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Emergence of Scaling in Random Networks Albert-Laszlo Barabsi & Reka Albert

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Barabasi Director of Northeastern University’s Center for Complex Network Research Diseaseome- linking of diseases through shared genes Human Dynamics – understanding human behavior using statistical physics http://en.wikipedia.org/wiki/Albert- L%C3%A1szl%C3%B3_Barab%C3%A1si

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Albert Professor of Physics and Adjunct Professor of Biology at Pennsylvania State University Boolean modeling of biological systems Network Theory http://en.wikipedia.org/wiki/R%C3 %A9ka_Albert

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Traditional Theories – Random Graphs Erdos – Renyi : edges are independent, all are equally likely Watts – Strogatz : Small world – small average shortest path length, large clustering coefficient

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Observations Emergence of Scaling in Random Networks. Barabasi and Albert. Science 286, 509 (1999)

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Proposed Model to Represent Scale Invariance (Scale Free) 2 Requirements Incorporation of growth Preferential Attachment Emergence of Scaling in Random Networks. Barabasi and Albert. Science 286, 509 (1999)

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Growth Assumptions of ER and WS – fixed N More realistic to assume an increasing N Emergence of Scaling in Random Networks. Barabasi and Albert. Science 286, 509 (1999)

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Preferential Attachment (Yule/Simon Process) ER and WS assume equal probability of connection Data suggests “rich get richer” – nodes have greater chance of connecting to nodes that have more neighbors Positive Feedback Emergence of Scaling in Random Networks. Barabasi and Albert. Science 286, 509 (1999)

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Proposed Model Emergence of Scaling in Random Networks. Barabasi and Albert. Science 286, 509 (1999) Model

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Conclusions of the Model Emergence of Scaling in Random Networks. Barabasi and Albert. Science 286, 509 (1999)

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Growth and Preferential Attachment: Are both needed? Emergence of Scaling in Random Networks. Barabasi and Albert. Science 286, 509 (1999) Both Are Necessary

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Discussion Questions

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http://en.wikipedia.org/wiki/Albert-L%C3%A1szl%C3%B3_Barab%C3%A1si http://en.wikipedia.org/wiki/R%C3%A9ka_Albert Emergence of Scaling in Random Networks. Barabasi and Albert. Science 286, 509 (1999) Power-Law Distributions in empirical data. Clauset, Shalizi, and Newman. Siam Review 51, 661-703 (209)

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