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Six Degrees of Separation

Six Degrees of Separation. Teachers Teaching With Technology 2010 Annual Meeting - Atlanta, GA Ray Barton, Olympus High, SLC, UT. Connected: The Power of Six Degrees. Examples of networks. The Oracle of Kevin Bacon. The Human Disease Network.

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Six Degrees of Separation

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  1. Six Degrees of Separation Teachers Teaching With Technology 2010 Annual Meeting - Atlanta, GA Ray Barton, Olympus High, SLC, UT

  2. Connected: The Power of Six Degrees

  3. Examples of networks

  4. The Oracle of Kevin Bacon

  5. The Human Disease Network • Diseases seem to share most of their genes with other diseases. • Type 2 diabetes and prostate cancer both appear to be influenced by variation in the JAZF1 gene

  6. The Internet • Map of the shortest route from a test website to about 100,000 others • Like colors indicate similar web addresses

  7. Connected: The Power of Six Degrees

  8. Social Networks The Entire World • If you had 100 friends and each friend had 100 friends and so on... what could be the maximum degree of separation between you and anyone in the world? • What assumptions did you make in your calculations?

  9. How many friends would each person need under these assumptions in order to have a maximum of six degrees of separation?

  10. Mapping real-world networksWatts & Strogatz • The Six Degrees of Kevin Bacon

  11. Two Network Models • Watts & Strogatz (Small World) • Very small average shortest path length • Large clustering coefficient (cliques) • Erdos-Renyi (Random) • Small average shortest path length – log(n) • Small clustering coefficient

  12. Mapping Real-world networksBarabasi • Mapping the Internet

  13. Which graph should represent the distribution of nodes if networks are random?

  14. Power Law • Hubs • 80-20 rule • Scale Free • f(cx)=kf(x)

  15. A node with twice as many hubs is • one fourth as likely • half as likely • twice as likely • four times as likely

  16. Why hubs? • The random network model assumes all nodes exist at the beginning of the network formation. This is not the case. • In scale free networks, older nodes have greater opportunity to acquire links • Preferential attachment – the rich get richer

  17. Network Robustness • Resistant to attacks on randomly selected nodes. • 50% random node failure but network still functions • Vulnerable to coordinated attacks on hubs • 5-15% hub failure can crash the network. • Scale-Free networks have a threshold of zero

  18. References • Connected: The Power of Six Degrees http://gephi.org/2008/how-kevin-bacon-cured-cancer/ • The Oracle of Kevin Bacon http://oracleofbacon.org/ • Scale-Free Networks by Albert-Laszlo Barabasi and Eric Bonabeau http://www.barabasilab.com/pubs/CCNR-ALB_Publications/200305-01_SciAmer-ScaleFree/200305-01_SciAmer-ScaleFree.pdf • Watts, D.J. (1999). Small Worlds: The Dynamics of Networks Between Order and Randomness. Princeton University Press. ISBN 0-691-00541-9 • Watts, D.J. (2004). Six Degrees: the science of a connected age. W.W. Norton & Company.ISBN 0-393-32542-3 http://olympusmath.wikispaces.com/Six+Degrees+of+Separation

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