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