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

2. 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

3. 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

4. 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

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

6. 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)

7. 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)

8. 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)

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

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

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

12. Discussion Questions

13. 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)