six degrees of separation
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Six Degrees of Separation
Teachers Teaching With Technology2010 Annual Meeting - Atlanta, GA
Ray Barton, Olympus High, SLC, UT
Connected: The Power of Six Degrees
Examples of networks
Network Nodes Edges
Societies People Friendships
Hollywood Actors Movies
Internet (virtual) Web Pages Links
Internet (Physical) Routers Communication Lines
Research Papers Citations
Cellular Metabolism Molecules Biochemical Reactions
Epidemics Hosts Infections
Health Disorders Diseases Genes
Nervous Systems Neurons Synapses
Economic Systems Business Entities Loans
The Oracle of Kevin Bacon
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
The Internet
Map of the shortest route from a test website to about 100,000 others
Like colors indicate similar web addresses
Connected: The Power of Six Degrees
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?
How many friends would each person need under these assumptions in order to have a maximum of six degrees of separation?
Mapping real-world networksWatts & Strogatz
The Six Degrees of Kevin Bacon
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
Mapping Real-world networksBarabasi
Mapping the Internet
Which graph should represent the distribution of nodes if networks are random?
Power Law
Hubs 80-20 rule Scale Free f(cx)=kf(x)
A node with twice as many hubs is
A. one fourth as likelyB. half as likelyC. twice as likely D. four times as likely
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
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
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 Bonabeauhttp://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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