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During the course of the Complex Networks, we study the different concept regarding the complex computer networking. The main points upon which in these lecture slides focused are:Network Resilience, Effects of Node, Edge Removal, Power Grid, Biological Networks, Fraction, Nodes or Edges, Connected Components, Related to Percolation, Giant Component Forms
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corresponds to random failure of links
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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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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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)
http://projects.si.umich. edu/netlearn/NetLogo4/ LatticePercolation.html
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574 nodes in giant component (^) 427 nodes in giant component Docsity.com
Source: Error and attack tolerance of complex networks. Réka Albert, Hawoong Jeong and Albert-László Barabási. Docsity.com
random failure targeted attack
Source: Error and attack tolerance of complex networks. Réka Albert, Hawoong Jeong and Albert-László Barabási Docsity.com
Source: Error and attack tolerance of complex networks. Réka Albert, Hawoong Jeong and Albert-László Barabási Docsity.com
Source: Error and attack tolerance of complex networks. Réka Albert, Hawoong Jeong and Albert-László Barabási Docsity.com
Source: Eric J. Lerner, http://www.aip.org/tip/INPHFA/vol-9/iss-5/p8.html Docsity.com
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Source: Albert et al., ‘Structural vulnerability of the North American power grid Docsity.com
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