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

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Presentation transcript:

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

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 L%C3%A1szl%C3%B3_Barab%C3%A1si

Albert Professor of Physics and Adjunct Professor of Biology at Pennsylvania State University Boolean modeling of biological systems Network Theory %A9ka_Albert

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

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

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)

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)

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)

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

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

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

Discussion Questions

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, (209)