Group Study MAE 298
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This 8 page Class Notes was uploaded by Consuelo Herman DDS on Tuesday September 8, 2015. The Class Notes belongs to MAE 298 at University of California - Davis taught by Staff in Fall. Since its upload, it has received 29 views. For similar materials see /class/187472/mae-298-university-of-california-davis in Engineering Mechanical & Aero at University of California - Davis.
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Date Created: 09/08/15
MAE 298 Lecture 4 April 11 2006 Exploring network robustness Recall Preferential Attachment random graphs The Barabasi and Albert model A discrete time process 0 Start with single isolated node a At each time step a new node arrives o This node makes m connections to already existing nodes Why m edges 0 We are interested in the limit of large graph size Probability o Probability incoming node attaches to node j P7 t l 1 djZjdj o Probability incoming node attaches to any node of of degree k nodes of degree k nodes x degree of that node degree sum over all nodes km 2 km 2k dk Zmn Network evolution Process on the degree sequence 0 Note that pk will change in time So we show denote this explicitly pm a Also when a node of degree k gains an attachment it becomes a node of degree k 1 a When the new node arrives it increases by one the number of nodes of degree m Recursion for pm k 1k 2m mm1m2 2 W Z k2k1m3 39pm k2k1k 39 m1 2mm1 pk k2k1k Forkgtgt1 Pk N 76 3 Simulating PA Basic code for simulating PA with m 1 using R runPA H functionN100 outLinki is the parent of i outLink H numericN numlinksi is number totallinks in and out for node i numLinks H numericN1 fori in 2N p H samplec1i1size1probnumLinks1i1 outLinki H p numLinksp H numLinksp1 returnlistoutLink numLinks Visualizing a PA graph m 1 at n 5000 7 9 quot r f 70 V l i a m M quotiiWV y 399 V iquot I r 1 AA 1 IV quot Exploring PA networks Demo o R Graphviz We will use these as tools to explore Network robustness defined here as maintaining connectivity despite node and edge deletion o Rest of lecture will be interactive demo
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