Teachers Teaching With Technology 2010 Annual Meeting - Atlanta, GA Ray Barton, Olympus High, SLC, UT

NetworkNodesEdges SocietiesPeopleFriendships HollywoodActorsMovies Internet (virtual)Web PagesLinks Internet (Physical)RoutersCommunication Lines ResearchPapersCitations Cellular MetabolismMoleculesBiochemical Reactions EpidemicsHostsInfections Health DisordersDiseasesGenes Nervous SystemsNeuronsSynapses Economic SystemsBusiness EntitiesLoans

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

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

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?

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

The Six Degrees of Kevin Bacon

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

Mapping the Internet

Hubs rule Scale Free f(cx)=kf(x)

A. one fourth as likely B. half as likely C. twice as likely D. four times as likely

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

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

Connected: The Power of Six Degrees The Oracle of Kevin Bacon Scale-Free Networks by Albert-Laszlo Barabasi and Eric Bonabeau Watts, D.J. (1999). Small Worlds: The Dynamics of Networks Between Order and Randomness. Princeton University Press. ISBN Watts, D.J. (2004). Six Degrees: the science of a connected age. W.W. Norton & Company. ISBN