
Relatively HIGH Clustering Coefficient

Relatively LOW Characteristic Path
Length

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 there’s a
heightened probability that A is
connected to C.
C =
Where:
• “triangles” are K 3 graphs
• “connected triples” are nonisomorphic paths of length two
One Triangle
8 Connected Triples
So the Clustering Coefficient is
3/8.

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
A
D
C
B
E
First, find the distances between all the
vertices and each average length.
A – 1, 1, 2, 2
B – 1, 1, 2, 2
C – 1, 1, 1, 1
D – 1, 2, 2, 2
E – 1, 2, 2, 2
mean(A) = 6/4
mean(B) = 6/4
mean(C) = 4/4
mean(D) = 7/4
mean(E) = 7/4
Next, take the median of the averages.
Median ( 4/4, 6/4, 6/4, 7/4, 7/4 ) = 6/4
So, the Characteristic Path Length of this
graph is 6/4.
 New topic
Not much information
 Likely to be very important in the future
 My honors project
Social networks on campus
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