Download Six Degrees of Separation - Olympus High Mathematics

Teachers Teaching With Technology
2010 Annual Meeting - Atlanta, GA
Ray Barton, Olympus High, SLC, UT
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
 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
 80-20 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
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