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project1 - 525 Computing Project 1 Fall 2011 Its a small...

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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 node-incidence 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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