyi random graph? e.g. each node has an average degree of 4.

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Site percolation on lattices

Fill each square with probability p

 low p: small isolated islands

 p critical : giant component forms, occupying finite fraction of infinite lattice. Size of other components is power law distributed

 p above critical : giant component rapidly spreads to span the lattice Size of other components is O(1)

Interactive

demonstration:

http://projects.si.umich. edu/netlearn/NetLogo4/ LatticePercolation.html

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Scale-free networks are resilient with respect

to random attack

 gnutella network

 20% of nodes removed

574 nodes in giant component (^) 427 nodes in giant component Docsity.com

random failures vs. attacks

Source: Error and attack tolerance of complex networks. Réka Albert, Hawoong Jeong and Albert-László Barabási. Docsity.com

Network resilience to targeted attacks

 Scale-free graphs are resilient to random attacks, but sensitive to

targeted attacks.

 For random networks there is smaller difference between the two

random failure targeted attack

Source: Error and attack tolerance of complex networks. Réka Albert, Hawoong Jeong and Albert-László Barabási Docsity.com

Real networks

Source: Error and attack tolerance of complex networks. Réka Albert, Hawoong Jeong and Albert-László Barabási Docsity.com

 the first few %

of nodes

removed

Source: Error and attack tolerance of complex networks. Réka Albert, Hawoong Jeong and Albert-László Barabási Docsity.com

Power grid

 Electric power does not travel just by the shortest route from source

to sink, but also by parallel flow paths through other parts of the

system.

 Where the network jogs around large geographical obstacles, such

as the Rocky Mountains in the West or the Great Lakes in the East,

loop flows around the obstacle are set up that can drive as much as

1 GW of power in a circle, taking up transmission line capacity

without delivering power to consumers.

Source: Eric J. Lerner, http://www.aip.org/tip/INPHFA/vol-9/iss-5/p8.html Docsity.com

Cascading failures

 Each node has a load and a capacity that says

how much load it can tolerate.

 When a node is removed from the network its

load is redistributed to the remaining nodes.

 If the load of a node exceeds its capacity, then

the node fails

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Degree distribution is exponential

Source: Albert et al., ‘Structural vulnerability of the North American power grid Docsity.com

power grid structural resilience

 efficiency is impacted the most if the node removed is the one with

the highest load

highest load generator/transmission station removed

Source: Modeling cascading failures in the North American power grid; R. Kinney, P. Crucitti, R. Albert, and V. Latora Docsity.com