525 Computing Project 1, Fall 2011
*
It’s a small world, after all
In the 1960s, Stanley Milgram conducted an experiment to determine the
diameter of the social network of the united states.
Beginning with a few
people in Kansas and Nebraska, participants were asked to mail a package
to someone in Boston, but they could only do so by mailing it to people they
new. Surprisingly, most of the packages only had to be mailed three times
to reach their end point.
Later experiments found that to reach a foreign
country, the number of hops was usually at most six. This gave rise to the
expression “six degrees of separation.”
In this project, we will study shortest path problems and see how loosely
connected graphs can have very small diameter.
Recall that a
graph
G
is just a collection of nodes
N
and links between
them which we call
edges
,
E
.
There are two matrices of interest.
I
is the
nodeincidence matrix and
A
is the adjacency matrix.
K
will denote the
average degree of a vertex and
N
will denote the number of nodes. Use the
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 Fall '11
 Recth
 Graph Theory, shortest path, Network theory

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