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Relatively HIGH Clustering Coefficient Relatively LOW Characteristic Path Length

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Measure of degree to which vertices in a graph tend to cluster together If A is connected to B and B is connected to C, then theres a heightened probability that A is connected to C.

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C = Where: triangles are K graphs connected triples are nonisomorphic paths of length two 3

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One Triangle 8 Connected Triples So the Clustering Coefficient is 3/8.

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The average number of steps along the shortest paths for all possible pairs of vertices in the graph The median of the means of shortest distances between all pairs of vertices

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First, find the distances between all the vertices and each average length. A – 1, 1, 2, 2 mean(A) = 6/4 B – 1, 1, 2, 2mean(B) = 6/4 C – 1, 1, 1, 1mean(C) = 4/4 D – 1, 2, 2, 2mean(D) = 7/4 E – 1, 2, 2, 2mean(E) = 7/4 Next, take the median of the averages. Median ( 4/4, 6/4, 6/4, 7/4, 7/4 ) = 6/4 A C D B E So, the Characteristic Path Length of this graph is 6/4.

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New topic Not much information Likely to be very important in the future My honors project Social networks on campus

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http://polymer.bu.edu/~amaral/Sex_partners/idahlia_web.jpg http://film-buff.tripod.com/kevinbacon.jpg http://insanityoverrated.files.wordpress.com/2009/02/six-degrees1.jpg http://en.wikipedia.org/wiki/Small_world_experiment http://en.wikipedia.org/wiki/Small-world_network http://en.wikipedia.org/wiki/Clustering_coefficient http://getoutfoxed.com/files/small-world-ring-with-rando.png http://www.amazon.com/Small-Worlds-Duncan-J-Watts/dp/0691005419

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COMS 6998-06 Network Theory Week 4: September 29, 2010 Dragomir R. Radev Wednesdays, 6:10-8 PM 325 Pupin Terrace Fall 2010.

COMS 6998-06 Network Theory Week 4: September 29, 2010 Dragomir R. Radev Wednesdays, 6:10-8 PM 325 Pupin Terrace Fall 2010.

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